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+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0080", "section": "Supplementary Material", "page_start": 12, "page_end": 12, "type": "TableOfContents", "text": "A Theoretical Analysis of ALIEN 12 A.1 Watermark Constraint and Score Discrepancy 12 A.2 Proof of Reverse SDE Drift Term Correction 12 A.3 Derivation of UNet Target Noise 12 B Implementation Details 13 B.1 Algorithm Pseudocode 13 B.2 Hyperparameters and Training Settings 13 C Experimental Setup and Extended Experiments 14 C.1 Dataset Settings 14 C.2 Robustness Evaluation Settings 15 C.3 Extended Experiments 15 D Extended Related Work 16 D.1 Watermarking Schemes Taxonomy 16", "source": "marker_v2", "marker_block_id": "/page/11/TableOfContents/1"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0081", "section": "A. Theoretical Analysis of ALIEN", "page_start": 13, "page_end": 13, "type": "Text", "text": "In this section, we provide a rigorous derivation establishing the analytical link between the watermark constraint in the z_0 -space and the necessary correction to the probability flow drift term. This derivation proves that ALIEN is theoretically grounded in the VP-SDE framework and is inherently sampler-agnostic.", "source": "marker_v2", "marker_block_id": "/page/12/Text/2"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0082", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Text", "text": "1. Watermark Constraint Definition Our objective is to embed a fixed watermark residual \\delta_{wm} into the latent representation. We define this as a geometric constraint on the estimated clean data manifold. Let \\hat{\\mathbf{z}}_0 denote the original estimate derived from the model \\theta , and \\hat{\\mathbf{z}}_0^{wm} denote the target watermarked estimate:", "source": "marker_v2", "marker_block_id": "/page/12/Text/4"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0083", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\hat{\\mathbf{z}}_0^{wm} = \\hat{\\mathbf{z}}_0 + \\delta_{wm}. \\tag{6}", "source": "marker_v2", "marker_block_id": "/page/12/Equation/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0084", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Text", "text": "2. Derivation of Score Function Difference \\Delta Score Under the VP-SDE framework, Tweedie's formula establishes a linear bijection between the score function \\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t) and the denoised estimate \\hat{\\mathbf{z}}_0 :", "source": "marker_v2", "marker_block_id": "/page/12/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0085", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t) = -\\frac{\\mathbf{z}_t - \\sqrt{\\bar{\\alpha}_t} \\hat{\\mathbf{z}}_0}{1 - \\bar{\\alpha}_t}. (7)", "source": "marker_v2", "marker_block_id": "/page/12/Equation/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0086", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Text", "text": "To enforce the watermark constraint (Eq. 6), the score function must shift to \\nabla_{\\mathbf{z}_t} \\log p_t^{wm} . By substituting the constraint \\hat{\\mathbf{z}}_0 - \\hat{\\mathbf{z}}_0^{wm} = -\\delta_{wm} , we derive the score discrepancy \\Delta S core:", "source": "marker_v2", "marker_block_id": "/page/12/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0087", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\Delta \\text{Score} = \\nabla_{\\mathbf{z}_{t}} \\log p_{t}^{wm} - \\nabla_{\\mathbf{z}_{t}} \\log p_{t} = -\\frac{1}{1 - \\bar{\\alpha}_{t}} \\left( -\\sqrt{\\bar{\\alpha}_{t}} (\\hat{\\mathbf{z}}_{0}^{wm} - \\hat{\\mathbf{z}}_{0}) \\right) = \\frac{\\sqrt{\\bar{\\alpha}_{t}}}{1 - \\bar{\\alpha}_{t}} \\delta_{wm}. (8)", "source": "marker_v2", "marker_block_id": "/page/12/Equation/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0088", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Text", "text": "Definition of Reverse Drift \\mathbf{F}_{rev} The generation trajectory in diffusion models is governed by the reverse-time SDE. The deterministic component of this process, known as the drift term \\mathbf{F}_{rev} , is defined as:", "source": "marker_v2", "marker_block_id": "/page/12/Text/11"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0089", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\mathbf{F}_{rev}(\\mathbf{z}_t, t) = \\mathbf{f}(\\mathbf{z}_t, t) - g^2(t) \\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t). \\tag{9}", "source": "marker_v2", "marker_block_id": "/page/12/Equation/12"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0090", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Text", "text": "where \\mathbf{f}(\\mathbf{z}_t, t) is the forward drift and g(t) is the diffusion coefficient.", "source": "marker_v2", "marker_block_id": "/page/12/Text/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0091", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Text", "text": "Derivation of Drift Correction \\Delta \\mathbf{F}_{rev} We calculate the modification to the drift term required to accommodate the watermark. Since the forward physics \\mathbf{f}(\\mathbf{z}_t, t) remains invariant, the drift correction depends solely on the score shift:", "source": "marker_v2", "marker_block_id": "/page/12/Text/14"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0092", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\Delta \\mathbf{F}_{rev} = \\mathbf{F}_{rev}^{wm} - \\mathbf{F}_{rev}^{orig} = -g^2(t) \\left(\\Delta \\text{Score}\\right). \\tag{10}", "source": "marker_v2", "marker_block_id": "/page/12/Equation/15"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0093", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Text", "text": "Substituting Eq. (8) into the expression above, we obtain the explicit form of the Watermark Drift Force:", "source": "marker_v2", "marker_block_id": "/page/12/Text/16"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0094", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\Delta \\mathbf{F}_{rev}(\\mathbf{z}_t, t) = -g^2(t) \\frac{\\sqrt{\\bar{\\alpha}_t}}{1 - \\bar{\\alpha}_t} \\delta_{wm}. \\tag{11}", "source": "marker_v2", "marker_block_id": "/page/12/Equation/17"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0095", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Text", "text": "Theorem: The spatial constraint \\delta_{wm} imposes a constant, deterministic force \\Delta \\mathbf{F}_{rev} on the probability flow. Because \\mathbf{F}_{rev} is the shared driving term for both the stochastic reverse SDE and the deterministic Probability Flow ODE (PF-ODE), this correction guarantees that the watermark embedding is robust across different samplers.", "source": "marker_v2", "marker_block_id": "/page/12/Text/18"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0096", "section": "A.3. Derivation of Noise Prediction Target \\epsilon^{target}", "page_start": 13, "page_end": 13, "type": "Text", "text": "To implement the theoretical drift correction \\Delta \\mathbf{F}_{rev} in practice, we modulate the output of the U-Net \\vartheta .", "source": "marker_v2", "marker_block_id": "/page/12/Text/20"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0097", "section": "A.3. Derivation of Noise Prediction Target \\epsilon^{target}", "page_start": 13, "page_end": 13, "type": "Text", "text": "Score-Noise Relationship The neural network \\epsilon_{\\vartheta} approximates the score function via the relation:", "source": "marker_v2", "marker_block_id": "/page/12/Text/21"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0098", "section": "A.3. Derivation of Noise Prediction Target \\epsilon^{target}", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t) = -\\frac{\\epsilon_{\\vartheta}(\\mathbf{z}_t, t)}{\\sqrt{1 - \\bar{\\alpha}_t}}. (12)", "source": "marker_v2", "marker_block_id": "/page/12/Equation/22"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0099", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Code", "text": "715 716 Phase I: Watermark Embedding 717 2: Input: Pre-trained U-Net \\theta, Encoder E_s, Scheduler S, VAE Decoder \\mathcal{D}_{VAE}, Prompt c, Secret m, Injection Interval 718 [T_{start}, T_{end}], Strength \\lambda 719 3: Output: Watermarked Image \\mathbf{x}_{wm} 720 4: \\delta_{wm} \\leftarrow E_s(\\mathbf{m}) 721 5: \\mathbf{z}_t \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I}) 6: for t = T down to 1 do \\mathbf{t} \\leftarrow S. \\mathsf{timesteps}[t] 724 \\epsilon_{\\theta}^{t} \\leftarrow \\text{CFG}(\\theta, \\mathbf{z}_{t}, \\mathbf{t}, \\mathbf{c}) 725 if t \\leq T_{end} and t \\geq T_{start} then 726 // Modulate the prediction target 727 \\boldsymbol{\\epsilon}_{\\theta}^{t} \\leftarrow \\boldsymbol{\\epsilon}_{\\theta}^{t} - \\lambda \\cdot \\left(\\frac{\\sqrt{\\bar{\\alpha}_{t}}}{\\sqrt{1 - \\bar{\\alpha}_{t}}}\\right) \\cdot \\delta_{wm} 728 12: 730 \\mathbf{z}_t \\leftarrow S.\\text{step}(\\epsilon_{\\theta}^t, \\mathbf{t}, \\mathbf{z}_t).\\text{prev\\_sample} 14: end for 731 15: \\mathbf{x}_{wm} \\leftarrow \\mathcal{D}_{VAE}(\\mathbf{z}_t) 732 733 Phase II: Watermark Extraction 17: Input: Watermarked Image \\mathbf{x}_{wm}, VAE Encoder \\mathcal{E}_{VAE}, Watermark Decoder D_s 734 735 18: Output: Extracted Secret m' 19: // Encode image back to watermarked latent 736 737 20: \\mathbf{z}_0 \\leftarrow \\mathcal{E}_{VAE}(\\mathbf{x}_{wm}) 738 21: // Extract secret message from latent 22: \\mathbf{m}' \\leftarrow D_s(\\mathbf{z}_0) 739", "source": "marker_v2", "marker_block_id": "/page/13/Code/2"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0100", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Text", "text": "Mapping Drift Correction to \\epsilon -Space We equate the score difference derived from the drift requirement to the difference in noise prediction. Using \\Delta Score = -\\frac{1}{\\sqrt{1-\\bar{\\alpha}_t}}(\\epsilon^{target} - \\epsilon_{\\vartheta}) = -\\frac{\\Delta \\epsilon}{\\sqrt{1-\\bar{\\alpha}_t}} , we have:", "source": "marker_v2", "marker_block_id": "/page/13/Text/3"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0101", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Equation", "text": "-\\frac{\\Delta \\epsilon}{\\sqrt{1-\\bar{\\alpha}_t}} = \\frac{\\sqrt{\\bar{\\alpha}_t}}{1-\\bar{\\alpha}_t} \\delta_{wm}. \\tag{13}", "source": "marker_v2", "marker_block_id": "/page/13/Equation/4"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0102", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Text", "text": "Final Update Rule Solving for the correction term \\Delta \\epsilon :", "source": "marker_v2", "marker_block_id": "/page/13/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0103", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Equation", "text": "\\Delta \\epsilon = -\\sqrt{1 - \\bar{\\alpha}_t} \\cdot \\frac{\\sqrt{\\bar{\\alpha}_t}}{1 - \\bar{\\alpha}_t} \\delta_{wm} = -\\frac{\\sqrt{\\bar{\\alpha}_t}}{\\sqrt{1 - \\bar{\\alpha}_t}} \\delta_{wm}. \\tag{14}", "source": "marker_v2", "marker_block_id": "/page/13/Equation/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0104", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Text", "text": "Thus, the final target noise \\epsilon^{target} required to enforce the watermark is:", "source": "marker_v2", "marker_block_id": "/page/13/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0105", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Equation", "text": "\\epsilon^{target} = \\epsilon_{\\vartheta} + \\Delta \\epsilon = \\epsilon_{\\vartheta} - \\left(\\frac{\\sqrt{\\bar{\\alpha}_t}}{\\sqrt{1 - \\bar{\\alpha}_t}}\\right) \\delta_{wm}. \\tag{15}", "source": "marker_v2", "marker_block_id": "/page/13/Equation/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0106", "section": "B.1. Algorithm Pseudocode", "page_start": 14, "page_end": 14, "type": "Text", "text": "23: Return m<sup>2</sup>", "source": "marker_v2", "marker_block_id": "/page/13/Text/16"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0107", "section": "B.1. Algorithm Pseudocode", "page_start": 14, "page_end": 14, "type": "Text", "text": "The core logic of the ALIEN watermarking framework is detailed in Algorithm 2. This algorithm outlines the complete process of watermark embedding during the reverse diffusion process and the subsequent extraction from the latent space.", "source": "marker_v2", "marker_block_id": "/page/13/Text/11"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0108", "section": "B.2. Hyperparameters and Training Settings", "page_start": 14, "page_end": 14, "type": "Text", "text": "Watermark Generation Module Training. We train the Imperceptible Latent Watermark Generation module using the AdamW optimizer with a learning rate of 5 \\times 10^{-5} and a weight decay of 1 \\times 10^{-5} . We construct a synthetic training set of", "source": "marker_v2", "marker_block_id": "/page/13/Text/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0109", "section": "B.2. Hyperparameters and Training Settings", "page_start": 15, "page_end": 15, "type": "TableGroup", "text": "Table 8. Detailed Robustness Evaluation Settings. We categorize attacks into four distinct groups. Note that Image Processing attacks are grouped by type (Photometry, Geometry, Degradation) to conserve space. Category Method & Parameters Image Processing Photometry: Brightness (×6.0), Contrast (×12.0) Geometry: Resize (s = 0.5), Center Crop(s = 0.4), Random Crop(s = 0.4) Degradation: Gaussian Noise (σ = 0.25), Blur (radius = 1.5), JPEG (Q = 50) Reconstructive VAE Compression: VAE-B (Balle et al. ´ , 2018) (Q = 1), VAE-C (Cheng et al., 2020) (Q = 1) Generative Attack: Regen-Diff (Zhao et al., 2024) (SD v1.5, Strength S = 0.2), Rinsing (N = 2, 4) Adversarial Adv-Emb: PGD-based Latent Attack (An et al., 2024) Forgery Imprinting: Latent optimization via inversion (Muller et al. ¨ , 2025) Reprompting: Inverse the image to initial latent and regeneration (Muller et al. ¨ , 2025) Average: Estimate watermark pattern by averaging residuals (Yang et al., 2024b)", "source": "marker_v2", "marker_block_id": "/page/14/TableGroup/487"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0110", "section": "B.2. Hyperparameters and Training Settings", "page_start": 15, "page_end": 15, "type": "PictureGroup", "text": "Figure 10. Visual Robustness Examples. Comparison of the watermarked image under various attacks: (a) Original, (b) Brightness, (c) Contrast, (d) JPEG Compression, (e) Gaussian Blur, (f) Gaussian Noise, (g) Center Crop (C.C.), (h) Random Crop (R.C.), (i) VAE Compression (BMSHJ), and (j) VAE Compression (Cheng).", "source": "marker_v2", "marker_block_id": "/page/14/PictureGroup/488"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0111", "section": "B.2. Hyperparameters and Training Settings", "page_start": 15, "page_end": 15, "type": "Text", "text": "10,000 images generated based on COCO2014 (Lin et al., 2014) prompts. The model is trained for 50,000 steps with a batch size of 16. To ensure training stability and perceptual quality, we impose a maximum gradient norm of 10 − 2 . The total objective combines the secret recovery loss (Lsec), pixel-wise reconstruction loss (Lmse), and perceptual loss (Llpips using AlexNet backbone). The loss weights are set to λsec = 1.0, λmse = 30.0, and λlpips = 0.3. Notably, λmse and λlpips are linearly ramped up from 0 to their peak values over the first 5,000 steps to facilitate stable convergence in the early training phase.", "source": "marker_v2", "marker_block_id": "/page/14/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0112", "section": "B.2. Hyperparameters and Training Settings", "page_start": 15, "page_end": 15, "type": "Text", "text": "Injection Settings. During the inference phase, ALIEN-Q injects watermarks within the sampling interval of steps 20–45 (with injection strength λ = 0.85), while ALIEN-R extends the injection window to cover steps 0–50 (λ = 1.0) for enhanced robustness.", "source": "marker_v2", "marker_block_id": "/page/14/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0113", "section": "C.1. Dataset Settings", "page_start": 15, "page_end": 15, "type": "Text", "text": "Evaluation Datasets. We utilize two distinct datasets to comprehensively evaluate both watermarking performance and image generation quality: For measuring detection accuracy (TPR@1%FPR) and payload capacity (Bit Accuracy), we", "source": "marker_v2", "marker_block_id": "/page/14/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0114", "section": "C.1. Dataset Settings", "page_start": 16, "page_end": 16, "type": "TableGroup", "text": "Table 9. Breakdown of Performance Gains. We compare ALIEN against the best-performing baseline (Best SOTA) for each metric/condition. Panel A calculates the average relative improvement across 5 quality metrics (33.1%). Panel B highlights the robustness gain across 15 distinct conditions (12 Generative + 3 Stability). The final 14.0% is the weighted average gain over these 15 conditions. Panel A: Quality Improvement (ALIEN-Q vs. Best SOTA) Metric Description Best SOTA Method ALIEN-Q Improvement FID ↓ Frechet Inception Distance ´ 24.42 (G.S.) Lower is better 24.29 +0.5% PSNR ↑ Peak Signal-to-Noise Ratio 29.09 (StableSig.) Higher is better 32.41 +11.4% SSIM ↑ Structural Similarity 0.922 (ZoDiac) Higher is better 0.949 +2.9% SIFID ↓ Single Image FID 0.105 (StableSig.) Lower is better 0.023 +78.1% DreamSim ↓ Perceptual Similarity 0.011 (StableSig.) Lower is better 0.003 +72.7% Average Quality Improvement +33.1% Panel B: Robustness Improvement (ALIEN-R vs. Training-free SOTA) Condition Category Specifics Best SOTA Metric ALIEN-R Gain 1. Generative Variant (12 conditions) Average Acc. across 12 conditions (4 Schedulers × Regen/Rinse) ∼0.84 Acc. ∼0.90 +6.5% 2. Sampler Stability Average Acc. across 3 stochastic samplers ∼0.56 Acc. ∼1.00 +44.0% (3 conditions) (DPM++ SDE, Euler a, DPM2 a) Table 10. Comparison of Imperceptibility and Robustness. We compare 48-bit and 128-bit payloads. Fidelity is reported as Mean ± Std. Dev. Robustness is reported as Detection Accuracy. Abbreviations: No Att. (No Attack), Comp. (Compression), Comb. (Combined Attack).", "source": "marker_v2", "marker_block_id": "/page/15/TableGroup/583"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0115", "section": "C.1. Dataset Settings", "page_start": 16, "page_end": 16, "type": "Table", "text": "Payload Imperceptibility Metrics Robustness (Bit Accuracy) No Att. Blur Noise JPEG Resize Sharp Bright Contr. Sat. PSNR(↑) SSIM(↑) LPIPS(↓) Comb. 48 Bits 31.17±0.90 0.62±0.03 0.097±0.01 0.99 0.99 0.92 0.99 0.99 0.99 0.99 0.99 0.99 0.87 128 Bits 30.79±0.85 0.59±0.03 0.151±0.01 0.99 0.99 0.90 0.98 0.99 0.99 0.99 0.99 0.99 0.82", "source": "marker_v2", "marker_block_id": "/page/15/Table/4"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0116", "section": "C.1. Dataset Settings", "page_start": 16, "page_end": 16, "type": "Text", "text": "employ the Stable Diffusion-Prompts (SDP) dataset (Gustavosta, 2023) . We randomly select 350 prompts from the dataset to generate image pairs (watermarked vs. clean) for distinct evaluation. For evaluating generative fidelity, specifically Frechet ´ Inception Distance (FID), we utilize the MS-COCO dataset (Lin et al., 2014) . We randomly sample 5,000 captions from the MS-COCO validation set to generate 5,000 watermarked images and compute the FID score against the corresponding real reference images to ensure standardized quality comparison.", "source": "marker_v2", "marker_block_id": "/page/15/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0117", "section": "C.1. Dataset Settings", "page_start": 16, "page_end": 16, "type": "Text", "text": "Generation Configuration. We conduct experiments on two representative Latent Diffusion Models: Stable Diffusion v1.5 and Stable Diffusion v2.1. Unless otherwise specified, we use the DDIM sampler with 50 inference steps. The classifier-free guidance scale is set to 7.5. All generated images are of resolution 512 × 512. All experiments were conducted on a single NVIDIA RTX 3090 GPU.", "source": "marker_v2", "marker_block_id": "/page/15/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0118", "section": "C.3. Extended Experiments", "page_start": 16, "page_end": 16, "type": "Text", "text": "Detailed Performance Gain Analysis. To substantiate the claims made in the abstract, we provide a detailed breakdown of the performance improvements. Table 9 illustrates the calculation of the 33.1% quality improvement and 14.0% robustness improvement compared to the state-of-the-art (SOTA) methods.", "source": "marker_v2", "marker_block_id": "/page/15/Text/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0119", "section": "C.3. Extended Experiments", "page_start": 16, "page_end": 16, "type": "Text", "text": "Impact of Payload Size. We further investigate the impact of payload size on the trade-off between watermark capacity, imperceptibility, and robustness. As demonstrated in Table 10, increasing the payload capacity from 48 bits to 128 bits results in only a minor decrease in fidelity metrics, exemplified by a slight PSNR drop from 31.17 dB to 30.79 dB. This result validates that ALIEN effectively supports high-capacity embedding while maintaining visual quality comparable to low-capacity settings.", "source": "marker_v2", "marker_block_id": "/page/15/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0120", "section": "C.3. Extended Experiments", "page_start": 17, "page_end": 17, "type": "TableGroup", "text": "Table 11. Impact of Fixed Thresholding on False Positive Rates (ROBIN Scheme). Comparison of clean image means (µclean) versus the optimal threshold for Cropping (τcrop) using the ROBIN watermarking method. For both SD v1.5 and v2.1, benign degradations like Blurring and JPEG shift µclean below τcrop (marked with ×). Attack Stable Diffusion v1.5 (τcrop = 39.45) Stable Diffusion v2.1 (τcrop = 55.80) Clean Mean Opt. τ Fixed τ Risk Clean Mean Opt. τ Fixed τ Risk No Attack 40.08 38.28 ✓ 55.90 52.74 ✓ Cropping 40.25 39.45 - 55.86 55.80 - Blurring 32.38 30.31 × 52.65 50.24 × JPEG 37.22 36.91 × 55.65 53.57 × Color Jitter 36.91 36.85 × 54.04 51.39 × Noise 41.63 40.02 ✓ 57.07 55.62 ✓", "source": "marker_v2", "marker_block_id": "/page/16/TableGroup/465"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0121", "section": "C.3. Extended Experiments", "page_start": 17, "page_end": 17, "type": "Text", "text": "Threshold Determination for Distance-Based Methods. We evaluate the impact of distribution shifts caused by image degradations on threshold determination for the distance-based method, ROBIN. As shown in Table 11, using a fixed threshold derived from a challenging scenario (Cropping, τ = 39.45) poses risks when applied to other distortions. We observe a clear distribution shift in the metric space for degradations that suppress high-frequency information. For instance, the mean metric of unwatermarked images under Blurring drops to 32.38, falling below the fixed cropping threshold of 39.45. Since detection occurs when the metric is below the threshold, this shift results in increased False Positive Rates (FPR), where benign, low-quality images are misclassified.", "source": "marker_v2", "marker_block_id": "/page/16/Text/3"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0122", "section": "D. Extended Related Work", "page_start": 17, "page_end": 17, "type": "Text", "text": "This section provides a detailed review and taxonomy of existing watermarking methods for generative models.", "source": "marker_v2", "marker_block_id": "/page/16/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0123", "section": "D.1. Watermarking Schemes Taxonomy", "page_start": 17, "page_end": 17, "type": "Text", "text": "We categorize existing watermarking methods for generative models into five primary classes based on their embedding stage: Random Seed Modification, U-Net Modification, VAE Modification, Latent Space Modification, and Post-Processing.", "source": "marker_v2", "marker_block_id": "/page/16/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0124", "section": "D.1. Watermarking Schemes Taxonomy", "page_start": 17, "page_end": 17, "type": "Text", "text": "Random Seed Modification (Initial Latent). Methods in this category embed watermarks by changing in the sampling process of the initial latent variables. For instance, Tree-Ring (Wen et al., 2024) modifies the initial noise vector in the Fourier domain to embed a ring-shaped pattern, which is detectable via diffusion inversion. Gaussian Shading (Yang et al., 2024c) employs a constrained sampling strategy to apply specific patterns to the initial latent.", "source": "marker_v2", "marker_block_id": "/page/16/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0125", "section": "D.1. Watermarking Schemes Taxonomy", "page_start": 17, "page_end": 17, "type": "Text", "text": "Model Modification. These approaches embed watermarks by fine-tuning specific components of the generative model to ensure watermark preservation during generation. Stable Signature (Fernandez et al., 2023) fine-tunes the VAE decoder to embed the watermark into the pixel space during the latent-to-image decoding stage. Aqualora (Feng et al., 2024) modifies the U-Net to inject the watermark during the iterative denoising process.", "source": "marker_v2", "marker_block_id": "/page/16/Text/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0126", "section": "D.1. Watermarking Schemes Taxonomy", "page_start": 17, "page_end": 17, "type": "Text", "text": "Latent Space Optimization. Unlike static encoding methods, these approaches formulate watermark embedding as an optimization problem within the latent space. Zodiac (Zhang et al., 2024) embeds the watermark by iteratively optimizing the initial latent variable to ensure high detectability in the generated output. ROBIN (Huang et al., 2024) focuses on optimizing the intermediate latent representations during the diffusion process. It incorporates learnable prompts to align the watermarked latents with the text condition.", "source": "marker_v2", "marker_block_id": "/page/16/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0127", "section": "D.1. Watermarking Schemes Taxonomy", "page_start": 17, "page_end": 17, "type": "Text", "text": "Post-Processing Methods. These techniques apply digital watermarking algorithms to the image after it has been fully generated, operating independently of the generation pipeline. StegaStamp (Tancik et al., 2020) is a deep learning-based encoder-decoder framework that embeds invisible hyperlinks or bit-strings into the final image output.", "source": "marker_v2", "marker_block_id": "/page/16/Text/11"}

icml26/6b484833-bf42-4409-a685-ed34a504bfa9/appendix_text_v3.txt

@@ -0,0 +1,143 @@
+[p. 12 | section: Supplementary Material | type: TableOfContents]
+A Theoretical Analysis of ALIEN 12 A.1 Watermark Constraint and Score Discrepancy 12 A.2 Proof of Reverse SDE Drift Term Correction 12 A.3 Derivation of UNet Target Noise 12 B Implementation Details 13 B.1 Algorithm Pseudocode 13 B.2 Hyperparameters and Training Settings 13 C Experimental Setup and Extended Experiments 14 C.1 Dataset Settings 14 C.2 Robustness Evaluation Settings 15 C.3 Extended Experiments 15 D Extended Related Work 16 D.1 Watermarking Schemes Taxonomy 16
+
+[p. 13 | section: A. Theoretical Analysis of ALIEN | type: Text]
+In this section, we provide a rigorous derivation establishing the analytical link between the watermark constraint in the z_0 -space and the necessary correction to the probability flow drift term. This derivation proves that ALIEN is theoretically grounded in the VP-SDE framework and is inherently sampler-agnostic.
+
+[p. 13 | section: A.1. Watermark Constraint and Score Function Discrepancy | type: Text]
+1. Watermark Constraint Definition Our objective is to embed a fixed watermark residual \delta_{wm} into the latent representation. We define this as a geometric constraint on the estimated clean data manifold. Let \hat{\mathbf{z}}_0 denote the original estimate derived from the model \theta , and \hat{\mathbf{z}}_0^{wm} denote the target watermarked estimate:
+
+[p. 13 | section: A.1. Watermark Constraint and Score Function Discrepancy | type: Equation]
+\hat{\mathbf{z}}_0^{wm} = \hat{\mathbf{z}}_0 + \delta_{wm}. \tag{6}
+
+[p. 13 | section: A.1. Watermark Constraint and Score Function Discrepancy | type: Text]
+2. Derivation of Score Function Difference \Delta Score Under the VP-SDE framework, Tweedie's formula establishes a linear bijection between the score function \nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t) and the denoised estimate \hat{\mathbf{z}}_0 :
+
+[p. 13 | section: A.1. Watermark Constraint and Score Function Discrepancy | type: Equation]
+\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t) = -\frac{\mathbf{z}_t - \sqrt{\bar{\alpha}_t} \hat{\mathbf{z}}_0}{1 - \bar{\alpha}_t}. (7)
+
+[p. 13 | section: A.1. Watermark Constraint and Score Function Discrepancy | type: Text]
+To enforce the watermark constraint (Eq. 6), the score function must shift to \nabla_{\mathbf{z}_t} \log p_t^{wm} . By substituting the constraint \hat{\mathbf{z}}_0 - \hat{\mathbf{z}}_0^{wm} = -\delta_{wm} , we derive the score discrepancy \Delta S core:
+
+[p. 13 | section: A.1. Watermark Constraint and Score Function Discrepancy | type: Equation]
+\Delta \text{Score} = \nabla_{\mathbf{z}_{t}} \log p_{t}^{wm} - \nabla_{\mathbf{z}_{t}} \log p_{t} = -\frac{1}{1 - \bar{\alpha}_{t}} \left( -\sqrt{\bar{\alpha}_{t}} (\hat{\mathbf{z}}_{0}^{wm} - \hat{\mathbf{z}}_{0}) \right) = \frac{\sqrt{\bar{\alpha}_{t}}}{1 - \bar{\alpha}_{t}} \delta_{wm}. (8)
+
+[p. 13 | section: A.2. Proof of Reverse SDE Drift Term Correction \Delta \mathbf{F}_{rev} | type: Text]
+Definition of Reverse Drift \mathbf{F}_{rev} The generation trajectory in diffusion models is governed by the reverse-time SDE. The deterministic component of this process, known as the drift term \mathbf{F}_{rev} , is defined as:
+
+[p. 13 | section: A.2. Proof of Reverse SDE Drift Term Correction \Delta \mathbf{F}_{rev} | type: Equation]
+\mathbf{F}_{rev}(\mathbf{z}_t, t) = \mathbf{f}(\mathbf{z}_t, t) - g^2(t) \nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t). \tag{9}
+
+[p. 13 | section: A.2. Proof of Reverse SDE Drift Term Correction \Delta \mathbf{F}_{rev} | type: Text]
+where \mathbf{f}(\mathbf{z}_t, t) is the forward drift and g(t) is the diffusion coefficient.
+
+[p. 13 | section: A.2. Proof of Reverse SDE Drift Term Correction \Delta \mathbf{F}_{rev} | type: Text]
+Derivation of Drift Correction \Delta \mathbf{F}_{rev} We calculate the modification to the drift term required to accommodate the watermark. Since the forward physics \mathbf{f}(\mathbf{z}_t, t) remains invariant, the drift correction depends solely on the score shift:
+
+[p. 13 | section: A.2. Proof of Reverse SDE Drift Term Correction \Delta \mathbf{F}_{rev} | type: Equation]
+\Delta \mathbf{F}_{rev} = \mathbf{F}_{rev}^{wm} - \mathbf{F}_{rev}^{orig} = -g^2(t) \left(\Delta \text{Score}\right). \tag{10}
+
+[p. 13 | section: A.2. Proof of Reverse SDE Drift Term Correction \Delta \mathbf{F}_{rev} | type: Text]
+Substituting Eq. (8) into the expression above, we obtain the explicit form of the Watermark Drift Force:
+
+[p. 13 | section: A.2. Proof of Reverse SDE Drift Term Correction \Delta \mathbf{F}_{rev} | type: Equation]
+\Delta \mathbf{F}_{rev}(\mathbf{z}_t, t) = -g^2(t) \frac{\sqrt{\bar{\alpha}_t}}{1 - \bar{\alpha}_t} \delta_{wm}. \tag{11}
+
+[p. 13 | section: A.2. Proof of Reverse SDE Drift Term Correction \Delta \mathbf{F}_{rev} | type: Text]
+Theorem: The spatial constraint \delta_{wm} imposes a constant, deterministic force \Delta \mathbf{F}_{rev} on the probability flow. Because \mathbf{F}_{rev} is the shared driving term for both the stochastic reverse SDE and the deterministic Probability Flow ODE (PF-ODE), this correction guarantees that the watermark embedding is robust across different samplers.
+
+[p. 13 | section: A.3. Derivation of Noise Prediction Target \epsilon^{target} | type: Text]
+To implement the theoretical drift correction \Delta \mathbf{F}_{rev} in practice, we modulate the output of the U-Net \vartheta .
+
+[p. 13 | section: A.3. Derivation of Noise Prediction Target \epsilon^{target} | type: Text]
+Score-Noise Relationship The neural network \epsilon_{\vartheta} approximates the score function via the relation:
+
+[p. 13 | section: A.3. Derivation of Noise Prediction Target \epsilon^{target} | type: Equation]
+\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t) = -\frac{\epsilon_{\vartheta}(\mathbf{z}_t, t)}{\sqrt{1 - \bar{\alpha}_t}}. (12)
+
+[p. 14 | section: Algorithm 2 ALIEN Watermarking | type: Code]
+715 716 Phase I: Watermark Embedding 717 2: Input: Pre-trained U-Net \theta, Encoder E_s, Scheduler S, VAE Decoder \mathcal{D}_{VAE}, Prompt c, Secret m, Injection Interval 718 [T_{start}, T_{end}], Strength \lambda 719 3: Output: Watermarked Image \mathbf{x}_{wm} 720 4: \delta_{wm} \leftarrow E_s(\mathbf{m}) 721 5: \mathbf{z}_t \sim \mathcal{N}(\mathbf{0}, \mathbf{I}) 6: for t = T down to 1 do \mathbf{t} \leftarrow S. \mathsf{timesteps}[t] 724 \epsilon_{\theta}^{t} \leftarrow \text{CFG}(\theta, \mathbf{z}_{t}, \mathbf{t}, \mathbf{c}) 725 if t \leq T_{end} and t \geq T_{start} then 726 // Modulate the prediction target 727 \boldsymbol{\epsilon}_{\theta}^{t} \leftarrow \boldsymbol{\epsilon}_{\theta}^{t} - \lambda \cdot \left(\frac{\sqrt{\bar{\alpha}_{t}}}{\sqrt{1 - \bar{\alpha}_{t}}}\right) \cdot \delta_{wm} 728 12: 730 \mathbf{z}_t \leftarrow S.\text{step}(\epsilon_{\theta}^t, \mathbf{t}, \mathbf{z}_t).\text{prev\_sample} 14: end for 731 15: \mathbf{x}_{wm} \leftarrow \mathcal{D}_{VAE}(\mathbf{z}_t) 732 733 Phase II: Watermark Extraction 17: Input: Watermarked Image \mathbf{x}_{wm}, VAE Encoder \mathcal{E}_{VAE}, Watermark Decoder D_s 734 735 18: Output: Extracted Secret m' 19: // Encode image back to watermarked latent 736 737 20: \mathbf{z}_0 \leftarrow \mathcal{E}_{VAE}(\mathbf{x}_{wm}) 738 21: // Extract secret message from latent 22: \mathbf{m}' \leftarrow D_s(\mathbf{z}_0) 739
+
+[p. 14 | section: Algorithm 2 ALIEN Watermarking | type: Text]
+Mapping Drift Correction to \epsilon -Space We equate the score difference derived from the drift requirement to the difference in noise prediction. Using \Delta Score = -\frac{1}{\sqrt{1-\bar{\alpha}_t}}(\epsilon^{target} - \epsilon_{\vartheta}) = -\frac{\Delta \epsilon}{\sqrt{1-\bar{\alpha}_t}} , we have:
+
+[p. 14 | section: Algorithm 2 ALIEN Watermarking | type: Equation]
+-\frac{\Delta \epsilon}{\sqrt{1-\bar{\alpha}_t}} = \frac{\sqrt{\bar{\alpha}_t}}{1-\bar{\alpha}_t} \delta_{wm}. \tag{13}
+
+[p. 14 | section: Algorithm 2 ALIEN Watermarking | type: Text]
+Final Update Rule Solving for the correction term \Delta \epsilon :
+
+[p. 14 | section: Algorithm 2 ALIEN Watermarking | type: Equation]
+\Delta \epsilon = -\sqrt{1 - \bar{\alpha}_t} \cdot \frac{\sqrt{\bar{\alpha}_t}}{1 - \bar{\alpha}_t} \delta_{wm} = -\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}} \delta_{wm}. \tag{14}
+
+[p. 14 | section: Algorithm 2 ALIEN Watermarking | type: Text]
+Thus, the final target noise \epsilon^{target} required to enforce the watermark is:
+
+[p. 14 | section: Algorithm 2 ALIEN Watermarking | type: Equation]
+\epsilon^{target} = \epsilon_{\vartheta} + \Delta \epsilon = \epsilon_{\vartheta} - \left(\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}}\right) \delta_{wm}. \tag{15}
+
+[p. 14 | section: B.1. Algorithm Pseudocode | type: Text]
+23: Return m<sup>2</sup>
+
+[p. 14 | section: B.1. Algorithm Pseudocode | type: Text]
+The core logic of the ALIEN watermarking framework is detailed in Algorithm 2. This algorithm outlines the complete process of watermark embedding during the reverse diffusion process and the subsequent extraction from the latent space.
+
+[p. 14 | section: B.2. Hyperparameters and Training Settings | type: Text]
+Watermark Generation Module Training. We train the Imperceptible Latent Watermark Generation module using the AdamW optimizer with a learning rate of 5 \times 10^{-5} and a weight decay of 1 \times 10^{-5} . We construct a synthetic training set of
+
+[p. 15 | section: B.2. Hyperparameters and Training Settings | type: TableGroup]
+Table 8. Detailed Robustness Evaluation Settings. We categorize attacks into four distinct groups. Note that Image Processing attacks are grouped by type (Photometry, Geometry, Degradation) to conserve space. Category Method & Parameters Image Processing Photometry: Brightness (×6.0), Contrast (×12.0) Geometry: Resize (s = 0.5), Center Crop(s = 0.4), Random Crop(s = 0.4) Degradation: Gaussian Noise (σ = 0.25), Blur (radius = 1.5), JPEG (Q = 50) Reconstructive VAE Compression: VAE-B (Balle et al. ´ , 2018) (Q = 1), VAE-C (Cheng et al., 2020) (Q = 1) Generative Attack: Regen-Diff (Zhao et al., 2024) (SD v1.5, Strength S = 0.2), Rinsing (N = 2, 4) Adversarial Adv-Emb: PGD-based Latent Attack (An et al., 2024) Forgery Imprinting: Latent optimization via inversion (Muller et al. ¨ , 2025) Reprompting: Inverse the image to initial latent and regeneration (Muller et al. ¨ , 2025) Average: Estimate watermark pattern by averaging residuals (Yang et al., 2024b)
+
+[p. 15 | section: B.2. Hyperparameters and Training Settings | type: PictureGroup]
+Figure 10. Visual Robustness Examples. Comparison of the watermarked image under various attacks: (a) Original, (b) Brightness, (c) Contrast, (d) JPEG Compression, (e) Gaussian Blur, (f) Gaussian Noise, (g) Center Crop (C.C.), (h) Random Crop (R.C.), (i) VAE Compression (BMSHJ), and (j) VAE Compression (Cheng).
+
+[p. 15 | section: B.2. Hyperparameters and Training Settings | type: Text]
+10,000 images generated based on COCO2014 (Lin et al., 2014) prompts. The model is trained for 50,000 steps with a batch size of 16. To ensure training stability and perceptual quality, we impose a maximum gradient norm of 10 − 2 . The total objective combines the secret recovery loss (Lsec), pixel-wise reconstruction loss (Lmse), and perceptual loss (Llpips using AlexNet backbone). The loss weights are set to λsec = 1.0, λmse = 30.0, and λlpips = 0.3. Notably, λmse and λlpips are linearly ramped up from 0 to their peak values over the first 5,000 steps to facilitate stable convergence in the early training phase.
+
+[p. 15 | section: B.2. Hyperparameters and Training Settings | type: Text]
+Injection Settings. During the inference phase, ALIEN-Q injects watermarks within the sampling interval of steps 20–45 (with injection strength λ = 0.85), while ALIEN-R extends the injection window to cover steps 0–50 (λ = 1.0) for enhanced robustness.
+
+[p. 15 | section: C.1. Dataset Settings | type: Text]
+Evaluation Datasets. We utilize two distinct datasets to comprehensively evaluate both watermarking performance and image generation quality: For measuring detection accuracy (TPR@1%FPR) and payload capacity (Bit Accuracy), we
+
+[p. 16 | section: C.1. Dataset Settings | type: TableGroup]
+Table 9. Breakdown of Performance Gains. We compare ALIEN against the best-performing baseline (Best SOTA) for each metric/condition. Panel A calculates the average relative improvement across 5 quality metrics (33.1%). Panel B highlights the robustness gain across 15 distinct conditions (12 Generative + 3 Stability). The final 14.0% is the weighted average gain over these 15 conditions. Panel A: Quality Improvement (ALIEN-Q vs. Best SOTA) Metric Description Best SOTA Method ALIEN-Q Improvement FID ↓ Frechet Inception Distance ´ 24.42 (G.S.) Lower is better 24.29 +0.5% PSNR ↑ Peak Signal-to-Noise Ratio 29.09 (StableSig.) Higher is better 32.41 +11.4% SSIM ↑ Structural Similarity 0.922 (ZoDiac) Higher is better 0.949 +2.9% SIFID ↓ Single Image FID 0.105 (StableSig.) Lower is better 0.023 +78.1% DreamSim ↓ Perceptual Similarity 0.011 (StableSig.) Lower is better 0.003 +72.7% Average Quality Improvement +33.1% Panel B: Robustness Improvement (ALIEN-R vs. Training-free SOTA) Condition Category Specifics Best SOTA Metric ALIEN-R Gain 1. Generative Variant (12 conditions) Average Acc. across 12 conditions (4 Schedulers × Regen/Rinse) ∼0.84 Acc. ∼0.90 +6.5% 2. Sampler Stability Average Acc. across 3 stochastic samplers ∼0.56 Acc. ∼1.00 +44.0% (3 conditions) (DPM++ SDE, Euler a, DPM2 a) Table 10. Comparison of Imperceptibility and Robustness. We compare 48-bit and 128-bit payloads. Fidelity is reported as Mean ± Std. Dev. Robustness is reported as Detection Accuracy. Abbreviations: No Att. (No Attack), Comp. (Compression), Comb. (Combined Attack).
+
+[p. 16 | section: C.1. Dataset Settings | type: Table]
+Payload Imperceptibility Metrics Robustness (Bit Accuracy) No Att. Blur Noise JPEG Resize Sharp Bright Contr. Sat. PSNR(↑) SSIM(↑) LPIPS(↓) Comb. 48 Bits 31.17±0.90 0.62±0.03 0.097±0.01 0.99 0.99 0.92 0.99 0.99 0.99 0.99 0.99 0.99 0.87 128 Bits 30.79±0.85 0.59±0.03 0.151±0.01 0.99 0.99 0.90 0.98 0.99 0.99 0.99 0.99 0.99 0.82
+
+[p. 16 | section: C.1. Dataset Settings | type: Text]
+employ the Stable Diffusion-Prompts (SDP) dataset (Gustavosta, 2023) . We randomly select 350 prompts from the dataset to generate image pairs (watermarked vs. clean) for distinct evaluation. For evaluating generative fidelity, specifically Frechet ´ Inception Distance (FID), we utilize the MS-COCO dataset (Lin et al., 2014) . We randomly sample 5,000 captions from the MS-COCO validation set to generate 5,000 watermarked images and compute the FID score against the corresponding real reference images to ensure standardized quality comparison.
+
+[p. 16 | section: C.1. Dataset Settings | type: Text]
+Generation Configuration. We conduct experiments on two representative Latent Diffusion Models: Stable Diffusion v1.5 and Stable Diffusion v2.1. Unless otherwise specified, we use the DDIM sampler with 50 inference steps. The classifier-free guidance scale is set to 7.5. All generated images are of resolution 512 × 512. All experiments were conducted on a single NVIDIA RTX 3090 GPU.
+
+[p. 16 | section: C.3. Extended Experiments | type: Text]
+Detailed Performance Gain Analysis. To substantiate the claims made in the abstract, we provide a detailed breakdown of the performance improvements. Table 9 illustrates the calculation of the 33.1% quality improvement and 14.0% robustness improvement compared to the state-of-the-art (SOTA) methods.
+
+[p. 16 | section: C.3. Extended Experiments | type: Text]
+Impact of Payload Size. We further investigate the impact of payload size on the trade-off between watermark capacity, imperceptibility, and robustness. As demonstrated in Table 10, increasing the payload capacity from 48 bits to 128 bits results in only a minor decrease in fidelity metrics, exemplified by a slight PSNR drop from 31.17 dB to 30.79 dB. This result validates that ALIEN effectively supports high-capacity embedding while maintaining visual quality comparable to low-capacity settings.
+
+[p. 17 | section: C.3. Extended Experiments | type: TableGroup]
+Table 11. Impact of Fixed Thresholding on False Positive Rates (ROBIN Scheme). Comparison of clean image means (µclean) versus the optimal threshold for Cropping (τcrop) using the ROBIN watermarking method. For both SD v1.5 and v2.1, benign degradations like Blurring and JPEG shift µclean below τcrop (marked with ×). Attack Stable Diffusion v1.5 (τcrop = 39.45) Stable Diffusion v2.1 (τcrop = 55.80) Clean Mean Opt. τ Fixed τ Risk Clean Mean Opt. τ Fixed τ Risk No Attack 40.08 38.28 ✓ 55.90 52.74 ✓ Cropping 40.25 39.45 - 55.86 55.80 - Blurring 32.38 30.31 × 52.65 50.24 × JPEG 37.22 36.91 × 55.65 53.57 × Color Jitter 36.91 36.85 × 54.04 51.39 × Noise 41.63 40.02 ✓ 57.07 55.62 ✓
+
+[p. 17 | section: C.3. Extended Experiments | type: Text]
+Threshold Determination for Distance-Based Methods. We evaluate the impact of distribution shifts caused by image degradations on threshold determination for the distance-based method, ROBIN. As shown in Table 11, using a fixed threshold derived from a challenging scenario (Cropping, τ = 39.45) poses risks when applied to other distortions. We observe a clear distribution shift in the metric space for degradations that suppress high-frequency information. For instance, the mean metric of unwatermarked images under Blurring drops to 32.38, falling below the fixed cropping threshold of 39.45. Since detection occurs when the metric is below the threshold, this shift results in increased False Positive Rates (FPR), where benign, low-quality images are misclassified.
+
+[p. 17 | section: D. Extended Related Work | type: Text]
+This section provides a detailed review and taxonomy of existing watermarking methods for generative models.
+
+[p. 17 | section: D.1. Watermarking Schemes Taxonomy | type: Text]
+We categorize existing watermarking methods for generative models into five primary classes based on their embedding stage: Random Seed Modification, U-Net Modification, VAE Modification, Latent Space Modification, and Post-Processing.
+
+[p. 17 | section: D.1. Watermarking Schemes Taxonomy | type: Text]
+Random Seed Modification (Initial Latent). Methods in this category embed watermarks by changing in the sampling process of the initial latent variables. For instance, Tree-Ring (Wen et al., 2024) modifies the initial noise vector in the Fourier domain to embed a ring-shaped pattern, which is detectable via diffusion inversion. Gaussian Shading (Yang et al., 2024c) employs a constrained sampling strategy to apply specific patterns to the initial latent.
+
+[p. 17 | section: D.1. Watermarking Schemes Taxonomy | type: Text]
+Model Modification. These approaches embed watermarks by fine-tuning specific components of the generative model to ensure watermark preservation during generation. Stable Signature (Fernandez et al., 2023) fine-tunes the VAE decoder to embed the watermark into the pixel space during the latent-to-image decoding stage. Aqualora (Feng et al., 2024) modifies the U-Net to inject the watermark during the iterative denoising process.
+
+[p. 17 | section: D.1. Watermarking Schemes Taxonomy | type: Text]
+Latent Space Optimization. Unlike static encoding methods, these approaches formulate watermark embedding as an optimization problem within the latent space. Zodiac (Zhang et al., 2024) embeds the watermark by iteratively optimizing the initial latent variable to ensure high detectability in the generated output. ROBIN (Huang et al., 2024) focuses on optimizing the intermediate latent representations during the diffusion process. It incorporates learnable prompts to align the watermarked latents with the text condition.
+
+[p. 17 | section: D.1. Watermarking Schemes Taxonomy | type: Text]
+Post-Processing Methods. These techniques apply digital watermarking algorithms to the image after it has been fully generated, operating independently of the generation pipeline. StegaStamp (Tancik et al., 2020) is a deep learning-based encoder-decoder framework that embeds invisible hyperlinks or bit-strings into the final image output.

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+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0001", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "Text-to-image diffusion models, such as Stable Diffusion (Rombach et al., 2022) and DALL·E (Ramesh et al., 2022) , have demonstrated impressive capabilities in generating high-quality images. To safeguard the intellectual property of generative models (Gowal & Kohli, 2023) and facilitate misuse tracking (Barrett, 2023) , Governments are increasingly calling for regulations (European Union, 2024; Biden, 2023) to mandate watermark adoption. Robust and imperceptible watermarking of generated images has become a critical and urgent research focus. Post-processing watermarking (Cox et al., 2007) is applied to the contents gener-", "source": "marker_v2", "marker_block_id": "/page/0/Text/17"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0002", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "FigureGroup", "text": "Figure 1. (a) Latent modification, (b) Constrained sampling, (c) Iterative optimization, (d) Our ALIEN with principled embedding.", "source": "marker_v2", "marker_block_id": "/page/0/FigureGroup/568"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0003", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "ated by the diffusion model, but its robustness is insufficient for reliable detection in real-world applications (Ren et al., 2024) . Some studies consider model distribution scenarios (Rezaei et al., 2024; Ci et al., 2024; Feng et al., 2024; Wang et al., 2025) . Diffusion models are fine-tuned to embed watermarks into the model parameters, which inevitably limits efficiency and scalability.", "source": "marker_v2", "marker_block_id": "/page/0/Text/22"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0004", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "Recent research has concentrated on semantic watermarking (Lee & Cho, 2025) , which aims to embed watermark signals into the semantic or latent features to better resist imageprocessing-based attacks (Zhao et al., 2024) . Watermarking methods based on initial latent variable modifications (Wen et al., 2024; Ci et al., 2025) embed watermarks by directly modifying or adding perturbations to the initial latents (Fig. 1( a)). While the mechanism is intuitive, the mapping between the initial latent space and the final image is highly complex and nonlinear, making direct modifications prone to semantic drift. Furthermore, to maintain invisibility, the amount of modification to the initial latents is strictly limited, making it difficult to increase watermark capacity. To ensure high capacity and lossless watermark embedding, Watermarks based on the Gaussian-Constrained Identifiable Subspace Sampling (Yang et al., 2024c; Gunn et al., 2024)", "source": "marker_v2", "marker_block_id": "/page/0/Text/23"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0005", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "combined with cryptography, divide the initial latent space into non-overlapping identifiable subspaces, forcing users to sample from subspaces associated with specific watermark information (Fig. 1( b)). This rigid constraint on the initial latent space limits generative diversity. Watermarking methods based on optimization (Huang et al., 2024; Zhang et al., 2024) perform watermark optimization in the latent space to better balance robustness and fidelity (Fig. 1( c)). However, their reliance on computationally intensive heuristic optimization to iteratively find the optimal watermark, leading to substantial training overhead and prone to local optima. Furthermore, detection of semantic watermarking typically depends on diffusion inversion, which limits applicability to reversible samplers (Lu et al., 2022) and watermarks become undetectable when images are generated with irreversible samplers (Karras et al., 2022) . Attackers can exploit this vulnerability to remove watermarks by regenerating images with irreversible schedulers. (An et al., 2024) .", "source": "marker_v2", "marker_block_id": "/page/1/Text/1"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0006", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "Despite the progress made by aforementioned semantic watermarking schemes in robust embedding, they circumvent a fundamental issue: the inability to derive a precise and efficient watermark embedding mechanism from the generative principles of diffusion models. Current optimization or constraint-based methods essentially avoid this problem, instead relying on computationally intensive optimization or sampling constraints. These approaches inherently limits the fidelity, efficiency, and diversity.", "source": "marker_v2", "marker_block_id": "/page/1/Text/2"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0007", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "To address these issues, we propose an Analytical Watermarking Framework for Controllable Generation (ALIEN). As shown in Fig. 1( d), unlike existing methods that rely on computationally intensive heuristic latent variable optimization or constraints on initial latent sampling, we start with the reverse process of the Stochastic Differential Equation of the diffusion model and present the first analytic derivation of the watermark residual propagation mechanism. Specifically, given a target watermark residual, we analytically derive a time-dependent modulation coefficient that transforms this target into a precise correction term for the noise prediction. By injecting this correction at each denoising step, we effectively modify the underlying probability flow of the diffusion model. This imposes a deterministic force that seamlessly guides the generation trajectory toward the watermarked state regardless of the sampling path, thereby eliminating the need for iterative optimization and ensuring compatibility with various samplers. ALIEN achieves a principled watermark embedding pattern, rather than relying on heuristic methods. Without the need for iterative optimization, we inject the precisely modulated watermark into the noise prediction target at each step of the denoising process.", "source": "marker_v2", "marker_block_id": "/page/1/Text/3"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0008", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "Our contributions are three-fold: (1) We achieve the first analytic derivation of watermark propagation for seamless,", "source": "marker_v2", "marker_block_id": "/page/1/Text/4"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0009", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "low-inference-cost embedding, eliminating the need for iterative optimization. (2) Since the watermark is precisely compensated based on diffusion model, ALIEN preserves semantic consistency and visual fidelity by leveraging precise theoretical compensation for the watermark signal. (3) The ALIEN watermark embedding mechanism is independent of specific initial latent variables and sampler types (including irreversible samplers), solving the issue of strong reliance on reversible samplers of semantic watermarking.", "source": "marker_v2", "marker_block_id": "/page/1/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0010", "section": "2. Related Work", "page_start": 2, "page_end": 2, "type": "Text", "text": "Diffusion models exhibit exceptional performance in image generation (Dhariwal & Nichol, 2021) , leveraging the methodology (Ho et al., 2020; Song et al., 2020b) and the sampling techniques (Song et al., 2020a; Song & Ermon, 2020) . LDMs optimize image generation within the latent space of the pretrained Variational Autoencoder (VAE), which further accelerates the practical applications of diffusion models. During the inference phase, LDM first samples an initial latent z T ∈ R c×w×h from a standard Gaussian distribution N (0, I), where T denotes the total time step of the diffusion model. Following iterative denoising, the latent vector evolves into the noise-free representation z0. The final image x 0 is reconstructed by the VAE decoder from z0. Safeguarding the intellectual property of generated content and preventing misuse have become critical research priorities. This paper focuses on critical issues of fidelity, efficiency, and controllability in existing approaches for integrating watermarking into the diffusion process.", "source": "marker_v2", "marker_block_id": "/page/1/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0011", "section": "2. Related Work", "page_start": 2, "page_end": 2, "type": "Text", "text": "Watermarking in Latent Diffusion Models aims at tracking the origin and ensuring the accountability of the generated content. For a comprehensive context regarding the taxonomy of existing watermarking methods a detailed review is provided in Appendix D. We specifically focus on prior work integrating watermarking during the diffusion process. Latent modification Watermark such as Tree-Ring (Wen et al., 2024) and RingID (Ci et al., 2025) embed watermarks in the Fourier space of the initial latent which leads to semantic drift. Constrained sampling watermark such as Gaussian Shading (Yang et al., 2024c) , GaussMarker (Li et al., 2025) and PRC (Gunn et al., 2024) utilize cryptographic principles to modify the sampling pattern, but strict constraints limit the sampling range, resulting in reduced controllability. Optimization-based methods such as Zodiac (Zhang et al., 2024) and Robin (Huang et al., 2024) , optimize latent variables for higher semantic consistency, but reliance on heuristic optimization incurs computational costs. The detection of aforementioned methods depends on diffusion inversion, limiting their function to reversible samplers and is ineffective with irreversible samplers. Our method achieves low-overhead and universally applicable watermark via analytic derivation.", "source": "marker_v2", "marker_block_id": "/page/1/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0012", "section": "2. Related Work", "page_start": 3, "page_end": 3, "type": "Caption", "text": "Figure 2. The ALIEN framework consists of two main stages: (Top) Imperceptible Latent Watermark Generation, where a secret encoder E_s and decoder D_s are trained to embed a message m into a robust latent residual \\delta_w while preserving image quality. (Bottom) Analytic SDE Reverse Drift Correction, which applies the time-dependent modulation to the noise prediction. This principled correction steers the generative trajectory to satisfy the watermark constraint in a sampler-agnostic manner.", "source": "marker_v2", "marker_block_id": "/page/2/Caption/2"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0013", "section": "3. Methodology", "page_start": 3, "page_end": 3, "type": "Text", "text": "132133", "source": "marker_v2", "marker_block_id": "/page/2/Text/29"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0014", "section": "3.1. Framework of ALIEN", "page_start": 3, "page_end": 3, "type": "Text", "text": "We extend to achieve applicability and theoretical controllability of semantic watermarking. As demonstrated in Fig. 2, our ALIEN embeds the watermark in intermediate diffusion states to manipulate the generation trajectory through precise correction of the probability flow. To generate imperceptible watermark residuals, we implement an Imperceptible Latent Watermark Generation module to generate the invisible and robust watermark residual in the latent space. For principled embedding, we propose Analytic SDE Reverse Drift Correction, which analytically derives the necessary modifications to the probability flow required by the diffusion model for watermark embedding under Variance Preserving Stochastic Differential Equation (VP-SDE) (Song et al., 2020b), providing an explicit correction target for noise prediction that is compatible with both stochastic and deterministic sampling processes. This derived target is implemented via the Modulation of Noise Prediction Target module, which specifies the requisite adjustment to the model's noise prediction output, thereby realizing the controlled and imperceptible semantic watermarking.", "source": "marker_v2", "marker_block_id": "/page/2/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0015", "section": "3.2. Imperceptible Latent Watermark Generation", "page_start": 3, "page_end": 3, "type": "Text", "text": "To generate an imperceptible yet robust watermark residual, we jointly train a secret encoder E_s and a watermark decoder D_s . Ideally, the watermarked latent representation z_w should be conditioned on both the input latent z_0 and the", "source": "marker_v2", "marker_block_id": "/page/2/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0016", "section": "3.2. Imperceptible Latent Watermark Generation", "page_start": 3, "page_end": 3, "type": "Text", "text": "message m to enhance imperceptibility. However, utilizing a z_0 -dependent watermark becomes impractical as the intermediate latent states of the diffusion model are not readily accessible for deterministic conditioning. Therefore, we opt to embed a cover-agnostic watermark prominent in the latent space. Specifically, the secret residual \\delta_w=E(m) is added to the input latent z_0 , forming the watermarked latent z_w=z_0+\\delta_w . The watermarked image x_w is generated as x_w=\\mathcal{D}(z_w) , and the message is extracted by applying the decoder D_s to z_w , yielding m'=D_s(z_w) . We employ the Binary Cross-Entropy loss to optimize for the accuracy of message extraction between the original message m and the decoded message m'.", "source": "marker_v2", "marker_block_id": "/page/2/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0017", "section": "3.2. Imperceptible Latent Watermark Generation", "page_start": 3, "page_end": 3, "type": "Text", "text": "To ensure the visual consistency of the watermark, we compute the LPIPS loss (Zhang et al., 2018) and the Mean Squared Error loss between the watermarked image x_w and the reconstructed image x_r , rather than between x_w and the original image x_o . This choice is necessary because the VAE compression and reconstruction already introduce a measurable irrecoverable quality gap between x_o and x_r . Optimizing against x_o would necessitate the watermark training process to compensate for VAE reconstruction errors, which would increase complexity and hinder embedding effectiveness. Our training objective can be summarized below, where \\lambda_1 and \\lambda_2 are coefficients:", "source": "marker_v2", "marker_block_id": "/page/2/Text/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0018", "section": "3.2. Imperceptible Latent Watermark Generation", "page_start": 3, "page_end": 3, "type": "Equation", "text": "\\mathcal{L}_{T} = \\mathcal{L}_{BCE}^{(m,m')} + \\lambda_{1} \\mathcal{L}_{LPIPS}^{(x_{r},x_{w})} + \\lambda_{2} \\mathcal{L}_{MSE}^{(x_{r},x_{w})}, (1)", "source": "marker_v2", "marker_block_id": "/page/2/Equation/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0019", "section": "3.2. Imperceptible Latent Watermark Generation", "page_start": 3, "page_end": 3, "type": "Text", "text": "where \\mathcal{L}_{BCE} is the Binary Cross-Entropy loss, \\mathcal{L}_{LPIPS} is the Learned Perceptual Image Patch Similarity loss (Zhang", "source": "marker_v2", "marker_block_id": "/page/2/Text/11"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0020", "section": "Algorithm 1 ALIEN Watermarking", "page_start": 4, "page_end": 4, "type": "Text", "text": "17: Return D_s(\\mathcal{E}_{VAE}(\\mathbf{x}_{wm}))", "source": "marker_v2", "marker_block_id": "/page/3/Text/41"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0021", "section": "Algorithm 1 ALIEN Watermarking", "page_start": 4, "page_end": 4, "type": "Code", "text": "PHASE I: EMBEDDING 2: Input: Pre-trained U-Net \\theta, Encoder E_s, Scheduler S, VAE \\mathcal{D}_{VAE}, Prompt c, Secret m, Strength \\lambda, Interval [T_{start}, T_{end}] 3: Output: Watermarked Image \\mathbf{x}_{wm} 4: \\delta_{wm} \\leftarrow E_s(\\mathbf{m}) 5: \\mathbf{z}_t \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I}) 6: for t = T down to 1 do \\epsilon_{\\theta}^{t} \\leftarrow \\text{CFG}(\\theta, \\mathbf{z}_{t}, S.\\text{steps}[t], \\mathbf{c}) \\begin{aligned} & \\text{if } T_{start} \\leq t \\leq T_{end} \\text{ then} \\\\ & \\epsilon_{\\theta}^t \\leftarrow \\epsilon_{\\theta}^t - \\lambda \\cdot \\left(\\frac{\\sqrt{\\bar{\\alpha}_t}}{\\sqrt{1 - \\bar{\\alpha}_t}}\\right) \\cdot \\delta_{wm} \\end{aligned} 10: \\mathbf{z}_t \\leftarrow S.\\text{step}(\\epsilon_{\\theta}^t, t, \\mathbf{z}_t).\\text{prev\\_sample} 11: 12: end for 13: \\mathbf{x}_{wm} \\leftarrow \\mathcal{D}_{VAE}(\\mathbf{z}_t) PHASE II: EXTRACTION 15: Input: Image \\mathbf{x}_{wm}, \\mathcal{E}_{VAE}, Decoder D_s 16: Output: Secret m'", "source": "marker_v2", "marker_block_id": "/page/3/Code/2"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0022", "section": "Algorithm 1 ALIEN Watermarking", "page_start": 4, "page_end": 4, "type": "Text", "text": "et al., 2018), and \\mathcal{L}_{MSE} is the Mean Squared Error loss. Existing studies (Wang et al., 2025; Meng et al., 2024) demonstrate that injecting and detecting watermarks in the latent space can inherently resist various common distortions. We follow prior practice by omitting the distortion layer during training (validated in Tab. 4). The effectiveness of watermark remains unaffected even if an adversary finetunes U-Net \\theta and \\mathcal{D} on clean images and uses a fine-tuned latent decoder \\mathcal{D}' to generate images (validated in Fig. 8).", "source": "marker_v2", "marker_block_id": "/page/3/Text/3"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0023", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "To achieve precise watermark embedding over the generative process, we leverage the VP-SDE to analytically derive the exact probability flow correction required for watermark embedding.", "source": "marker_v2", "marker_block_id": "/page/3/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0024", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "\\mathbf{z}_0 Constraint. Our goal is to embed a predetermined watermark residual \\delta_{wm} into the final denoised latent \\mathbf{z}_0 , resulting in the \\mathbf{z}_0 -space constraint \\hat{\\mathbf{z}}_0^{wm} = \\hat{\\mathbf{z}}_0^{orig} + \\delta_{wm} , where \\hat{\\mathbf{z}}_0^{wm} and \\hat{\\mathbf{z}}_0^{orig} are the clean data estimates predicted by the U-Net for the current latent state \\mathbf{z}_t , with and without the watermark, respectively.", "source": "marker_v2", "marker_block_id": "/page/3/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0025", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "Score Function. Under the VP-SDE, The diffusion process is defined by a forward SDE that gradually perturbs clean data into noise:", "source": "marker_v2", "marker_block_id": "/page/3/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0026", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Equation", "text": "d\\mathbf{z} = \\mathbf{f}(\\mathbf{z}, t)dt + g(t)d\\mathbf{w},", "source": "marker_v2", "marker_block_id": "/page/3/Equation/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0027", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "where \\mathbf{f}(\\mathbf{z}, t) : \\mathbb{R}^d \\to \\mathbb{R}^d denotes the drift coefficient, while g(t) \\in \\mathbb{R} represents the scalar diffusion coefficient, with", "source": "marker_v2", "marker_block_id": "/page/3/Text/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0028", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "(b) Injection Strength Schedule", "source": "marker_v2", "marker_block_id": "/page/3/Text/12"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0029", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "Generation Step", "source": "marker_v2", "marker_block_id": "/page/3/Text/43"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0030", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Caption", "text": "Figure 3. Comparison of ALIEN-R and ALIEN-Q. (a) The L2 norm of noise prediction during the diffusion process. (b) The evolution of injection strength \\frac{\\sqrt{\\alpha_t}}{\\sqrt{1-\\bar{\\alpha}_t}} .", "source": "marker_v2", "marker_block_id": "/page/3/Caption/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0031", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "\\mathbf{w}(t) denoting the standard Wiener process. The reverse generation process of the diffusion model is governed by a reverse-time stochastic differential equation:", "source": "marker_v2", "marker_block_id": "/page/3/Text/14"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0032", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Equation", "text": "d\\mathbf{z} = \\underbrace{[\\mathbf{f}(\\mathbf{z}, t) - g^{2}(t)\\nabla_{\\mathbf{z}}\\log p_{t}(\\mathbf{z})]}_{\\text{Reverse Drift }\\mathbf{F}_{rev}} dt + g(t)d\\bar{\\mathbf{w}}, \\quad (2)", "source": "marker_v2", "marker_block_id": "/page/3/Equation/15"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0033", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "where \\bar{\\mathbf{w}} denotes the standard Wiener process in reverse time. To realize the watermark z_0 constraint, we precisely control the probability flow, which requires determining the necessary correction \\Delta \\mathbf{F}_{rev} for the reverse SDE drift term. Since \\Delta \\mathbf{F}_{rev} relies on the score function \\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t) , analytically quantifying the difference in the score function becomes a direct path to derive \\Delta \\mathbf{F}_{rev} . The score function is exactly and linearly related to the difference between \\mathbf{z}_t and its denoised estimate \\hat{\\mathbf{z}}_0 . This analytical relationship is mathematically described as follows:", "source": "marker_v2", "marker_block_id": "/page/3/Text/16"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0034", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Equation", "text": "\\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t) = -\\frac{1}{1 - \\bar{\\alpha}_t} (\\mathbf{z}_t - \\sqrt{\\bar{\\alpha}_t} \\hat{\\mathbf{z}}_0). (3)", "source": "marker_v2", "marker_block_id": "/page/3/Equation/17"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0035", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "Applying the analytical mapping Eq.3 allows us to analytically determine the difference in the score function induced by the \\mathbf{z}_0 constraint, thereby translating the watermark residual \\delta_{wm} into the required shift in the score function space.", "source": "marker_v2", "marker_block_id": "/page/3/Text/18"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0036", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "Probability Flow Correction. Based on the analytical structure of VP-SDE for the reverse drift term \\mathbf{F}_{rev} , we derive", "source": "marker_v2", "marker_block_id": "/page/3/Text/19"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0037", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 5, "page_end": 5, "type": "TableGroup", "text": "Method G.S. StegaStamp Tree-Ring ROBIN ZoDiac AquaLoRA StableSig. ALIEN-Q ALIEN-R Original Image No Original Watermarked Image Residual (×10) Metrics PSNR:—— SSIM: :—— LPIPS: :—— PSNR:29.26 SSIM:0.909 LPIPS:0.065 PSNR:14.25 SSIM:0.570 LPIPS:0.488 PSNR:24.64 SSIM:0.917 LPIPS:0.091 PSNR:28.46 SSIM:0.921 LPIPS:0.046 SSIM:0.776 PSNR:29.61 SSIM:0.891 LPIPS:0.039 PSNR:33.29 SSIM:0.942 LPIPS:0.020 PSNR:27.24 SSIM:0.855 LPIPS:0.107 Figure 4. Qualitative comparison of watermarked samples and 10 \\times magnified residuals. We compare ALIEN with baselines covering post-processing (StegaStamp), latent modification (Tree-Ring), optimization (ROBIN, ZoDiac), and fine-tuning (AquaLoRA, StableSig.).", "source": "marker_v2", "marker_block_id": "/page/4/TableGroup/217"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0038", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 5, "page_end": 5, "type": "TableGroup", "text": "Table 1. Quantitative Comparison of Visual Quality and Fidelity across Watermarking Schemes. D.S. denotes the Dreamsim (Fu et al., 2023) metric. Method FID CLIP PSNR SSIM SIFID D.S. No WM 24.31 0.3368 _ StegaS. 24.56 0.3363 28.59 0.878 0.189 0.021 ZoDiac _ 28.01 0.922 0.121 0.022 AquaL. 24.79 0.3366 17.07 0.664 0.183 0.139 TreeR. 24.63 0.3370 12.76 0.429 0.741 0.291 G.S. 24.42 0.3378 _ _ ROBIN 24.61 0.3366 22.96 0.756 0.212 0.057 StableS. 24.56 0.3367 29.09 0.878 0.105 0.011 ALIEN-Q 24.29 0.3369 32.41 0.949 0.023 0.003 ALIEN-R 24.74 0.3366 20.42 0.745 0.227 0.061", "source": "marker_v2", "marker_block_id": "/page/4/TableGroup/218"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0039", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 5, "page_end": 5, "type": "Text", "text": "the required reverse SDE drift correction \\Delta \\mathbf{F}_{rev} to enforce the watermark constraint (Details provided in Appendix A). The resulting correction term \\Delta \\mathbf{F}_{rev} is analytically defined by the following expression:", "source": "marker_v2", "marker_block_id": "/page/4/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0040", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\Delta \\mathbf{F}_{rev}(\\mathbf{z}_t, t) = -g^2(t) \\frac{\\sqrt{\\bar{\\alpha}_t}}{1 - \\bar{\\alpha}_t} \\delta_{wm}. (4)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0041", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 5, "page_end": 5, "type": "Text", "text": "This analytical derivation Eq.4 provides the theoretical foundation for the ALIEN framework. It precisely quantifies the correction \\Delta \\mathbf{F}_{rev} required by the watermark objective \\delta_{wm} within the SDE probability flow framework. Since this correction targets the score function of the latent distribution, it demonstrates that the watermark is sampler-agnostic.", "source": "marker_v2", "marker_block_id": "/page/4/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0042", "section": "3.4. Modulation of Noise Prediction Target", "page_start": 5, "page_end": 5, "type": "Text", "text": "To achieve the practical implementation of the SDE drift correction \\Delta \\mathbf{F}_{rev} , we analytically relate the SDE reverse drift correction to the noise prediction offset of U-Net within the VP-SDE framework (Details provided in Appendix A), we derive the required compensation signal \\Delta \\epsilon_{wm} necessary", "source": "marker_v2", "marker_block_id": "/page/4/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0043", "section": "3.4. Modulation of Noise Prediction Target", "page_start": 5, "page_end": 5, "type": "TableGroup", "text": "Table 2. Stability Evaluation measured by Detection Confidence. We assess robustness across Samplers (DPM++ SDE, Euler a., DPM2 a.), Inference Steps (25, 50), Guidance Scale (10, 20), and Model Versions (v1.5, v2.1). Method Sa ampler Steps Sc ale Model DPM-SDE Eulera DPM2a 25 50 10 20 v1.5 v2.1 StegaS. 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.990 0.999 StableS. 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 TreeR. 0.000 0.000 0.000 0.963 0.963 0.963 0.963 0.958 0.963 G.S. 0.557 0.586 0.552 0.999 0.999 0.999 0.999 0.999 0.999 AquaL. 0.952 0.953 0.939 0.945 0.955 0.940 0.939 0.954 ALIEN-Q 0.989 0.979 0.972 0.985 0.990 0.982 0.975 0.989 0.991 ALIEN-R 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999", "source": "marker_v2", "marker_block_id": "/page/4/TableGroup/219"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0044", "section": "3.4. Modulation of Noise Prediction Target", "page_start": 5, "page_end": 5, "type": "Text", "text": "to enforce the \\mathbf{z}_0 constraint:", "source": "marker_v2", "marker_block_id": "/page/4/Text/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0045", "section": "3.4. Modulation of Noise Prediction Target", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\Delta \\epsilon_{wm} = -\\frac{\\sqrt{\\bar{\\alpha}_t}}{\\sqrt{1 - \\bar{\\alpha}_t}} \\delta_{wm}. (5)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/14"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0046", "section": "3.4. Modulation of Noise Prediction Target", "page_start": 5, "page_end": 5, "type": "Text", "text": "Refer to Eq. (5), to realize a fixed watermark residual \\delta_{wm} in the \\mathbf{z}_0 space, the U-Net will introduce a time-dependent compensation signal \\Delta\\epsilon_{wm} proportional to the watermark residual in its noise prediction. As illustrated in Fig. 3, the injection coefficient exhibits a surge approaching \\mathbf{z}_0 , implying that late-stage injection yields stronger constraints but risks visual fidelity. We adjust the injection magnitude and timestep range to formulate two configurations: ALIEN-Q (Quality-Oriented) and ALIEN-R (Robustness-Oriented). The procedure is outlined in Alg. 1.", "source": "marker_v2", "marker_block_id": "/page/4/Text/15"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0047", "section": "4.1. Experimental Setup", "page_start": 5, "page_end": 5, "type": "Text", "text": "Watermarking Baselines. We compare ALIEN with mainstream latent semantic watermarking schemes across three primary categories: the initial latent variable modification", "source": "marker_v2", "marker_block_id": "/page/4/Text/18"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0048", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "TableGroup", "text": "Table 3. Robustness Evaluation across variant Regenerative Attacks. Each cell reports performance under three attacks: Regeneration → Rinse-2X → Rinse-4X. Values denote Detection Confidence/ TPR@1%FPR. Method Scheduler (Cell Format: Regen. Data | Rinse-2X Data | Rinse-4X Data) DDIM DPM++ 2M SDE Euler a DPM2 a StegaS. 0.692/0.957 | 0.578/0.347 | 0.531/0.102 0.636/0.575 | 0.562/0.182 | 0.502/0.000 0.624/0.631 | 0.542/0.180 | 0.513/0.000 0.615/0.591 | 0.556/0.120 | 0.495/0.000 ZoDiac 0.938/1.000 | 0.743/0.104 | 0.527/0.032 0.693/0.585 | 0.670/0.431 | 0.562/0.125 0.643/0.315 | 0.643/0.250 | 0.628/0.210 0.833/0.650 | 0.572/0.281 | 0.520/0.152 TreeR. 0.868/1.000 | 0.724/0.861 | 0.408/0.489 0.855/0.918 | 0.824/0.905 | 0.753/0.851 0.821/0.941 | 0.449/0.512 | 0.277/0.306 0.647/0.755 | 0.531/0.656 | 0.326/0.427 G.S. 0.978/1.000 | 0.898/1.000 | 0.845/1.000 0.943/1.000 | 0.953/1.000 | 0.926/1.000 0.946/1.000 | 0.847/1.000 | 0.695/0.905 0.923/1.000 | 0.858/1.000 | 0.711/0.915 AquaL. 0.757/0.742 | 0.627/0.145 | 0.573/0.000 0.879/0.942 | 0.833/0.858 | 0.696/0.486 0.663/0.225 | 0.618/0.078 | 0.551/0.000 0.679/0.371 | 0.604/0.086 | 0.536/0.029 ROBIN —- /0.638 | —- /0.242 | —- /0.153 —- /1.000 | —- /0.728 | —- /0.275 —- /0.980 | —- /0.705 | —- /0.486 —- /0.075 | —- /0.105 | —- /0.100 StableS. 0.496/0.000 | 0.477/0.000 | 0.521/0.000 0.512/0.000 | 0.512/0.000 | 0.510/0.000 0.498/0.000 | 0.520/0.000 | 0.513/0.000 0.506/0.000 | 0.485/0.000 | 0.502/0.000 ALIEN-Q 0.848/1.000 | 0.752/0.865 | 0.618/0.342 0.935/1.000 | 0.898/1.000 | 0.842/0.942 0.866/1.000 | 0.661/0.581 | 0.563/0.163 0.857/1.000 | 0.673/0.636 | 0.581/0.124 ALIEN-R 0.999/1.000 | 0.908/1.000 | 0.829/1.000 0.999/1.000 | 0.989/1.000 | 0.967/1.000 0.988/1.000 | 0.908/1.000 | 0.731/0.727 0.989/1.000 | 0.878/1.000 | 0.742/0.875", "source": "marker_v2", "marker_block_id": "/page/5/TableGroup/859"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0049", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "TableGroup", "text": "Gaussian Shading Tree-ring AquaLoRA ALIEN-Q ALIEN-R DDIM Original No Original DDIM Watermarked DPM2 a Watermarked Euler a Watermarked DPM++ 2M SDE Watermarked Figure 5. Visual Comparison under Different Generation Schedulers (DDIM, DPM2 a, Euler a, and DPM++ 2M SDE).", "source": "marker_v2", "marker_block_id": "/page/5/TableGroup/860"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0050", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "method Tree-Ring (Wen et al., 2024) ; the constrained sampling method Gaussian Shading (Yang et al., 2024c) ; and the iterative optimization methods ROBIN (Huang et al., 2024) and Zodiac (Zhang et al., 2024) . Additionally, we select the fine-tuning based method Stable Signature (Fernandez et al., 2023) and Aqualora (Feng et al., 2024) , as well as the post-processing image watermarking technique StegaStamp (Tancik et al., 2020) . Implementation details can be found in Appendix B.2.", "source": "marker_v2", "marker_block_id": "/page/5/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0051", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Models and Tasks. Following existing research (Yang et al., 2024c) , we implement the ALIEN framework on Stable Diffusion v1.5 and Stable Diffusion v2.1. We evaluate our method across two tasks: (1) Detection. All compared methods are configured as single-bit watermarks with a unified pattern. The detection threshold is set individually for each method to achieve a False Positive Rate (FPR) of approximately 1%. (2) Traceability. Multi-bit watermarking methods are evaluated using Bit Accuracy. Single-bit methods, including Tree-ring, Zodiac, and Robin, are excluded due to their lack of watermark capacity. We use prompts", "source": "marker_v2", "marker_block_id": "/page/5/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0052", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "PictureGroup", "text": "Figure 6. Visual Comparison under Regeneration Attacks (DDIM, DPM2 a, Euler a, and DPM++ 2M SDE).", "source": "marker_v2", "marker_block_id": "/page/5/PictureGroup/861"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0053", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "from Stable Diffusion-Prompts (SDP) (Gustavosta, 2023) , setting the Guidance Scale to 7.5 and the number of sampling steps to 50. Both TPR@1%FPR and Bit Accuracy are computed over 350 watermarked images.", "source": "marker_v2", "marker_block_id": "/page/5/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0054", "section": "4.2. Comparison to Baselines", "page_start": 6, "page_end": 6, "type": "Text", "text": "Watermark Fidelity. We employ PSNR (Hore & Ziou, 2010) and SSIM (Wang et al., 2004) for pixel fidelity, LPIPS (Zhang et al., 2018) and DreamSim (Fu et al., 2023) for perceptual similarity, FID (Heusel et al., 2017) and SIFID (Yang et al., 2024a) for realism, and CLIP Score (Radford et al., 2021) for semantic alignment. As shown in Tab. 1, ALIEN-Q achieves state-of-the-art imperceptibility, significantly outperforming all baselines. It yields the highest pixel fidelity of 32.41 dB PSNR and the best perceptual quality of 0.003 DreamSim, while maintaining FID and CLIP scores comparable to non-watermarked images.", "source": "marker_v2", "marker_block_id": "/page/5/Text/12"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0055", "section": "4.2. Comparison to Baselines", "page_start": 6, "page_end": 6, "type": "Text", "text": "Watermark Stability. We validate watermark stability across three dimensions: Sampler Agnosticism covers both", "source": "marker_v2", "marker_block_id": "/page/5/Text/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0056", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "TableGroup", "text": "Table 4. Comprehensive Comparison of Watermark Robustness. Performance is reported in decimal scale (0-1). Higher values are better (↑). The Avg. column represents the mean performance across all 11 attacks (excluding No Attack). Top section: TPR@1%FPR; Bottom section: Bit Accuracy. Metrics Method No Photo netric De egradati on Ge eometric ; C enerative Avg. Attack Bright. Contr. JPEG Blur Noise ReScale C.C. R.C. VAE-B VAE-C Diff. StegaS. 1.000 0.964 1.000 1.000 1.000 1.000 1.000 0.964 0.975 1.000 1.000 1.000 0.991 StableS. 1.000 0.958 1.000 0.781 0.973 0.042 0.935 1.000 1.000 0.000 0.079 0.000 0.611 AquaL. 1.000 0.289 0.507 1.000 1.000 0.932 1.000 0.127 0.258 0.975 0.958 0.742 0.708 TreeR. 1.000 0.775 0.909 1.000 1.000 0.954 0.968 0.013 0.021 0.954 1.000 1.000 0.778 TPR@ G.S. 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.981 0.979 1.000 1.000 1.000 0.996 Thre1%FPR ROBIN 1.000 0.913 0.684 0.921 1.000 0.013 0.935 1.000 1.000 1.000 1.000 0.638 0.826 ZoDiac 1.000 0.535 0.375 0.959 0.979 0.357 0.965 0.017 0.021 0.660 0.685 1.000 0.592 ALIEN-Q 1.000 0.783 1.000 0.954 1.000 0.645 1.000 0.153 0.311 0.965 0.970 0.945 0.793 ALIEN-R 1.000 1.000 1.000 1.000 1.000 0.979 1.000 0.989 0.988 1.000 1.000 1.000 0.996 StegaS. 0.999 0.811 0.850 0.999 0.999 0.821 0.999 0.667 0.681 0.837 0.816 0.692 0.834 StableS. 0.998 0.892 0.851 0.712 0.845 0.535 0.878 0.991 0.993 0.506 0.541 0.489 0.748 Bit Acc. AquaL. 0.954 0.583 0.672 0.935 0.954 0.810 0.925 0.573 0.648 0.845 0.856 0.757 0.778 Bit Acc. G.S. 0.999 0.939 0.964 0.995 0.999 0.903 0.996 0.657 0.655 0.996 0.997 0.978 0.916 ALIEN-Q 0.989 0.753 0.803 0.889 0.936 0.689 0.903 0.581 0.601 0.834 0.853 0.848 0.790 ALIEN-R 0.999 0.949 0.992 0.999 0.999 0.855 0.999 0.826 0.835 0.979 0.983 0.999 0.947", "source": "marker_v2", "marker_block_id": "/page/6/TableGroup/285"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0057", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "FigureGroup", "text": "Figure 7. Robustness against VAE embedding attacks. Results are averaged across KLVAE8, KLVAE16, and SDXL variants.", "source": "marker_v2", "marker_block_id": "/page/6/FigureGroup/286"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0058", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "FigureGroup", "text": "Figure 8. Bit accuracy comparison against Stable Signature across VAE fine-tuning and replacement.", "source": "marker_v2", "marker_block_id": "/page/6/FigureGroup/287"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0059", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "Text", "text": "deterministic (DDIM) and irreversible samplers (Euler Ancestral (Karras et al., 2022), DPM++ 2M Ancestral (Karras et al., 2022), DPM++ SDE (Lu et al., 2025)); Component Adaptability involves substituting different VAE and U-Net versions; and Hyperparameter Stability examines sensitivity to Guidance Scale and Inference Steps. As shown in Tab. 2, existing training-free methods exhibit vulnerability to stochastic samplers. Specifically, Tree-Ring and Gaussian Shading fail completely under DPM++ SDE, Euler a., and DPM2 a., where accuracy hovers near the randomguess baseline. ALIEN achieves state-of-the-art sampler agnosticism by maintaining high bit accuracy exceeding 0.97 across all tested schedulers. Our method demonstrates consistent stability across varying inference steps, guidance scales, and model versions.", "source": "marker_v2", "marker_block_id": "/page/6/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0060", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "Text", "text": "Watermark Efficiency. We evaluate the computational overhead across two primary dimensions: Preparation Cost , the one-time offline cost, and Runtime Cost , the online perimage latency for embedding and extraction. The comparative results are detailed in Tab. 7. ALIEN achieves latencies of 0.079 seconds for embedding and 0.023 seconds for ex-", "source": "marker_v2", "marker_block_id": "/page/6/Text/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0061", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "Text", "text": "traction, maintaining speeds comparable to post-processing baselines while being orders of magnitude faster than the optimization-based method Zodiac, which requires over 122 seconds per image.", "source": "marker_v2", "marker_block_id": "/page/6/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0062", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "Text", "text": "Watermark Robustness. We examine watermark's robustness against three typical kinds of adversarial attacks, including image processing attacks (Hore & Ziou, 2010) for transforming generated images, adversarial attacks (An et al., 2024) for disturbing watermark verification, and reconstructive attacks (Zhao et al., 2023) for re-generating nonwatermarked images. Please refer to the Supplementary Materials for detailed parameter settings. As demonstrated in Tab. 4, ALIEN-R achieves state-of-the-art stability against standard distortions by maintaining a True Positive Rate of 0.996. In adversarial embedding scenarios illustrated in Fig. 7, ALIEN-R exhibits exceptional resistance where latent semantic watermarking baselines degrade rapidly. Tab. 3 shows that against reconstructive attacks, ALIEN-R sustains a high confidence exceeding 0.875 even after four re-generation rounds, whereas competitors like StegaStamp and Stable Signature collapse to near-zero.", "source": "marker_v2", "marker_block_id": "/page/6/Text/11"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0063", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 5. Quantitative comparison under Forgery Attacks. Lower values indicate better resistance (\\downarrow) . Config G.S. Tree-Ring ALIEN (Ours) comig Acc. / PSNR Acc. / PSNR Acc. / PSNR Scenario A: Average Forgery 10 Imgs 0.952 / 12.23 0.882 / 18.86 0.539 / 20.06 50 Imgs 0.969 / 12.79 0.908 / 20.34 0.605 / 25.29 100 Imgs 0.969 / 12.65 0.910 / 20.95 0.708 / 26.48 Scenario B: Reprompt Forgery SD-V2.1 1.000 / 0.931 / 0.533 /", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/326"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0064", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "FigureGroup", "text": "Figure 9. Robustness against Imprinting Forgery Attack.", "source": "marker_v2", "marker_block_id": "/page/7/FigureGroup/327"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0065", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "Text", "text": "Forgery Resistance. Following existing research (Müller et al., 2025; Yang et al., 2024b), we evaluate the security of our method against three representative forgery attacks: imprinting forgery, reprompting forgery, and average forgery. Imprinting and reprompting forgeries rely on latent optimization via diffusion inversion. ALIEN exhibits superior resistance to these attacks compared to initial-latent-based watermarks. While baselines like Tree-Ring and Gaussian Shading can be successfully forged using only a single image, ALIEN remains unaffected. Average Forgery involves estimating the watermark pattern by collecting pairs of watermarked and non-watermarked images. While baselines like Tree-Ring exhibit vulnerability with confidence exceeding 0.9, ALIEN maintains a suppressed confidence of 0.711, effectively preventing the rapid extraction of the watermark pattern. The practical challenges in acquiring large-scale specific-user data within real-world API scenarios significantly elevate the security threshold.", "source": "marker_v2", "marker_block_id": "/page/7/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0066", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "Text", "text": "Impact of Timestep Range. As shown in Tab. 6, we conducted an ablation study on the injection interval to investigate the trade-off between imperceptibility and robustness. Injecting the watermark across the full reverse process from step 50 down to 1 ensures perfect detection with 1.000 accuracy but introduces significant perceptual degradation, resulting in a PSNR drop to 20.42 dB under Strength B. Narrowing the window to early diffusion stages such as steps 45 to 20 significantly recovers image quality, where the PSNR", "source": "marker_v2", "marker_block_id": "/page/7/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0067", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 6. Ablation study on Timestep Range under different Watermark Strengths. We compare Image Quality (PSNR) and Detection Performance (Det./Acc.) across two strength settings. Range Strengt \\mathbf{th} \\mathbf{A} (\\lambda = 0.5) Strength B ( \\lambda = 1.0 ) (t_{start} \\rightarrow t_{end}) PSNR Det. / Acc. PSNR Det. / Acc. \\begin{array}{c} 1 \\to 50 \\\\ 25 \\to 50 \\\\ 25 \\to 40 \\\\ 10 \\to 25 \\\\ 20 \\to 45 \\end{array} 24.55 30.53 40.94 31.54 33.76 1.000 / 1.000 1.000 / 1.000 0.718 / 0.747 0.614 / 0.421 0.882 / 1.000 20.42 26.27 23.10 26.83 31.10 1.000 / 1.000 1.000 / 1.000 0.852 / 1.000 0.681 / 0.721 0.989 / 1.000 Table 7. Performance Comparison regarding Computational Efficiency. <sup>‡</sup> indicates data estimated from original papers.", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/328"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0068", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "Table", "text": "Method P rep. Time ( h) Embed. E 111011101 Pre-train Fine-tune Optimize Time (s) Time (s) T.R. _ _ _ 0.011 3.575 G.S. _ 0.102 4.212 ROBIN _ _ 0.4 0.125 1.248 Zodiac _ 122.4 3.601 StegaS. 30 0.108 0.028 S.S. 48^{\\ddagger} 0.1 _ _ 0.014 AquaL. 40^{\\ddagger} 15 ‡ _ _ 0.026 ALIEN 22 _ _ 0.079 0.023", "source": "marker_v2", "marker_block_id": "/page/7/Table/11"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0069", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "Text", "text": "increases to 33.76 dB under Strength A while maintaining a high detection rate.", "source": "marker_v2", "marker_block_id": "/page/7/Text/12"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0070", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "Text", "text": "Impact of Watermark Strength. As shown in Tab. 6, the injection coefficient \\lambda directly modulates the magnitude of the probability flow correction. Increasing the strength from \\lambda=0.5 in Strength A to \\lambda=1.0 in Strength B consistently improves detection performance across all ranges. we select the range from 45 to 20 combined with moderate strength as the optimal configuration for ALIEN-Q to maximize quality while ensuring reliable detection.", "source": "marker_v2", "marker_block_id": "/page/7/Text/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0071", "section": "5. Conclusion", "page_start": 8, "page_end": 8, "type": "Text", "text": "Unlike prior approaches relying on heuristic latent modifications, sampling constraints, or computationally intensive optimization, we propose ALIEN, which presents the first analytical derivation of the time-dependent modulation coefficient. This principled approach precisely guides the diffusion of watermark residuals via probability flow modulation, achieving sampler-agnostic embedding. ALIEN overcomes the security vulnerabilities associated with diffusion inversion and irreversible samplers while ensuring high fidelity and low inference cost. Experimental results demonstrate that ALIEN outperforms existing methods in both quality and robustness. Future research will focus on developing content-aware latent watermarking to further enhance security against forgery attacks.", "source": "marker_v2", "marker_block_id": "/page/7/Text/15"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0072", "section": "6. Impact Statement", "page_start": 9, "page_end": 9, "type": "Text", "text": "Ensuring the accountability and intellectual property protection of generative models has become a critical priority. This paper introduces ALIEN, a principled watermarking framework that enables robust and sampler-agnostic provenance tracking for Latent Diffusion Models. By overcoming the vulnerability of existing methods to irreversible samplers and diverse attacks, we believe our approach effectively mitigates risks such as copyright infringement and malicious misuse, thereby contributing to the development of safer and more trustworthy generative AI.", "source": "marker_v2", "marker_block_id": "/page/8/Text/2"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0073", "section": "References", "page_start": 9, "page_end": 9, "type": "ListGroup", "text": "An, B., Ding, M., Rabbani, T., Agrawal, A., Xu, Y., Deng, C., Zhu, S., Mohamed, A., Wen, Y., Goldstein, T., et al. Waves: Benchmarking the robustness of image watermarks. arXiv preprint arXiv:2401.08573 , 2024. Balle, J., Minnen, D., Singh, S., Hwang, S. J., and Johnston, ´ N. Variational image compression with a scale hyperprior. arXiv preprint arXiv:1802.01436 , 2018. Barrett, C. Identifying and mitigating the security risks of generative ai. arXiv preprint arXiv:2308.14840 , 2023. Biden, J. R. Executive order on the safe, secure, and trustworthy development and use of artificial intelligence, 2023. URL /briefing-room/statements-releases/20 23/07/07/fact-sheet-executive-order-o n-artificial-intelligence/ . Cheng, Z., Sun, H., Takeuchi, M., and Katto, J. Learned image compression with discretized gaussian mixture likelihoods and attention modules. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pp. 7939–7948, 2020. Ci, H., Song, Y., Yang, P., Xie, J., and Shou, M. Z. Wmadapter: Adding watermark control to latent diffusion models. arXiv preprint arXiv:2406.08337 , 2024. Ci, H., Yang, P., Song, Y., and Shou, M. Z. Ringid: Rethinking tree-ring watermarking for enhanced multi-key identification. In European Conference on Computer Vision , pp. 338–354. Springer, 2025. Cox, I., Miller, M., Bloom, J., Fridrich, J., and Kalker, T. Digital watermarking and steganography . Morgan kaufmann, 2007. Dhariwal, P. and Nichol, A. Diffusion models beat gans on image synthesis. Advances in neural information processing systems , 34:8780–8794, 2021.", "source": "marker_v2", "marker_block_id": "/page/8/ListGroup/523"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0074", "section": "References", "page_start": 9, "page_end": 9, "type": "ListGroup", "text": "European Union. Artificial intelligence act: Regulation (eu) 2024/1689 of the european parliament and of the council, June 2024. URL: eu/legal-content/EN/TXT/?uri=CELEX: 32024R1689 , Accessed: 2024-09-24. Feng, W., Zhou, W., He, J., Zhang, J., Wei, T., Li, G., Zhang, T., Zhang, W., and Yu, N. Aqualora: Toward white-box protection for customized stable diffusion models via watermark lora. arXiv preprint arXiv:2405.11135 , 2024. Fernandez, P., Couairon, G., Jegou, H., Douze, M., and ´ Furon, T. The stable signature: Rooting watermarks in latent diffusion models. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pp. 22466– 22477, 2023. Fu, S., Tamir, N., Sundaram, S., Chai, L., Zhang, R., Dekel, T., and Isola, P. Dreamsim: Learning new dimensions of human visual similarity using synthetic data. arXiv preprint arXiv:2306.09344 , 2023. Gowal, S. and Kohli, P. Identifying ai-generated images with synthid. g/identifying-ai-generated-images-wit h-synthid , 2023. Accessed: 2023-09-23. Gunn, S., Zhao, X., and Song, D. An undetectable watermark for generative image models. arXiv preprint arXiv:2410.07369 , 2024. Gustavosta. Stable diffusion prompts dataset, May 2023. URL Gustavosta/Stable-Diffusion-Prompts . Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., and Hochreiter, S. Gans trained by a two time-scale update rule converge to a local nash equilibrium. Advances in neural information processing systems , 30, 2017. Ho, J., Jain, A., and Abbeel, P. Denoising diffusion probabilistic models. Advances in neural information process ing systems , 33:6840–6851, 2020. Hore, A. and Ziou, D. Image quality metrics: Psnr vs. ssim. In 2010 20th international conference on pattern recognition , pp. 2366–2369. IEEE, 2010. Huang, H., Wu, Y., and Wang, Q. Robin: Robust and invisible watermarks for diffusion models with adversarial optimization. Advances in Neural Information Processing Systems , 37:3937–3963, 2024. Karras, T., Aittala, M., Aila, T., and Laine, S. Elucidating the design space of diffusion-based generative models. Advances in neural information processing systems , 35: 26565–26577, 2022.", "source": "marker_v2", "marker_block_id": "/page/8/ListGroup/524"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0075", "section": "References", "page_start": 10, "page_end": 10, "type": "Text", "text": "Lee, S. J. and Cho, N. I. Semantic watermarking reinvented: Enhancing robustness and generation quality with fourier integrity. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pp. 18759–18769, 2025.", "source": "marker_v2", "marker_block_id": "/page/9/Text/497"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0076", "section": "References", "page_start": 10, "page_end": 10, "type": "ListGroup", "text": "Li, K., Huang, Z., Hou, X., and Hong, C. Gaussmarker: Robust dual-domain watermark for diffusion models. arXiv preprint arXiv:2506.11444 , 2025. Lin, T.-Y., Maire, M., Belongie, S., Hays, J., Perona, P., Ramanan, D., Dollar, P., and Zitnick, C. L. Microsoft coco: ´ Common objects in context. In Computer Vision–ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part V 13 , pp. 740– 755. Springer, 2014. Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J. Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps. Advances in Neural Information Processing Systems , 35:5775–5787, 2022. Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J. Dpmsolver++: Fast solver for guided sampling of diffusion probabilistic models. Machine Intelligence Research , pp. 1–22, 2025. Meng, Z., Peng, B., and Dong, J. Latent watermark: Inject and detect watermarks in latent diffusion space. arXiv preprint arXiv:2404.00230 , 2024. Muller, A., Lukovnikov, D., Thietke, J., Fischer, A., and ¨ Quiring, E. Black-box forgery attacks on semantic watermarks for diffusion models. In Proceedings of the Computer Vision and Pattern Recognition Conference , pp. 20937–20946, 2025. Radford, A., Kim, J. W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., Krueger, G., and Sutskever, I. Learning transferable visual models from natural language supervision. In ICML , 2021. Ramesh, A., Dhariwal, P., Nichol, A., Chu, C., and Chen, M. Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.06125 , 1(2):3, 2022. Ren, K., Yang, Z., Lu, L., Liu, J., Li, Y., Wan, J., Zhao, X., Feng, X., and Shao, S. Sok: On the role and future of aigc watermarking in the era of gen-ai. arXiv preprint arXiv:2411.11478 , 2024. Rezaei, A., Akbari, M., Alvar, S. R., Fatemi, A., and Zhang, Y. Lawa: Using latent space for in-generation image watermarking. In European Conference on Computer Vision , pp. 118–136. Springer, 2024.", "source": "marker_v2", "marker_block_id": "/page/9/ListGroup/495"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0077", "section": "References", "page_start": 10, "page_end": 10, "type": "ListGroup", "text": "Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , pp. 10684–10695, June 2022. Song, J., Meng, C., and Ermon, S. Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 , 2020a. Song, Y. and Ermon, S. Improved techniques for training score-based generative models. Advances in neural information processing systems , 33:12438–12448, 2020. Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456 , 2020b. Tancik, M., Mildenhall, B., and Ng, R. Stegastamp: Invisible hyperlinks in physical photographs. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pp. 2117–2126, 2020. Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing , 13(4):600–612, 2004. Wang, Z., Guo, J., Zhu, J., Li, Y., Huang, H., Chen, M., and Tu, Z. Sleepermark: Towards robust watermark against fine-tuning text-to-image diffusion models. In Proceed ings of the Computer Vision and Pattern Recognition Conference , pp. 8213–8224, 2025. Wen, Y., Kirchenbauer, J., Geiping, J., and Goldstein, T. Tree-rings watermarks: Invisible fingerprints for diffusion images. Advances in Neural Information Processing Systems , 36, 2024. Yang, J., Liu, H., Guo, W., Rao, Z., Xu, Y., and Niu, D. Sifid: Reassess summary factual inconsistency detection with llm. arXiv preprint arXiv:2403.07557 , 2024a. Yang, P., Ci, H., Song, Y., and Shou, M. Z. Can simple averaging defeat modern watermarks? Advances in Neu ral Information Processing Systems , 37:56644–56673, 2024b. Yang, Z., Zeng, K., Chen, K., Fang, H., Zhang, W., and Yu, N. Gaussian shading: Provable performance-lossless image watermarking for diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pp. 12162–12171, 2024c. Zhang, L., Liu, X., Martin, A. V., Bearfield, C. X., Brun, Y., and Guan, H. Attack-resilient image watermarking using stable diffusion. Advances in Neural Information Processing Systems , 37:38480–38507, 2024.", "source": "marker_v2", "marker_block_id": "/page/9/ListGroup/496"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0078", "section": "References", "page_start": 11, "page_end": 11, "type": "Text", "text": "Zhang, R., Isola, P., Efros, A. A., Shechtman, E., and Wang, O. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition , pp. 586–595, 2018.", "source": "marker_v2", "marker_block_id": "/page/10/Text/193"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0079", "section": "References", "page_start": 11, "page_end": 11, "type": "ListGroup", "text": "Zhao, X., Zhang, K., Su, Z., Vasan, S., Grishchenko, I., Kruegel, C., Vigna, G., Wang, Y.-X., and Li, L. Invisible image watermarks are provably removable using generative ai. arXiv preprint arXiv:2306.01953 , 2023. Zhao, X., Zhang, K., Su, Z., Vasan, S., Grishchenko, I., Kruegel, C., Vigna, G., Wang, Y.-X., and Li, L. Invisible image watermarks are provably removable using generative ai. Advances in neural information processing systems , 37:8643–8672, 2024.", "source": "marker_v2", "marker_block_id": "/page/10/ListGroup/192"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0080", "section": "Supplementary Material", "page_start": 12, "page_end": 12, "type": "TableOfContents", "text": "A Theoretical Analysis of ALIEN 12 A.1 Watermark Constraint and Score Discrepancy 12 A.2 Proof of Reverse SDE Drift Term Correction 12 A.3 Derivation of UNet Target Noise 12 B Implementation Details 13 B.1 Algorithm Pseudocode 13 B.2 Hyperparameters and Training Settings 13 C Experimental Setup and Extended Experiments 14 C.1 Dataset Settings 14 C.2 Robustness Evaluation Settings 15 C.3 Extended Experiments 15 D Extended Related Work 16 D.1 Watermarking Schemes Taxonomy 16", "source": "marker_v2", "marker_block_id": "/page/11/TableOfContents/1"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0081", "section": "A. Theoretical Analysis of ALIEN", "page_start": 13, "page_end": 13, "type": "Text", "text": "In this section, we provide a rigorous derivation establishing the analytical link between the watermark constraint in the z_0 -space and the necessary correction to the probability flow drift term. This derivation proves that ALIEN is theoretically grounded in the VP-SDE framework and is inherently sampler-agnostic.", "source": "marker_v2", "marker_block_id": "/page/12/Text/2"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0082", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Text", "text": "1. Watermark Constraint Definition Our objective is to embed a fixed watermark residual \\delta_{wm} into the latent representation. We define this as a geometric constraint on the estimated clean data manifold. Let \\hat{\\mathbf{z}}_0 denote the original estimate derived from the model \\theta , and \\hat{\\mathbf{z}}_0^{wm} denote the target watermarked estimate:", "source": "marker_v2", "marker_block_id": "/page/12/Text/4"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0083", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\hat{\\mathbf{z}}_0^{wm} = \\hat{\\mathbf{z}}_0 + \\delta_{wm}. \\tag{6}", "source": "marker_v2", "marker_block_id": "/page/12/Equation/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0084", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Text", "text": "2. Derivation of Score Function Difference \\Delta Score Under the VP-SDE framework, Tweedie's formula establishes a linear bijection between the score function \\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t) and the denoised estimate \\hat{\\mathbf{z}}_0 :", "source": "marker_v2", "marker_block_id": "/page/12/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0085", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t) = -\\frac{\\mathbf{z}_t - \\sqrt{\\bar{\\alpha}_t} \\hat{\\mathbf{z}}_0}{1 - \\bar{\\alpha}_t}. (7)", "source": "marker_v2", "marker_block_id": "/page/12/Equation/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0086", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Text", "text": "To enforce the watermark constraint (Eq. 6), the score function must shift to \\nabla_{\\mathbf{z}_t} \\log p_t^{wm} . By substituting the constraint \\hat{\\mathbf{z}}_0 - \\hat{\\mathbf{z}}_0^{wm} = -\\delta_{wm} , we derive the score discrepancy \\Delta S core:", "source": "marker_v2", "marker_block_id": "/page/12/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0087", "section": "A.1. Watermark Constraint and Score Function Discrepancy", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\Delta \\text{Score} = \\nabla_{\\mathbf{z}_{t}} \\log p_{t}^{wm} - \\nabla_{\\mathbf{z}_{t}} \\log p_{t} = -\\frac{1}{1 - \\bar{\\alpha}_{t}} \\left( -\\sqrt{\\bar{\\alpha}_{t}} (\\hat{\\mathbf{z}}_{0}^{wm} - \\hat{\\mathbf{z}}_{0}) \\right) = \\frac{\\sqrt{\\bar{\\alpha}_{t}}}{1 - \\bar{\\alpha}_{t}} \\delta_{wm}. (8)", "source": "marker_v2", "marker_block_id": "/page/12/Equation/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0088", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Text", "text": "Definition of Reverse Drift \\mathbf{F}_{rev} The generation trajectory in diffusion models is governed by the reverse-time SDE. The deterministic component of this process, known as the drift term \\mathbf{F}_{rev} , is defined as:", "source": "marker_v2", "marker_block_id": "/page/12/Text/11"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0089", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\mathbf{F}_{rev}(\\mathbf{z}_t, t) = \\mathbf{f}(\\mathbf{z}_t, t) - g^2(t) \\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t). \\tag{9}", "source": "marker_v2", "marker_block_id": "/page/12/Equation/12"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0090", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Text", "text": "where \\mathbf{f}(\\mathbf{z}_t, t) is the forward drift and g(t) is the diffusion coefficient.", "source": "marker_v2", "marker_block_id": "/page/12/Text/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0091", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Text", "text": "Derivation of Drift Correction \\Delta \\mathbf{F}_{rev} We calculate the modification to the drift term required to accommodate the watermark. Since the forward physics \\mathbf{f}(\\mathbf{z}_t, t) remains invariant, the drift correction depends solely on the score shift:", "source": "marker_v2", "marker_block_id": "/page/12/Text/14"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0092", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\Delta \\mathbf{F}_{rev} = \\mathbf{F}_{rev}^{wm} - \\mathbf{F}_{rev}^{orig} = -g^2(t) \\left(\\Delta \\text{Score}\\right). \\tag{10}", "source": "marker_v2", "marker_block_id": "/page/12/Equation/15"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0093", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Text", "text": "Substituting Eq. (8) into the expression above, we obtain the explicit form of the Watermark Drift Force:", "source": "marker_v2", "marker_block_id": "/page/12/Text/16"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0094", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\Delta \\mathbf{F}_{rev}(\\mathbf{z}_t, t) = -g^2(t) \\frac{\\sqrt{\\bar{\\alpha}_t}}{1 - \\bar{\\alpha}_t} \\delta_{wm}. \\tag{11}", "source": "marker_v2", "marker_block_id": "/page/12/Equation/17"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0095", "section": "A.2. Proof of Reverse SDE Drift Term Correction \\Delta \\mathbf{F}_{rev}", "page_start": 13, "page_end": 13, "type": "Text", "text": "Theorem: The spatial constraint \\delta_{wm} imposes a constant, deterministic force \\Delta \\mathbf{F}_{rev} on the probability flow. Because \\mathbf{F}_{rev} is the shared driving term for both the stochastic reverse SDE and the deterministic Probability Flow ODE (PF-ODE), this correction guarantees that the watermark embedding is robust across different samplers.", "source": "marker_v2", "marker_block_id": "/page/12/Text/18"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0096", "section": "A.3. Derivation of Noise Prediction Target \\epsilon^{target}", "page_start": 13, "page_end": 13, "type": "Text", "text": "To implement the theoretical drift correction \\Delta \\mathbf{F}_{rev} in practice, we modulate the output of the U-Net \\vartheta .", "source": "marker_v2", "marker_block_id": "/page/12/Text/20"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0097", "section": "A.3. Derivation of Noise Prediction Target \\epsilon^{target}", "page_start": 13, "page_end": 13, "type": "Text", "text": "Score-Noise Relationship The neural network \\epsilon_{\\vartheta} approximates the score function via the relation:", "source": "marker_v2", "marker_block_id": "/page/12/Text/21"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0098", "section": "A.3. Derivation of Noise Prediction Target \\epsilon^{target}", "page_start": 13, "page_end": 13, "type": "Equation", "text": "\\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t) = -\\frac{\\epsilon_{\\vartheta}(\\mathbf{z}_t, t)}{\\sqrt{1 - \\bar{\\alpha}_t}}. (12)", "source": "marker_v2", "marker_block_id": "/page/12/Equation/22"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0099", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Code", "text": "715 716 Phase I: Watermark Embedding 717 2: Input: Pre-trained U-Net \\theta, Encoder E_s, Scheduler S, VAE Decoder \\mathcal{D}_{VAE}, Prompt c, Secret m, Injection Interval 718 [T_{start}, T_{end}], Strength \\lambda 719 3: Output: Watermarked Image \\mathbf{x}_{wm} 720 4: \\delta_{wm} \\leftarrow E_s(\\mathbf{m}) 721 5: \\mathbf{z}_t \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I}) 6: for t = T down to 1 do \\mathbf{t} \\leftarrow S. \\mathsf{timesteps}[t] 724 \\epsilon_{\\theta}^{t} \\leftarrow \\text{CFG}(\\theta, \\mathbf{z}_{t}, \\mathbf{t}, \\mathbf{c}) 725 if t \\leq T_{end} and t \\geq T_{start} then 726 // Modulate the prediction target 727 \\boldsymbol{\\epsilon}_{\\theta}^{t} \\leftarrow \\boldsymbol{\\epsilon}_{\\theta}^{t} - \\lambda \\cdot \\left(\\frac{\\sqrt{\\bar{\\alpha}_{t}}}{\\sqrt{1 - \\bar{\\alpha}_{t}}}\\right) \\cdot \\delta_{wm} 728 12: 730 \\mathbf{z}_t \\leftarrow S.\\text{step}(\\epsilon_{\\theta}^t, \\mathbf{t}, \\mathbf{z}_t).\\text{prev\\_sample} 14: end for 731 15: \\mathbf{x}_{wm} \\leftarrow \\mathcal{D}_{VAE}(\\mathbf{z}_t) 732 733 Phase II: Watermark Extraction 17: Input: Watermarked Image \\mathbf{x}_{wm}, VAE Encoder \\mathcal{E}_{VAE}, Watermark Decoder D_s 734 735 18: Output: Extracted Secret m' 19: // Encode image back to watermarked latent 736 737 20: \\mathbf{z}_0 \\leftarrow \\mathcal{E}_{VAE}(\\mathbf{x}_{wm}) 738 21: // Extract secret message from latent 22: \\mathbf{m}' \\leftarrow D_s(\\mathbf{z}_0) 739", "source": "marker_v2", "marker_block_id": "/page/13/Code/2"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0100", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Text", "text": "Mapping Drift Correction to \\epsilon -Space We equate the score difference derived from the drift requirement to the difference in noise prediction. Using \\Delta Score = -\\frac{1}{\\sqrt{1-\\bar{\\alpha}_t}}(\\epsilon^{target} - \\epsilon_{\\vartheta}) = -\\frac{\\Delta \\epsilon}{\\sqrt{1-\\bar{\\alpha}_t}} , we have:", "source": "marker_v2", "marker_block_id": "/page/13/Text/3"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0101", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Equation", "text": "-\\frac{\\Delta \\epsilon}{\\sqrt{1-\\bar{\\alpha}_t}} = \\frac{\\sqrt{\\bar{\\alpha}_t}}{1-\\bar{\\alpha}_t} \\delta_{wm}. \\tag{13}", "source": "marker_v2", "marker_block_id": "/page/13/Equation/4"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0102", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Text", "text": "Final Update Rule Solving for the correction term \\Delta \\epsilon :", "source": "marker_v2", "marker_block_id": "/page/13/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0103", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Equation", "text": "\\Delta \\epsilon = -\\sqrt{1 - \\bar{\\alpha}_t} \\cdot \\frac{\\sqrt{\\bar{\\alpha}_t}}{1 - \\bar{\\alpha}_t} \\delta_{wm} = -\\frac{\\sqrt{\\bar{\\alpha}_t}}{\\sqrt{1 - \\bar{\\alpha}_t}} \\delta_{wm}. \\tag{14}", "source": "marker_v2", "marker_block_id": "/page/13/Equation/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0104", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Text", "text": "Thus, the final target noise \\epsilon^{target} required to enforce the watermark is:", "source": "marker_v2", "marker_block_id": "/page/13/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0105", "section": "Algorithm 2 ALIEN Watermarking", "page_start": 14, "page_end": 14, "type": "Equation", "text": "\\epsilon^{target} = \\epsilon_{\\vartheta} + \\Delta \\epsilon = \\epsilon_{\\vartheta} - \\left(\\frac{\\sqrt{\\bar{\\alpha}_t}}{\\sqrt{1 - \\bar{\\alpha}_t}}\\right) \\delta_{wm}. \\tag{15}", "source": "marker_v2", "marker_block_id": "/page/13/Equation/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0106", "section": "B.1. Algorithm Pseudocode", "page_start": 14, "page_end": 14, "type": "Text", "text": "23: Return m<sup>2</sup>", "source": "marker_v2", "marker_block_id": "/page/13/Text/16"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0107", "section": "B.1. Algorithm Pseudocode", "page_start": 14, "page_end": 14, "type": "Text", "text": "The core logic of the ALIEN watermarking framework is detailed in Algorithm 2. This algorithm outlines the complete process of watermark embedding during the reverse diffusion process and the subsequent extraction from the latent space.", "source": "marker_v2", "marker_block_id": "/page/13/Text/11"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0108", "section": "B.2. Hyperparameters and Training Settings", "page_start": 14, "page_end": 14, "type": "Text", "text": "Watermark Generation Module Training. We train the Imperceptible Latent Watermark Generation module using the AdamW optimizer with a learning rate of 5 \\times 10^{-5} and a weight decay of 1 \\times 10^{-5} . We construct a synthetic training set of", "source": "marker_v2", "marker_block_id": "/page/13/Text/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0109", "section": "B.2. Hyperparameters and Training Settings", "page_start": 15, "page_end": 15, "type": "TableGroup", "text": "Table 8. Detailed Robustness Evaluation Settings. We categorize attacks into four distinct groups. Note that Image Processing attacks are grouped by type (Photometry, Geometry, Degradation) to conserve space. Category Method & Parameters Image Processing Photometry: Brightness (×6.0), Contrast (×12.0) Geometry: Resize (s = 0.5), Center Crop(s = 0.4), Random Crop(s = 0.4) Degradation: Gaussian Noise (σ = 0.25), Blur (radius = 1.5), JPEG (Q = 50) Reconstructive VAE Compression: VAE-B (Balle et al. ´ , 2018) (Q = 1), VAE-C (Cheng et al., 2020) (Q = 1) Generative Attack: Regen-Diff (Zhao et al., 2024) (SD v1.5, Strength S = 0.2), Rinsing (N = 2, 4) Adversarial Adv-Emb: PGD-based Latent Attack (An et al., 2024) Forgery Imprinting: Latent optimization via inversion (Muller et al. ¨ , 2025) Reprompting: Inverse the image to initial latent and regeneration (Muller et al. ¨ , 2025) Average: Estimate watermark pattern by averaging residuals (Yang et al., 2024b)", "source": "marker_v2", "marker_block_id": "/page/14/TableGroup/487"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0110", "section": "B.2. Hyperparameters and Training Settings", "page_start": 15, "page_end": 15, "type": "PictureGroup", "text": "Figure 10. Visual Robustness Examples. Comparison of the watermarked image under various attacks: (a) Original, (b) Brightness, (c) Contrast, (d) JPEG Compression, (e) Gaussian Blur, (f) Gaussian Noise, (g) Center Crop (C.C.), (h) Random Crop (R.C.), (i) VAE Compression (BMSHJ), and (j) VAE Compression (Cheng).", "source": "marker_v2", "marker_block_id": "/page/14/PictureGroup/488"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0111", "section": "B.2. Hyperparameters and Training Settings", "page_start": 15, "page_end": 15, "type": "Text", "text": "10,000 images generated based on COCO2014 (Lin et al., 2014) prompts. The model is trained for 50,000 steps with a batch size of 16. To ensure training stability and perceptual quality, we impose a maximum gradient norm of 10 − 2 . The total objective combines the secret recovery loss (Lsec), pixel-wise reconstruction loss (Lmse), and perceptual loss (Llpips using AlexNet backbone). The loss weights are set to λsec = 1.0, λmse = 30.0, and λlpips = 0.3. Notably, λmse and λlpips are linearly ramped up from 0 to their peak values over the first 5,000 steps to facilitate stable convergence in the early training phase.", "source": "marker_v2", "marker_block_id": "/page/14/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0112", "section": "B.2. Hyperparameters and Training Settings", "page_start": 15, "page_end": 15, "type": "Text", "text": "Injection Settings. During the inference phase, ALIEN-Q injects watermarks within the sampling interval of steps 20–45 (with injection strength λ = 0.85), while ALIEN-R extends the injection window to cover steps 0–50 (λ = 1.0) for enhanced robustness.", "source": "marker_v2", "marker_block_id": "/page/14/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0113", "section": "C.1. Dataset Settings", "page_start": 15, "page_end": 15, "type": "Text", "text": "Evaluation Datasets. We utilize two distinct datasets to comprehensively evaluate both watermarking performance and image generation quality: For measuring detection accuracy (TPR@1%FPR) and payload capacity (Bit Accuracy), we", "source": "marker_v2", "marker_block_id": "/page/14/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0114", "section": "C.1. Dataset Settings", "page_start": 16, "page_end": 16, "type": "TableGroup", "text": "Table 9. Breakdown of Performance Gains. We compare ALIEN against the best-performing baseline (Best SOTA) for each metric/condition. Panel A calculates the average relative improvement across 5 quality metrics (33.1%). Panel B highlights the robustness gain across 15 distinct conditions (12 Generative + 3 Stability). The final 14.0% is the weighted average gain over these 15 conditions. Panel A: Quality Improvement (ALIEN-Q vs. Best SOTA) Metric Description Best SOTA Method ALIEN-Q Improvement FID ↓ Frechet Inception Distance ´ 24.42 (G.S.) Lower is better 24.29 +0.5% PSNR ↑ Peak Signal-to-Noise Ratio 29.09 (StableSig.) Higher is better 32.41 +11.4% SSIM ↑ Structural Similarity 0.922 (ZoDiac) Higher is better 0.949 +2.9% SIFID ↓ Single Image FID 0.105 (StableSig.) Lower is better 0.023 +78.1% DreamSim ↓ Perceptual Similarity 0.011 (StableSig.) Lower is better 0.003 +72.7% Average Quality Improvement +33.1% Panel B: Robustness Improvement (ALIEN-R vs. Training-free SOTA) Condition Category Specifics Best SOTA Metric ALIEN-R Gain 1. Generative Variant (12 conditions) Average Acc. across 12 conditions (4 Schedulers × Regen/Rinse) ∼0.84 Acc. ∼0.90 +6.5% 2. Sampler Stability Average Acc. across 3 stochastic samplers ∼0.56 Acc. ∼1.00 +44.0% (3 conditions) (DPM++ SDE, Euler a, DPM2 a) Table 10. Comparison of Imperceptibility and Robustness. We compare 48-bit and 128-bit payloads. Fidelity is reported as Mean ± Std. Dev. Robustness is reported as Detection Accuracy. Abbreviations: No Att. (No Attack), Comp. (Compression), Comb. (Combined Attack).", "source": "marker_v2", "marker_block_id": "/page/15/TableGroup/583"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0115", "section": "C.1. Dataset Settings", "page_start": 16, "page_end": 16, "type": "Table", "text": "Payload Imperceptibility Metrics Robustness (Bit Accuracy) No Att. Blur Noise JPEG Resize Sharp Bright Contr. Sat. PSNR(↑) SSIM(↑) LPIPS(↓) Comb. 48 Bits 31.17±0.90 0.62±0.03 0.097±0.01 0.99 0.99 0.92 0.99 0.99 0.99 0.99 0.99 0.99 0.87 128 Bits 30.79±0.85 0.59±0.03 0.151±0.01 0.99 0.99 0.90 0.98 0.99 0.99 0.99 0.99 0.99 0.82", "source": "marker_v2", "marker_block_id": "/page/15/Table/4"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0116", "section": "C.1. Dataset Settings", "page_start": 16, "page_end": 16, "type": "Text", "text": "employ the Stable Diffusion-Prompts (SDP) dataset (Gustavosta, 2023) . We randomly select 350 prompts from the dataset to generate image pairs (watermarked vs. clean) for distinct evaluation. For evaluating generative fidelity, specifically Frechet ´ Inception Distance (FID), we utilize the MS-COCO dataset (Lin et al., 2014) . We randomly sample 5,000 captions from the MS-COCO validation set to generate 5,000 watermarked images and compute the FID score against the corresponding real reference images to ensure standardized quality comparison.", "source": "marker_v2", "marker_block_id": "/page/15/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0117", "section": "C.1. Dataset Settings", "page_start": 16, "page_end": 16, "type": "Text", "text": "Generation Configuration. We conduct experiments on two representative Latent Diffusion Models: Stable Diffusion v1.5 and Stable Diffusion v2.1. Unless otherwise specified, we use the DDIM sampler with 50 inference steps. The classifier-free guidance scale is set to 7.5. All generated images are of resolution 512 × 512. All experiments were conducted on a single NVIDIA RTX 3090 GPU.", "source": "marker_v2", "marker_block_id": "/page/15/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0118", "section": "C.3. Extended Experiments", "page_start": 16, "page_end": 16, "type": "Text", "text": "Detailed Performance Gain Analysis. To substantiate the claims made in the abstract, we provide a detailed breakdown of the performance improvements. Table 9 illustrates the calculation of the 33.1% quality improvement and 14.0% robustness improvement compared to the state-of-the-art (SOTA) methods.", "source": "marker_v2", "marker_block_id": "/page/15/Text/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0119", "section": "C.3. Extended Experiments", "page_start": 16, "page_end": 16, "type": "Text", "text": "Impact of Payload Size. We further investigate the impact of payload size on the trade-off between watermark capacity, imperceptibility, and robustness. As demonstrated in Table 10, increasing the payload capacity from 48 bits to 128 bits results in only a minor decrease in fidelity metrics, exemplified by a slight PSNR drop from 31.17 dB to 30.79 dB. This result validates that ALIEN effectively supports high-capacity embedding while maintaining visual quality comparable to low-capacity settings.", "source": "marker_v2", "marker_block_id": "/page/15/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0120", "section": "C.3. Extended Experiments", "page_start": 17, "page_end": 17, "type": "TableGroup", "text": "Table 11. Impact of Fixed Thresholding on False Positive Rates (ROBIN Scheme). Comparison of clean image means (µclean) versus the optimal threshold for Cropping (τcrop) using the ROBIN watermarking method. For both SD v1.5 and v2.1, benign degradations like Blurring and JPEG shift µclean below τcrop (marked with ×). Attack Stable Diffusion v1.5 (τcrop = 39.45) Stable Diffusion v2.1 (τcrop = 55.80) Clean Mean Opt. τ Fixed τ Risk Clean Mean Opt. τ Fixed τ Risk No Attack 40.08 38.28 ✓ 55.90 52.74 ✓ Cropping 40.25 39.45 - 55.86 55.80 - Blurring 32.38 30.31 × 52.65 50.24 × JPEG 37.22 36.91 × 55.65 53.57 × Color Jitter 36.91 36.85 × 54.04 51.39 × Noise 41.63 40.02 ✓ 57.07 55.62 ✓", "source": "marker_v2", "marker_block_id": "/page/16/TableGroup/465"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0121", "section": "C.3. Extended Experiments", "page_start": 17, "page_end": 17, "type": "Text", "text": "Threshold Determination for Distance-Based Methods. We evaluate the impact of distribution shifts caused by image degradations on threshold determination for the distance-based method, ROBIN. As shown in Table 11, using a fixed threshold derived from a challenging scenario (Cropping, τ = 39.45) poses risks when applied to other distortions. We observe a clear distribution shift in the metric space for degradations that suppress high-frequency information. For instance, the mean metric of unwatermarked images under Blurring drops to 32.38, falling below the fixed cropping threshold of 39.45. Since detection occurs when the metric is below the threshold, this shift results in increased False Positive Rates (FPR), where benign, low-quality images are misclassified.", "source": "marker_v2", "marker_block_id": "/page/16/Text/3"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0122", "section": "D. Extended Related Work", "page_start": 17, "page_end": 17, "type": "Text", "text": "This section provides a detailed review and taxonomy of existing watermarking methods for generative models.", "source": "marker_v2", "marker_block_id": "/page/16/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0123", "section": "D.1. Watermarking Schemes Taxonomy", "page_start": 17, "page_end": 17, "type": "Text", "text": "We categorize existing watermarking methods for generative models into five primary classes based on their embedding stage: Random Seed Modification, U-Net Modification, VAE Modification, Latent Space Modification, and Post-Processing.", "source": "marker_v2", "marker_block_id": "/page/16/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0124", "section": "D.1. Watermarking Schemes Taxonomy", "page_start": 17, "page_end": 17, "type": "Text", "text": "Random Seed Modification (Initial Latent). Methods in this category embed watermarks by changing in the sampling process of the initial latent variables. For instance, Tree-Ring (Wen et al., 2024) modifies the initial noise vector in the Fourier domain to embed a ring-shaped pattern, which is detectable via diffusion inversion. Gaussian Shading (Yang et al., 2024c) employs a constrained sampling strategy to apply specific patterns to the initial latent.", "source": "marker_v2", "marker_block_id": "/page/16/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0125", "section": "D.1. Watermarking Schemes Taxonomy", "page_start": 17, "page_end": 17, "type": "Text", "text": "Model Modification. These approaches embed watermarks by fine-tuning specific components of the generative model to ensure watermark preservation during generation. Stable Signature (Fernandez et al., 2023) fine-tunes the VAE decoder to embed the watermark into the pixel space during the latent-to-image decoding stage. Aqualora (Feng et al., 2024) modifies the U-Net to inject the watermark during the iterative denoising process.", "source": "marker_v2", "marker_block_id": "/page/16/Text/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0126", "section": "D.1. Watermarking Schemes Taxonomy", "page_start": 17, "page_end": 17, "type": "Text", "text": "Latent Space Optimization. Unlike static encoding methods, these approaches formulate watermark embedding as an optimization problem within the latent space. Zodiac (Zhang et al., 2024) embeds the watermark by iteratively optimizing the initial latent variable to ensure high detectability in the generated output. ROBIN (Huang et al., 2024) focuses on optimizing the intermediate latent representations during the diffusion process. It incorporates learnable prompts to align the watermarked latents with the text condition.", "source": "marker_v2", "marker_block_id": "/page/16/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0127", "section": "D.1. Watermarking Schemes Taxonomy", "page_start": 17, "page_end": 17, "type": "Text", "text": "Post-Processing Methods. These techniques apply digital watermarking algorithms to the image after it has been fully generated, operating independently of the generation pipeline. StegaStamp (Tancik et al., 2020) is a deep learning-based encoder-decoder framework that embeds invisible hyperlinks or bit-strings into the final image output.", "source": "marker_v2", "marker_block_id": "/page/16/Text/11"}

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+  "default_model_input": "model_text_v3.txt",
+  "appendix_input": "appendix_text_v3.txt",
+  "reference_input": "reference_text_v3.txt",
+  "source": "koala_icml26_due_queue",
+  "run_name": "icml26_20260429_1952_duequeue"
+}

icml26/6b484833-bf42-4409-a685-ed34a504bfa9/main_body_chunks.jsonl

@@ -0,0 +1,73 @@
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0000", "section": "Abstract", "page_start": 1, "page_end": 1, "type": "Text", "text": "Watermarking is a technical alternative to safeguarding intellectual property and reducing misuse. Existing methods focus on optimizing watermarked latent variables to balance watermark robustness and fidelity, as Latent diffusion models (LDMs) are considered a powerful tool for generative tasks. However, reliance on computationally intensive heuristic optimization for iterative signal refinement results in high training overhead and local optima entrapment. To address these issues, we propose an Analytical Watermarking Framework for Controllable Generation (ALIEN). We develop the first analytical derivation of the timedependent modulation coefficient that guides the diffusion of watermark residuals to achieve controllable watermark embedding pattern. Experimental results show that ALIEN-Q outperforms the state-of-the-art by 33.1% across 5 quality metrics, and ALIEN-R demonstrates 14.0% improved robustness against generative variant and stability threats compared to the state-of-the-art across 15 distinct conditions. Code can be available at", "source": "marker_v2", "marker_block_id": "/page/0/Text/15"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0001", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "Text-to-image diffusion models, such as Stable Diffusion (Rombach et al., 2022) and DALL·E (Ramesh et al., 2022) , have demonstrated impressive capabilities in generating high-quality images. To safeguard the intellectual property of generative models (Gowal & Kohli, 2023) and facilitate misuse tracking (Barrett, 2023) , Governments are increasingly calling for regulations (European Union, 2024; Biden, 2023) to mandate watermark adoption. Robust and imperceptible watermarking of generated images has become a critical and urgent research focus. Post-processing watermarking (Cox et al., 2007) is applied to the contents gener-", "source": "marker_v2", "marker_block_id": "/page/0/Text/17"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0002", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "FigureGroup", "text": "Figure 1. (a) Latent modification, (b) Constrained sampling, (c) Iterative optimization, (d) Our ALIEN with principled embedding.", "source": "marker_v2", "marker_block_id": "/page/0/FigureGroup/568"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0003", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "ated by the diffusion model, but its robustness is insufficient for reliable detection in real-world applications (Ren et al., 2024) . Some studies consider model distribution scenarios (Rezaei et al., 2024; Ci et al., 2024; Feng et al., 2024; Wang et al., 2025) . Diffusion models are fine-tuned to embed watermarks into the model parameters, which inevitably limits efficiency and scalability.", "source": "marker_v2", "marker_block_id": "/page/0/Text/22"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0004", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "Recent research has concentrated on semantic watermarking (Lee & Cho, 2025) , which aims to embed watermark signals into the semantic or latent features to better resist imageprocessing-based attacks (Zhao et al., 2024) . Watermarking methods based on initial latent variable modifications (Wen et al., 2024; Ci et al., 2025) embed watermarks by directly modifying or adding perturbations to the initial latents (Fig. 1( a)). While the mechanism is intuitive, the mapping between the initial latent space and the final image is highly complex and nonlinear, making direct modifications prone to semantic drift. Furthermore, to maintain invisibility, the amount of modification to the initial latents is strictly limited, making it difficult to increase watermark capacity. To ensure high capacity and lossless watermark embedding, Watermarks based on the Gaussian-Constrained Identifiable Subspace Sampling (Yang et al., 2024c; Gunn et al., 2024)", "source": "marker_v2", "marker_block_id": "/page/0/Text/23"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0005", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "combined with cryptography, divide the initial latent space into non-overlapping identifiable subspaces, forcing users to sample from subspaces associated with specific watermark information (Fig. 1( b)). This rigid constraint on the initial latent space limits generative diversity. Watermarking methods based on optimization (Huang et al., 2024; Zhang et al., 2024) perform watermark optimization in the latent space to better balance robustness and fidelity (Fig. 1( c)). However, their reliance on computationally intensive heuristic optimization to iteratively find the optimal watermark, leading to substantial training overhead and prone to local optima. Furthermore, detection of semantic watermarking typically depends on diffusion inversion, which limits applicability to reversible samplers (Lu et al., 2022) and watermarks become undetectable when images are generated with irreversible samplers (Karras et al., 2022) . Attackers can exploit this vulnerability to remove watermarks by regenerating images with irreversible schedulers. (An et al., 2024) .", "source": "marker_v2", "marker_block_id": "/page/1/Text/1"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0006", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "Despite the progress made by aforementioned semantic watermarking schemes in robust embedding, they circumvent a fundamental issue: the inability to derive a precise and efficient watermark embedding mechanism from the generative principles of diffusion models. Current optimization or constraint-based methods essentially avoid this problem, instead relying on computationally intensive optimization or sampling constraints. These approaches inherently limits the fidelity, efficiency, and diversity.", "source": "marker_v2", "marker_block_id": "/page/1/Text/2"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0007", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "To address these issues, we propose an Analytical Watermarking Framework for Controllable Generation (ALIEN). As shown in Fig. 1( d), unlike existing methods that rely on computationally intensive heuristic latent variable optimization or constraints on initial latent sampling, we start with the reverse process of the Stochastic Differential Equation of the diffusion model and present the first analytic derivation of the watermark residual propagation mechanism. Specifically, given a target watermark residual, we analytically derive a time-dependent modulation coefficient that transforms this target into a precise correction term for the noise prediction. By injecting this correction at each denoising step, we effectively modify the underlying probability flow of the diffusion model. This imposes a deterministic force that seamlessly guides the generation trajectory toward the watermarked state regardless of the sampling path, thereby eliminating the need for iterative optimization and ensuring compatibility with various samplers. ALIEN achieves a principled watermark embedding pattern, rather than relying on heuristic methods. Without the need for iterative optimization, we inject the precisely modulated watermark into the noise prediction target at each step of the denoising process.", "source": "marker_v2", "marker_block_id": "/page/1/Text/3"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0008", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "Our contributions are three-fold: (1) We achieve the first analytic derivation of watermark propagation for seamless,", "source": "marker_v2", "marker_block_id": "/page/1/Text/4"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0009", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "low-inference-cost embedding, eliminating the need for iterative optimization. (2) Since the watermark is precisely compensated based on diffusion model, ALIEN preserves semantic consistency and visual fidelity by leveraging precise theoretical compensation for the watermark signal. (3) The ALIEN watermark embedding mechanism is independent of specific initial latent variables and sampler types (including irreversible samplers), solving the issue of strong reliance on reversible samplers of semantic watermarking.", "source": "marker_v2", "marker_block_id": "/page/1/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0010", "section": "2. Related Work", "page_start": 2, "page_end": 2, "type": "Text", "text": "Diffusion models exhibit exceptional performance in image generation (Dhariwal & Nichol, 2021) , leveraging the methodology (Ho et al., 2020; Song et al., 2020b) and the sampling techniques (Song et al., 2020a; Song & Ermon, 2020) . LDMs optimize image generation within the latent space of the pretrained Variational Autoencoder (VAE), which further accelerates the practical applications of diffusion models. During the inference phase, LDM first samples an initial latent z T ∈ R c×w×h from a standard Gaussian distribution N (0, I), where T denotes the total time step of the diffusion model. Following iterative denoising, the latent vector evolves into the noise-free representation z0. The final image x 0 is reconstructed by the VAE decoder from z0. Safeguarding the intellectual property of generated content and preventing misuse have become critical research priorities. This paper focuses on critical issues of fidelity, efficiency, and controllability in existing approaches for integrating watermarking into the diffusion process.", "source": "marker_v2", "marker_block_id": "/page/1/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0011", "section": "2. Related Work", "page_start": 2, "page_end": 2, "type": "Text", "text": "Watermarking in Latent Diffusion Models aims at tracking the origin and ensuring the accountability of the generated content. For a comprehensive context regarding the taxonomy of existing watermarking methods a detailed review is provided in Appendix D. We specifically focus on prior work integrating watermarking during the diffusion process. Latent modification Watermark such as Tree-Ring (Wen et al., 2024) and RingID (Ci et al., 2025) embed watermarks in the Fourier space of the initial latent which leads to semantic drift. Constrained sampling watermark such as Gaussian Shading (Yang et al., 2024c) , GaussMarker (Li et al., 2025) and PRC (Gunn et al., 2024) utilize cryptographic principles to modify the sampling pattern, but strict constraints limit the sampling range, resulting in reduced controllability. Optimization-based methods such as Zodiac (Zhang et al., 2024) and Robin (Huang et al., 2024) , optimize latent variables for higher semantic consistency, but reliance on heuristic optimization incurs computational costs. The detection of aforementioned methods depends on diffusion inversion, limiting their function to reversible samplers and is ineffective with irreversible samplers. Our method achieves low-overhead and universally applicable watermark via analytic derivation.", "source": "marker_v2", "marker_block_id": "/page/1/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0012", "section": "2. Related Work", "page_start": 3, "page_end": 3, "type": "Caption", "text": "Figure 2. The ALIEN framework consists of two main stages: (Top) Imperceptible Latent Watermark Generation, where a secret encoder E_s and decoder D_s are trained to embed a message m into a robust latent residual \\delta_w while preserving image quality. (Bottom) Analytic SDE Reverse Drift Correction, which applies the time-dependent modulation to the noise prediction. This principled correction steers the generative trajectory to satisfy the watermark constraint in a sampler-agnostic manner.", "source": "marker_v2", "marker_block_id": "/page/2/Caption/2"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0013", "section": "3. Methodology", "page_start": 3, "page_end": 3, "type": "Text", "text": "132133", "source": "marker_v2", "marker_block_id": "/page/2/Text/29"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0014", "section": "3.1. Framework of ALIEN", "page_start": 3, "page_end": 3, "type": "Text", "text": "We extend to achieve applicability and theoretical controllability of semantic watermarking. As demonstrated in Fig. 2, our ALIEN embeds the watermark in intermediate diffusion states to manipulate the generation trajectory through precise correction of the probability flow. To generate imperceptible watermark residuals, we implement an Imperceptible Latent Watermark Generation module to generate the invisible and robust watermark residual in the latent space. For principled embedding, we propose Analytic SDE Reverse Drift Correction, which analytically derives the necessary modifications to the probability flow required by the diffusion model for watermark embedding under Variance Preserving Stochastic Differential Equation (VP-SDE) (Song et al., 2020b), providing an explicit correction target for noise prediction that is compatible with both stochastic and deterministic sampling processes. This derived target is implemented via the Modulation of Noise Prediction Target module, which specifies the requisite adjustment to the model's noise prediction output, thereby realizing the controlled and imperceptible semantic watermarking.", "source": "marker_v2", "marker_block_id": "/page/2/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0015", "section": "3.2. Imperceptible Latent Watermark Generation", "page_start": 3, "page_end": 3, "type": "Text", "text": "To generate an imperceptible yet robust watermark residual, we jointly train a secret encoder E_s and a watermark decoder D_s . Ideally, the watermarked latent representation z_w should be conditioned on both the input latent z_0 and the", "source": "marker_v2", "marker_block_id": "/page/2/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0016", "section": "3.2. Imperceptible Latent Watermark Generation", "page_start": 3, "page_end": 3, "type": "Text", "text": "message m to enhance imperceptibility. However, utilizing a z_0 -dependent watermark becomes impractical as the intermediate latent states of the diffusion model are not readily accessible for deterministic conditioning. Therefore, we opt to embed a cover-agnostic watermark prominent in the latent space. Specifically, the secret residual \\delta_w=E(m) is added to the input latent z_0 , forming the watermarked latent z_w=z_0+\\delta_w . The watermarked image x_w is generated as x_w=\\mathcal{D}(z_w) , and the message is extracted by applying the decoder D_s to z_w , yielding m'=D_s(z_w) . We employ the Binary Cross-Entropy loss to optimize for the accuracy of message extraction between the original message m and the decoded message m'.", "source": "marker_v2", "marker_block_id": "/page/2/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0017", "section": "3.2. Imperceptible Latent Watermark Generation", "page_start": 3, "page_end": 3, "type": "Text", "text": "To ensure the visual consistency of the watermark, we compute the LPIPS loss (Zhang et al., 2018) and the Mean Squared Error loss between the watermarked image x_w and the reconstructed image x_r , rather than between x_w and the original image x_o . This choice is necessary because the VAE compression and reconstruction already introduce a measurable irrecoverable quality gap between x_o and x_r . Optimizing against x_o would necessitate the watermark training process to compensate for VAE reconstruction errors, which would increase complexity and hinder embedding effectiveness. Our training objective can be summarized below, where \\lambda_1 and \\lambda_2 are coefficients:", "source": "marker_v2", "marker_block_id": "/page/2/Text/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0018", "section": "3.2. Imperceptible Latent Watermark Generation", "page_start": 3, "page_end": 3, "type": "Equation", "text": "\\mathcal{L}_{T} = \\mathcal{L}_{BCE}^{(m,m')} + \\lambda_{1} \\mathcal{L}_{LPIPS}^{(x_{r},x_{w})} + \\lambda_{2} \\mathcal{L}_{MSE}^{(x_{r},x_{w})}, (1)", "source": "marker_v2", "marker_block_id": "/page/2/Equation/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0019", "section": "3.2. Imperceptible Latent Watermark Generation", "page_start": 3, "page_end": 3, "type": "Text", "text": "where \\mathcal{L}_{BCE} is the Binary Cross-Entropy loss, \\mathcal{L}_{LPIPS} is the Learned Perceptual Image Patch Similarity loss (Zhang", "source": "marker_v2", "marker_block_id": "/page/2/Text/11"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0020", "section": "Algorithm 1 ALIEN Watermarking", "page_start": 4, "page_end": 4, "type": "Text", "text": "17: Return D_s(\\mathcal{E}_{VAE}(\\mathbf{x}_{wm}))", "source": "marker_v2", "marker_block_id": "/page/3/Text/41"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0021", "section": "Algorithm 1 ALIEN Watermarking", "page_start": 4, "page_end": 4, "type": "Code", "text": "PHASE I: EMBEDDING 2: Input: Pre-trained U-Net \\theta, Encoder E_s, Scheduler S, VAE \\mathcal{D}_{VAE}, Prompt c, Secret m, Strength \\lambda, Interval [T_{start}, T_{end}] 3: Output: Watermarked Image \\mathbf{x}_{wm} 4: \\delta_{wm} \\leftarrow E_s(\\mathbf{m}) 5: \\mathbf{z}_t \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I}) 6: for t = T down to 1 do \\epsilon_{\\theta}^{t} \\leftarrow \\text{CFG}(\\theta, \\mathbf{z}_{t}, S.\\text{steps}[t], \\mathbf{c}) \\begin{aligned} & \\text{if } T_{start} \\leq t \\leq T_{end} \\text{ then} \\\\ & \\epsilon_{\\theta}^t \\leftarrow \\epsilon_{\\theta}^t - \\lambda \\cdot \\left(\\frac{\\sqrt{\\bar{\\alpha}_t}}{\\sqrt{1 - \\bar{\\alpha}_t}}\\right) \\cdot \\delta_{wm} \\end{aligned} 10: \\mathbf{z}_t \\leftarrow S.\\text{step}(\\epsilon_{\\theta}^t, t, \\mathbf{z}_t).\\text{prev\\_sample} 11: 12: end for 13: \\mathbf{x}_{wm} \\leftarrow \\mathcal{D}_{VAE}(\\mathbf{z}_t) PHASE II: EXTRACTION 15: Input: Image \\mathbf{x}_{wm}, \\mathcal{E}_{VAE}, Decoder D_s 16: Output: Secret m'", "source": "marker_v2", "marker_block_id": "/page/3/Code/2"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0022", "section": "Algorithm 1 ALIEN Watermarking", "page_start": 4, "page_end": 4, "type": "Text", "text": "et al., 2018), and \\mathcal{L}_{MSE} is the Mean Squared Error loss. Existing studies (Wang et al., 2025; Meng et al., 2024) demonstrate that injecting and detecting watermarks in the latent space can inherently resist various common distortions. We follow prior practice by omitting the distortion layer during training (validated in Tab. 4). The effectiveness of watermark remains unaffected even if an adversary finetunes U-Net \\theta and \\mathcal{D} on clean images and uses a fine-tuned latent decoder \\mathcal{D}' to generate images (validated in Fig. 8).", "source": "marker_v2", "marker_block_id": "/page/3/Text/3"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0023", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "To achieve precise watermark embedding over the generative process, we leverage the VP-SDE to analytically derive the exact probability flow correction required for watermark embedding.", "source": "marker_v2", "marker_block_id": "/page/3/Text/5"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0024", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "\\mathbf{z}_0 Constraint. Our goal is to embed a predetermined watermark residual \\delta_{wm} into the final denoised latent \\mathbf{z}_0 , resulting in the \\mathbf{z}_0 -space constraint \\hat{\\mathbf{z}}_0^{wm} = \\hat{\\mathbf{z}}_0^{orig} + \\delta_{wm} , where \\hat{\\mathbf{z}}_0^{wm} and \\hat{\\mathbf{z}}_0^{orig} are the clean data estimates predicted by the U-Net for the current latent state \\mathbf{z}_t , with and without the watermark, respectively.", "source": "marker_v2", "marker_block_id": "/page/3/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0025", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "Score Function. Under the VP-SDE, The diffusion process is defined by a forward SDE that gradually perturbs clean data into noise:", "source": "marker_v2", "marker_block_id": "/page/3/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0026", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Equation", "text": "d\\mathbf{z} = \\mathbf{f}(\\mathbf{z}, t)dt + g(t)d\\mathbf{w},", "source": "marker_v2", "marker_block_id": "/page/3/Equation/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0027", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "where \\mathbf{f}(\\mathbf{z}, t) : \\mathbb{R}^d \\to \\mathbb{R}^d denotes the drift coefficient, while g(t) \\in \\mathbb{R} represents the scalar diffusion coefficient, with", "source": "marker_v2", "marker_block_id": "/page/3/Text/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0028", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "(b) Injection Strength Schedule", "source": "marker_v2", "marker_block_id": "/page/3/Text/12"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0029", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "Generation Step", "source": "marker_v2", "marker_block_id": "/page/3/Text/43"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0030", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Caption", "text": "Figure 3. Comparison of ALIEN-R and ALIEN-Q. (a) The L2 norm of noise prediction during the diffusion process. (b) The evolution of injection strength \\frac{\\sqrt{\\alpha_t}}{\\sqrt{1-\\bar{\\alpha}_t}} .", "source": "marker_v2", "marker_block_id": "/page/3/Caption/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0031", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "\\mathbf{w}(t) denoting the standard Wiener process. The reverse generation process of the diffusion model is governed by a reverse-time stochastic differential equation:", "source": "marker_v2", "marker_block_id": "/page/3/Text/14"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0032", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Equation", "text": "d\\mathbf{z} = \\underbrace{[\\mathbf{f}(\\mathbf{z}, t) - g^{2}(t)\\nabla_{\\mathbf{z}}\\log p_{t}(\\mathbf{z})]}_{\\text{Reverse Drift }\\mathbf{F}_{rev}} dt + g(t)d\\bar{\\mathbf{w}}, \\quad (2)", "source": "marker_v2", "marker_block_id": "/page/3/Equation/15"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0033", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "where \\bar{\\mathbf{w}} denotes the standard Wiener process in reverse time. To realize the watermark z_0 constraint, we precisely control the probability flow, which requires determining the necessary correction \\Delta \\mathbf{F}_{rev} for the reverse SDE drift term. Since \\Delta \\mathbf{F}_{rev} relies on the score function \\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t) , analytically quantifying the difference in the score function becomes a direct path to derive \\Delta \\mathbf{F}_{rev} . The score function is exactly and linearly related to the difference between \\mathbf{z}_t and its denoised estimate \\hat{\\mathbf{z}}_0 . This analytical relationship is mathematically described as follows:", "source": "marker_v2", "marker_block_id": "/page/3/Text/16"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0034", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Equation", "text": "\\nabla_{\\mathbf{z}_t} \\log p_t(\\mathbf{z}_t) = -\\frac{1}{1 - \\bar{\\alpha}_t} (\\mathbf{z}_t - \\sqrt{\\bar{\\alpha}_t} \\hat{\\mathbf{z}}_0). (3)", "source": "marker_v2", "marker_block_id": "/page/3/Equation/17"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0035", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "Applying the analytical mapping Eq.3 allows us to analytically determine the difference in the score function induced by the \\mathbf{z}_0 constraint, thereby translating the watermark residual \\delta_{wm} into the required shift in the score function space.", "source": "marker_v2", "marker_block_id": "/page/3/Text/18"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0036", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 4, "page_end": 4, "type": "Text", "text": "Probability Flow Correction. Based on the analytical structure of VP-SDE for the reverse drift term \\mathbf{F}_{rev} , we derive", "source": "marker_v2", "marker_block_id": "/page/3/Text/19"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0037", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 5, "page_end": 5, "type": "TableGroup", "text": "Method G.S. StegaStamp Tree-Ring ROBIN ZoDiac AquaLoRA StableSig. ALIEN-Q ALIEN-R Original Image No Original Watermarked Image Residual (×10) Metrics PSNR:—— SSIM: :—— LPIPS: :—— PSNR:29.26 SSIM:0.909 LPIPS:0.065 PSNR:14.25 SSIM:0.570 LPIPS:0.488 PSNR:24.64 SSIM:0.917 LPIPS:0.091 PSNR:28.46 SSIM:0.921 LPIPS:0.046 SSIM:0.776 PSNR:29.61 SSIM:0.891 LPIPS:0.039 PSNR:33.29 SSIM:0.942 LPIPS:0.020 PSNR:27.24 SSIM:0.855 LPIPS:0.107 Figure 4. Qualitative comparison of watermarked samples and 10 \\times magnified residuals. We compare ALIEN with baselines covering post-processing (StegaStamp), latent modification (Tree-Ring), optimization (ROBIN, ZoDiac), and fine-tuning (AquaLoRA, StableSig.).", "source": "marker_v2", "marker_block_id": "/page/4/TableGroup/217"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0038", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 5, "page_end": 5, "type": "TableGroup", "text": "Table 1. Quantitative Comparison of Visual Quality and Fidelity across Watermarking Schemes. D.S. denotes the Dreamsim (Fu et al., 2023) metric. Method FID CLIP PSNR SSIM SIFID D.S. No WM 24.31 0.3368 _ StegaS. 24.56 0.3363 28.59 0.878 0.189 0.021 ZoDiac _ 28.01 0.922 0.121 0.022 AquaL. 24.79 0.3366 17.07 0.664 0.183 0.139 TreeR. 24.63 0.3370 12.76 0.429 0.741 0.291 G.S. 24.42 0.3378 _ _ ROBIN 24.61 0.3366 22.96 0.756 0.212 0.057 StableS. 24.56 0.3367 29.09 0.878 0.105 0.011 ALIEN-Q 24.29 0.3369 32.41 0.949 0.023 0.003 ALIEN-R 24.74 0.3366 20.42 0.745 0.227 0.061", "source": "marker_v2", "marker_block_id": "/page/4/TableGroup/218"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0039", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 5, "page_end": 5, "type": "Text", "text": "the required reverse SDE drift correction \\Delta \\mathbf{F}_{rev} to enforce the watermark constraint (Details provided in Appendix A). The resulting correction term \\Delta \\mathbf{F}_{rev} is analytically defined by the following expression:", "source": "marker_v2", "marker_block_id": "/page/4/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0040", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\Delta \\mathbf{F}_{rev}(\\mathbf{z}_t, t) = -g^2(t) \\frac{\\sqrt{\\bar{\\alpha}_t}}{1 - \\bar{\\alpha}_t} \\delta_{wm}. (4)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0041", "section": "3.3. Analytic SDE Reverse Drift Correction", "page_start": 5, "page_end": 5, "type": "Text", "text": "This analytical derivation Eq.4 provides the theoretical foundation for the ALIEN framework. It precisely quantifies the correction \\Delta \\mathbf{F}_{rev} required by the watermark objective \\delta_{wm} within the SDE probability flow framework. Since this correction targets the score function of the latent distribution, it demonstrates that the watermark is sampler-agnostic.", "source": "marker_v2", "marker_block_id": "/page/4/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0042", "section": "3.4. Modulation of Noise Prediction Target", "page_start": 5, "page_end": 5, "type": "Text", "text": "To achieve the practical implementation of the SDE drift correction \\Delta \\mathbf{F}_{rev} , we analytically relate the SDE reverse drift correction to the noise prediction offset of U-Net within the VP-SDE framework (Details provided in Appendix A), we derive the required compensation signal \\Delta \\epsilon_{wm} necessary", "source": "marker_v2", "marker_block_id": "/page/4/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0043", "section": "3.4. Modulation of Noise Prediction Target", "page_start": 5, "page_end": 5, "type": "TableGroup", "text": "Table 2. Stability Evaluation measured by Detection Confidence. We assess robustness across Samplers (DPM++ SDE, Euler a., DPM2 a.), Inference Steps (25, 50), Guidance Scale (10, 20), and Model Versions (v1.5, v2.1). Method Sa ampler Steps Sc ale Model DPM-SDE Eulera DPM2a 25 50 10 20 v1.5 v2.1 StegaS. 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.990 0.999 StableS. 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 TreeR. 0.000 0.000 0.000 0.963 0.963 0.963 0.963 0.958 0.963 G.S. 0.557 0.586 0.552 0.999 0.999 0.999 0.999 0.999 0.999 AquaL. 0.952 0.953 0.939 0.945 0.955 0.940 0.939 0.954 ALIEN-Q 0.989 0.979 0.972 0.985 0.990 0.982 0.975 0.989 0.991 ALIEN-R 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999", "source": "marker_v2", "marker_block_id": "/page/4/TableGroup/219"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0044", "section": "3.4. Modulation of Noise Prediction Target", "page_start": 5, "page_end": 5, "type": "Text", "text": "to enforce the \\mathbf{z}_0 constraint:", "source": "marker_v2", "marker_block_id": "/page/4/Text/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0045", "section": "3.4. Modulation of Noise Prediction Target", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\Delta \\epsilon_{wm} = -\\frac{\\sqrt{\\bar{\\alpha}_t}}{\\sqrt{1 - \\bar{\\alpha}_t}} \\delta_{wm}. (5)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/14"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0046", "section": "3.4. Modulation of Noise Prediction Target", "page_start": 5, "page_end": 5, "type": "Text", "text": "Refer to Eq. (5), to realize a fixed watermark residual \\delta_{wm} in the \\mathbf{z}_0 space, the U-Net will introduce a time-dependent compensation signal \\Delta\\epsilon_{wm} proportional to the watermark residual in its noise prediction. As illustrated in Fig. 3, the injection coefficient exhibits a surge approaching \\mathbf{z}_0 , implying that late-stage injection yields stronger constraints but risks visual fidelity. We adjust the injection magnitude and timestep range to formulate two configurations: ALIEN-Q (Quality-Oriented) and ALIEN-R (Robustness-Oriented). The procedure is outlined in Alg. 1.", "source": "marker_v2", "marker_block_id": "/page/4/Text/15"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0047", "section": "4.1. Experimental Setup", "page_start": 5, "page_end": 5, "type": "Text", "text": "Watermarking Baselines. We compare ALIEN with mainstream latent semantic watermarking schemes across three primary categories: the initial latent variable modification", "source": "marker_v2", "marker_block_id": "/page/4/Text/18"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0048", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "TableGroup", "text": "Table 3. Robustness Evaluation across variant Regenerative Attacks. Each cell reports performance under three attacks: Regeneration → Rinse-2X → Rinse-4X. Values denote Detection Confidence/ TPR@1%FPR. Method Scheduler (Cell Format: Regen. Data | Rinse-2X Data | Rinse-4X Data) DDIM DPM++ 2M SDE Euler a DPM2 a StegaS. 0.692/0.957 | 0.578/0.347 | 0.531/0.102 0.636/0.575 | 0.562/0.182 | 0.502/0.000 0.624/0.631 | 0.542/0.180 | 0.513/0.000 0.615/0.591 | 0.556/0.120 | 0.495/0.000 ZoDiac 0.938/1.000 | 0.743/0.104 | 0.527/0.032 0.693/0.585 | 0.670/0.431 | 0.562/0.125 0.643/0.315 | 0.643/0.250 | 0.628/0.210 0.833/0.650 | 0.572/0.281 | 0.520/0.152 TreeR. 0.868/1.000 | 0.724/0.861 | 0.408/0.489 0.855/0.918 | 0.824/0.905 | 0.753/0.851 0.821/0.941 | 0.449/0.512 | 0.277/0.306 0.647/0.755 | 0.531/0.656 | 0.326/0.427 G.S. 0.978/1.000 | 0.898/1.000 | 0.845/1.000 0.943/1.000 | 0.953/1.000 | 0.926/1.000 0.946/1.000 | 0.847/1.000 | 0.695/0.905 0.923/1.000 | 0.858/1.000 | 0.711/0.915 AquaL. 0.757/0.742 | 0.627/0.145 | 0.573/0.000 0.879/0.942 | 0.833/0.858 | 0.696/0.486 0.663/0.225 | 0.618/0.078 | 0.551/0.000 0.679/0.371 | 0.604/0.086 | 0.536/0.029 ROBIN —- /0.638 | —- /0.242 | —- /0.153 —- /1.000 | —- /0.728 | —- /0.275 —- /0.980 | —- /0.705 | —- /0.486 —- /0.075 | —- /0.105 | —- /0.100 StableS. 0.496/0.000 | 0.477/0.000 | 0.521/0.000 0.512/0.000 | 0.512/0.000 | 0.510/0.000 0.498/0.000 | 0.520/0.000 | 0.513/0.000 0.506/0.000 | 0.485/0.000 | 0.502/0.000 ALIEN-Q 0.848/1.000 | 0.752/0.865 | 0.618/0.342 0.935/1.000 | 0.898/1.000 | 0.842/0.942 0.866/1.000 | 0.661/0.581 | 0.563/0.163 0.857/1.000 | 0.673/0.636 | 0.581/0.124 ALIEN-R 0.999/1.000 | 0.908/1.000 | 0.829/1.000 0.999/1.000 | 0.989/1.000 | 0.967/1.000 0.988/1.000 | 0.908/1.000 | 0.731/0.727 0.989/1.000 | 0.878/1.000 | 0.742/0.875", "source": "marker_v2", "marker_block_id": "/page/5/TableGroup/859"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0049", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "TableGroup", "text": "Gaussian Shading Tree-ring AquaLoRA ALIEN-Q ALIEN-R DDIM Original No Original DDIM Watermarked DPM2 a Watermarked Euler a Watermarked DPM++ 2M SDE Watermarked Figure 5. Visual Comparison under Different Generation Schedulers (DDIM, DPM2 a, Euler a, and DPM++ 2M SDE).", "source": "marker_v2", "marker_block_id": "/page/5/TableGroup/860"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0050", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "method Tree-Ring (Wen et al., 2024) ; the constrained sampling method Gaussian Shading (Yang et al., 2024c) ; and the iterative optimization methods ROBIN (Huang et al., 2024) and Zodiac (Zhang et al., 2024) . Additionally, we select the fine-tuning based method Stable Signature (Fernandez et al., 2023) and Aqualora (Feng et al., 2024) , as well as the post-processing image watermarking technique StegaStamp (Tancik et al., 2020) . Implementation details can be found in Appendix B.2.", "source": "marker_v2", "marker_block_id": "/page/5/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0051", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "Models and Tasks. Following existing research (Yang et al., 2024c) , we implement the ALIEN framework on Stable Diffusion v1.5 and Stable Diffusion v2.1. We evaluate our method across two tasks: (1) Detection. All compared methods are configured as single-bit watermarks with a unified pattern. The detection threshold is set individually for each method to achieve a False Positive Rate (FPR) of approximately 1%. (2) Traceability. Multi-bit watermarking methods are evaluated using Bit Accuracy. Single-bit methods, including Tree-ring, Zodiac, and Robin, are excluded due to their lack of watermark capacity. We use prompts", "source": "marker_v2", "marker_block_id": "/page/5/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0052", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "PictureGroup", "text": "Figure 6. Visual Comparison under Regeneration Attacks (DDIM, DPM2 a, Euler a, and DPM++ 2M SDE).", "source": "marker_v2", "marker_block_id": "/page/5/PictureGroup/861"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0053", "section": "4.1. Experimental Setup", "page_start": 6, "page_end": 6, "type": "Text", "text": "from Stable Diffusion-Prompts (SDP) (Gustavosta, 2023) , setting the Guidance Scale to 7.5 and the number of sampling steps to 50. Both TPR@1%FPR and Bit Accuracy are computed over 350 watermarked images.", "source": "marker_v2", "marker_block_id": "/page/5/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0054", "section": "4.2. Comparison to Baselines", "page_start": 6, "page_end": 6, "type": "Text", "text": "Watermark Fidelity. We employ PSNR (Hore & Ziou, 2010) and SSIM (Wang et al., 2004) for pixel fidelity, LPIPS (Zhang et al., 2018) and DreamSim (Fu et al., 2023) for perceptual similarity, FID (Heusel et al., 2017) and SIFID (Yang et al., 2024a) for realism, and CLIP Score (Radford et al., 2021) for semantic alignment. As shown in Tab. 1, ALIEN-Q achieves state-of-the-art imperceptibility, significantly outperforming all baselines. It yields the highest pixel fidelity of 32.41 dB PSNR and the best perceptual quality of 0.003 DreamSim, while maintaining FID and CLIP scores comparable to non-watermarked images.", "source": "marker_v2", "marker_block_id": "/page/5/Text/12"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0055", "section": "4.2. Comparison to Baselines", "page_start": 6, "page_end": 6, "type": "Text", "text": "Watermark Stability. We validate watermark stability across three dimensions: Sampler Agnosticism covers both", "source": "marker_v2", "marker_block_id": "/page/5/Text/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0056", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "TableGroup", "text": "Table 4. Comprehensive Comparison of Watermark Robustness. Performance is reported in decimal scale (0-1). Higher values are better (↑). The Avg. column represents the mean performance across all 11 attacks (excluding No Attack). Top section: TPR@1%FPR; Bottom section: Bit Accuracy. Metrics Method No Photo netric De egradati on Ge eometric ; C enerative Avg. Attack Bright. Contr. JPEG Blur Noise ReScale C.C. R.C. VAE-B VAE-C Diff. StegaS. 1.000 0.964 1.000 1.000 1.000 1.000 1.000 0.964 0.975 1.000 1.000 1.000 0.991 StableS. 1.000 0.958 1.000 0.781 0.973 0.042 0.935 1.000 1.000 0.000 0.079 0.000 0.611 AquaL. 1.000 0.289 0.507 1.000 1.000 0.932 1.000 0.127 0.258 0.975 0.958 0.742 0.708 TreeR. 1.000 0.775 0.909 1.000 1.000 0.954 0.968 0.013 0.021 0.954 1.000 1.000 0.778 TPR@ G.S. 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.981 0.979 1.000 1.000 1.000 0.996 Thre1%FPR ROBIN 1.000 0.913 0.684 0.921 1.000 0.013 0.935 1.000 1.000 1.000 1.000 0.638 0.826 ZoDiac 1.000 0.535 0.375 0.959 0.979 0.357 0.965 0.017 0.021 0.660 0.685 1.000 0.592 ALIEN-Q 1.000 0.783 1.000 0.954 1.000 0.645 1.000 0.153 0.311 0.965 0.970 0.945 0.793 ALIEN-R 1.000 1.000 1.000 1.000 1.000 0.979 1.000 0.989 0.988 1.000 1.000 1.000 0.996 StegaS. 0.999 0.811 0.850 0.999 0.999 0.821 0.999 0.667 0.681 0.837 0.816 0.692 0.834 StableS. 0.998 0.892 0.851 0.712 0.845 0.535 0.878 0.991 0.993 0.506 0.541 0.489 0.748 Bit Acc. AquaL. 0.954 0.583 0.672 0.935 0.954 0.810 0.925 0.573 0.648 0.845 0.856 0.757 0.778 Bit Acc. G.S. 0.999 0.939 0.964 0.995 0.999 0.903 0.996 0.657 0.655 0.996 0.997 0.978 0.916 ALIEN-Q 0.989 0.753 0.803 0.889 0.936 0.689 0.903 0.581 0.601 0.834 0.853 0.848 0.790 ALIEN-R 0.999 0.949 0.992 0.999 0.999 0.855 0.999 0.826 0.835 0.979 0.983 0.999 0.947", "source": "marker_v2", "marker_block_id": "/page/6/TableGroup/285"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0057", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "FigureGroup", "text": "Figure 7. Robustness against VAE embedding attacks. Results are averaged across KLVAE8, KLVAE16, and SDXL variants.", "source": "marker_v2", "marker_block_id": "/page/6/FigureGroup/286"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0058", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "FigureGroup", "text": "Figure 8. Bit accuracy comparison against Stable Signature across VAE fine-tuning and replacement.", "source": "marker_v2", "marker_block_id": "/page/6/FigureGroup/287"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0059", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "Text", "text": "deterministic (DDIM) and irreversible samplers (Euler Ancestral (Karras et al., 2022), DPM++ 2M Ancestral (Karras et al., 2022), DPM++ SDE (Lu et al., 2025)); Component Adaptability involves substituting different VAE and U-Net versions; and Hyperparameter Stability examines sensitivity to Guidance Scale and Inference Steps. As shown in Tab. 2, existing training-free methods exhibit vulnerability to stochastic samplers. Specifically, Tree-Ring and Gaussian Shading fail completely under DPM++ SDE, Euler a., and DPM2 a., where accuracy hovers near the randomguess baseline. ALIEN achieves state-of-the-art sampler agnosticism by maintaining high bit accuracy exceeding 0.97 across all tested schedulers. Our method demonstrates consistent stability across varying inference steps, guidance scales, and model versions.", "source": "marker_v2", "marker_block_id": "/page/6/Text/8"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0060", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "Text", "text": "Watermark Efficiency. We evaluate the computational overhead across two primary dimensions: Preparation Cost , the one-time offline cost, and Runtime Cost , the online perimage latency for embedding and extraction. The comparative results are detailed in Tab. 7. ALIEN achieves latencies of 0.079 seconds for embedding and 0.023 seconds for ex-", "source": "marker_v2", "marker_block_id": "/page/6/Text/9"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0061", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "Text", "text": "traction, maintaining speeds comparable to post-processing baselines while being orders of magnitude faster than the optimization-based method Zodiac, which requires over 122 seconds per image.", "source": "marker_v2", "marker_block_id": "/page/6/Text/10"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0062", "section": "4.2. Comparison to Baselines", "page_start": 7, "page_end": 7, "type": "Text", "text": "Watermark Robustness. We examine watermark's robustness against three typical kinds of adversarial attacks, including image processing attacks (Hore & Ziou, 2010) for transforming generated images, adversarial attacks (An et al., 2024) for disturbing watermark verification, and reconstructive attacks (Zhao et al., 2023) for re-generating nonwatermarked images. Please refer to the Supplementary Materials for detailed parameter settings. As demonstrated in Tab. 4, ALIEN-R achieves state-of-the-art stability against standard distortions by maintaining a True Positive Rate of 0.996. In adversarial embedding scenarios illustrated in Fig. 7, ALIEN-R exhibits exceptional resistance where latent semantic watermarking baselines degrade rapidly. Tab. 3 shows that against reconstructive attacks, ALIEN-R sustains a high confidence exceeding 0.875 even after four re-generation rounds, whereas competitors like StegaStamp and Stable Signature collapse to near-zero.", "source": "marker_v2", "marker_block_id": "/page/6/Text/11"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0063", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 5. Quantitative comparison under Forgery Attacks. Lower values indicate better resistance (\\downarrow) . Config G.S. Tree-Ring ALIEN (Ours) comig Acc. / PSNR Acc. / PSNR Acc. / PSNR Scenario A: Average Forgery 10 Imgs 0.952 / 12.23 0.882 / 18.86 0.539 / 20.06 50 Imgs 0.969 / 12.79 0.908 / 20.34 0.605 / 25.29 100 Imgs 0.969 / 12.65 0.910 / 20.95 0.708 / 26.48 Scenario B: Reprompt Forgery SD-V2.1 1.000 / 0.931 / 0.533 /", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/326"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0064", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "FigureGroup", "text": "Figure 9. Robustness against Imprinting Forgery Attack.", "source": "marker_v2", "marker_block_id": "/page/7/FigureGroup/327"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0065", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "Text", "text": "Forgery Resistance. Following existing research (Müller et al., 2025; Yang et al., 2024b), we evaluate the security of our method against three representative forgery attacks: imprinting forgery, reprompting forgery, and average forgery. Imprinting and reprompting forgeries rely on latent optimization via diffusion inversion. ALIEN exhibits superior resistance to these attacks compared to initial-latent-based watermarks. While baselines like Tree-Ring and Gaussian Shading can be successfully forged using only a single image, ALIEN remains unaffected. Average Forgery involves estimating the watermark pattern by collecting pairs of watermarked and non-watermarked images. While baselines like Tree-Ring exhibit vulnerability with confidence exceeding 0.9, ALIEN maintains a suppressed confidence of 0.711, effectively preventing the rapid extraction of the watermark pattern. The practical challenges in acquiring large-scale specific-user data within real-world API scenarios significantly elevate the security threshold.", "source": "marker_v2", "marker_block_id": "/page/7/Text/6"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0066", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "Text", "text": "Impact of Timestep Range. As shown in Tab. 6, we conducted an ablation study on the injection interval to investigate the trade-off between imperceptibility and robustness. Injecting the watermark across the full reverse process from step 50 down to 1 ensures perfect detection with 1.000 accuracy but introduces significant perceptual degradation, resulting in a PSNR drop to 20.42 dB under Strength B. Narrowing the window to early diffusion stages such as steps 45 to 20 significantly recovers image quality, where the PSNR", "source": "marker_v2", "marker_block_id": "/page/7/Text/7"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0067", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Table 6. Ablation study on Timestep Range under different Watermark Strengths. We compare Image Quality (PSNR) and Detection Performance (Det./Acc.) across two strength settings. Range Strengt \\mathbf{th} \\mathbf{A} (\\lambda = 0.5) Strength B ( \\lambda = 1.0 ) (t_{start} \\rightarrow t_{end}) PSNR Det. / Acc. PSNR Det. / Acc. \\begin{array}{c} 1 \\to 50 \\\\ 25 \\to 50 \\\\ 25 \\to 40 \\\\ 10 \\to 25 \\\\ 20 \\to 45 \\end{array} 24.55 30.53 40.94 31.54 33.76 1.000 / 1.000 1.000 / 1.000 0.718 / 0.747 0.614 / 0.421 0.882 / 1.000 20.42 26.27 23.10 26.83 31.10 1.000 / 1.000 1.000 / 1.000 0.852 / 1.000 0.681 / 0.721 0.989 / 1.000 Table 7. Performance Comparison regarding Computational Efficiency. <sup>‡</sup> indicates data estimated from original papers.", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/328"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0068", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "Table", "text": "Method P rep. Time ( h) Embed. E 111011101 Pre-train Fine-tune Optimize Time (s) Time (s) T.R. _ _ _ 0.011 3.575 G.S. _ 0.102 4.212 ROBIN _ _ 0.4 0.125 1.248 Zodiac _ 122.4 3.601 StegaS. 30 0.108 0.028 S.S. 48^{\\ddagger} 0.1 _ _ 0.014 AquaL. 40^{\\ddagger} 15 ‡ _ _ 0.026 ALIEN 22 _ _ 0.079 0.023", "source": "marker_v2", "marker_block_id": "/page/7/Table/11"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0069", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "Text", "text": "increases to 33.76 dB under Strength A while maintaining a high detection rate.", "source": "marker_v2", "marker_block_id": "/page/7/Text/12"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0070", "section": "4.2. Comparison to Baselines", "page_start": 8, "page_end": 8, "type": "Text", "text": "Impact of Watermark Strength. As shown in Tab. 6, the injection coefficient \\lambda directly modulates the magnitude of the probability flow correction. Increasing the strength from \\lambda=0.5 in Strength A to \\lambda=1.0 in Strength B consistently improves detection performance across all ranges. we select the range from 45 to 20 combined with moderate strength as the optimal configuration for ALIEN-Q to maximize quality while ensuring reliable detection.", "source": "marker_v2", "marker_block_id": "/page/7/Text/13"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0071", "section": "5. Conclusion", "page_start": 8, "page_end": 8, "type": "Text", "text": "Unlike prior approaches relying on heuristic latent modifications, sampling constraints, or computationally intensive optimization, we propose ALIEN, which presents the first analytical derivation of the time-dependent modulation coefficient. This principled approach precisely guides the diffusion of watermark residuals via probability flow modulation, achieving sampler-agnostic embedding. ALIEN overcomes the security vulnerabilities associated with diffusion inversion and irreversible samplers while ensuring high fidelity and low inference cost. Experimental results demonstrate that ALIEN outperforms existing methods in both quality and robustness. Future research will focus on developing content-aware latent watermarking to further enhance security against forgery attacks.", "source": "marker_v2", "marker_block_id": "/page/7/Text/15"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0072", "section": "6. Impact Statement", "page_start": 9, "page_end": 9, "type": "Text", "text": "Ensuring the accountability and intellectual property protection of generative models has become a critical priority. This paper introduces ALIEN, a principled watermarking framework that enables robust and sampler-agnostic provenance tracking for Latent Diffusion Models. By overcoming the vulnerability of existing methods to irreversible samplers and diverse attacks, we believe our approach effectively mitigates risks such as copyright infringement and malicious misuse, thereby contributing to the development of safer and more trustworthy generative AI.", "source": "marker_v2", "marker_block_id": "/page/8/Text/2"}

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@@ -0,0 +1,218 @@
+[p. 1 | section: Abstract | type: Text]
+Watermarking is a technical alternative to safeguarding intellectual property and reducing misuse. Existing methods focus on optimizing watermarked latent variables to balance watermark robustness and fidelity, as Latent diffusion models (LDMs) are considered a powerful tool for generative tasks. However, reliance on computationally intensive heuristic optimization for iterative signal refinement results in high training overhead and local optima entrapment. To address these issues, we propose an Analytical Watermarking Framework for Controllable Generation (ALIEN). We develop the first analytical derivation of the timedependent modulation coefficient that guides the diffusion of watermark residuals to achieve controllable watermark embedding pattern. Experimental results show that ALIEN-Q outperforms the state-of-the-art by 33.1% across 5 quality metrics, and ALIEN-R demonstrates 14.0% improved robustness against generative variant and stability threats compared to the state-of-the-art across 15 distinct conditions. Code can be available at
+
+[p. 1 | section: 1. Introduction | type: Text]
+Text-to-image diffusion models, such as Stable Diffusion (Rombach et al., 2022) and DALL·E (Ramesh et al., 2022) , have demonstrated impressive capabilities in generating high-quality images. To safeguard the intellectual property of generative models (Gowal & Kohli, 2023) and facilitate misuse tracking (Barrett, 2023) , Governments are increasingly calling for regulations (European Union, 2024; Biden, 2023) to mandate watermark adoption. Robust and imperceptible watermarking of generated images has become a critical and urgent research focus. Post-processing watermarking (Cox et al., 2007) is applied to the contents gener-
+
+[p. 1 | section: 1. Introduction | type: FigureGroup]
+Figure 1. (a) Latent modification, (b) Constrained sampling, (c) Iterative optimization, (d) Our ALIEN with principled embedding.
+
+[p. 1 | section: 1. Introduction | type: Text]
+ated by the diffusion model, but its robustness is insufficient for reliable detection in real-world applications (Ren et al., 2024) . Some studies consider model distribution scenarios (Rezaei et al., 2024; Ci et al., 2024; Feng et al., 2024; Wang et al., 2025) . Diffusion models are fine-tuned to embed watermarks into the model parameters, which inevitably limits efficiency and scalability.
+
+[p. 1 | section: 1. Introduction | type: Text]
+Recent research has concentrated on semantic watermarking (Lee & Cho, 2025) , which aims to embed watermark signals into the semantic or latent features to better resist imageprocessing-based attacks (Zhao et al., 2024) . Watermarking methods based on initial latent variable modifications (Wen et al., 2024; Ci et al., 2025) embed watermarks by directly modifying or adding perturbations to the initial latents (Fig. 1( a)). While the mechanism is intuitive, the mapping between the initial latent space and the final image is highly complex and nonlinear, making direct modifications prone to semantic drift. Furthermore, to maintain invisibility, the amount of modification to the initial latents is strictly limited, making it difficult to increase watermark capacity. To ensure high capacity and lossless watermark embedding, Watermarks based on the Gaussian-Constrained Identifiable Subspace Sampling (Yang et al., 2024c; Gunn et al., 2024)
+
+[p. 2 | section: 1. Introduction | type: Text]
+combined with cryptography, divide the initial latent space into non-overlapping identifiable subspaces, forcing users to sample from subspaces associated with specific watermark information (Fig. 1( b)). This rigid constraint on the initial latent space limits generative diversity. Watermarking methods based on optimization (Huang et al., 2024; Zhang et al., 2024) perform watermark optimization in the latent space to better balance robustness and fidelity (Fig. 1( c)). However, their reliance on computationally intensive heuristic optimization to iteratively find the optimal watermark, leading to substantial training overhead and prone to local optima. Furthermore, detection of semantic watermarking typically depends on diffusion inversion, which limits applicability to reversible samplers (Lu et al., 2022) and watermarks become undetectable when images are generated with irreversible samplers (Karras et al., 2022) . Attackers can exploit this vulnerability to remove watermarks by regenerating images with irreversible schedulers. (An et al., 2024) .
+
+[p. 2 | section: 1. Introduction | type: Text]
+Despite the progress made by aforementioned semantic watermarking schemes in robust embedding, they circumvent a fundamental issue: the inability to derive a precise and efficient watermark embedding mechanism from the generative principles of diffusion models. Current optimization or constraint-based methods essentially avoid this problem, instead relying on computationally intensive optimization or sampling constraints. These approaches inherently limits the fidelity, efficiency, and diversity.
+
+[p. 2 | section: 1. Introduction | type: Text]
+To address these issues, we propose an Analytical Watermarking Framework for Controllable Generation (ALIEN). As shown in Fig. 1( d), unlike existing methods that rely on computationally intensive heuristic latent variable optimization or constraints on initial latent sampling, we start with the reverse process of the Stochastic Differential Equation of the diffusion model and present the first analytic derivation of the watermark residual propagation mechanism. Specifically, given a target watermark residual, we analytically derive a time-dependent modulation coefficient that transforms this target into a precise correction term for the noise prediction. By injecting this correction at each denoising step, we effectively modify the underlying probability flow of the diffusion model. This imposes a deterministic force that seamlessly guides the generation trajectory toward the watermarked state regardless of the sampling path, thereby eliminating the need for iterative optimization and ensuring compatibility with various samplers. ALIEN achieves a principled watermark embedding pattern, rather than relying on heuristic methods. Without the need for iterative optimization, we inject the precisely modulated watermark into the noise prediction target at each step of the denoising process.
+
+[p. 2 | section: 1. Introduction | type: Text]
+Our contributions are three-fold: (1) We achieve the first analytic derivation of watermark propagation for seamless,
+
+[p. 2 | section: 1. Introduction | type: Text]
+low-inference-cost embedding, eliminating the need for iterative optimization. (2) Since the watermark is precisely compensated based on diffusion model, ALIEN preserves semantic consistency and visual fidelity by leveraging precise theoretical compensation for the watermark signal. (3) The ALIEN watermark embedding mechanism is independent of specific initial latent variables and sampler types (including irreversible samplers), solving the issue of strong reliance on reversible samplers of semantic watermarking.
+
+[p. 2 | section: 2. Related Work | type: Text]
+Diffusion models exhibit exceptional performance in image generation (Dhariwal & Nichol, 2021) , leveraging the methodology (Ho et al., 2020; Song et al., 2020b) and the sampling techniques (Song et al., 2020a; Song & Ermon, 2020) . LDMs optimize image generation within the latent space of the pretrained Variational Autoencoder (VAE), which further accelerates the practical applications of diffusion models. During the inference phase, LDM first samples an initial latent z T ∈ R c×w×h from a standard Gaussian distribution N (0, I), where T denotes the total time step of the diffusion model. Following iterative denoising, the latent vector evolves into the noise-free representation z0. The final image x 0 is reconstructed by the VAE decoder from z0. Safeguarding the intellectual property of generated content and preventing misuse have become critical research priorities. This paper focuses on critical issues of fidelity, efficiency, and controllability in existing approaches for integrating watermarking into the diffusion process.
+
+[p. 2 | section: 2. Related Work | type: Text]
+Watermarking in Latent Diffusion Models aims at tracking the origin and ensuring the accountability of the generated content. For a comprehensive context regarding the taxonomy of existing watermarking methods a detailed review is provided in Appendix D. We specifically focus on prior work integrating watermarking during the diffusion process. Latent modification Watermark such as Tree-Ring (Wen et al., 2024) and RingID (Ci et al., 2025) embed watermarks in the Fourier space of the initial latent which leads to semantic drift. Constrained sampling watermark such as Gaussian Shading (Yang et al., 2024c) , GaussMarker (Li et al., 2025) and PRC (Gunn et al., 2024) utilize cryptographic principles to modify the sampling pattern, but strict constraints limit the sampling range, resulting in reduced controllability. Optimization-based methods such as Zodiac (Zhang et al., 2024) and Robin (Huang et al., 2024) , optimize latent variables for higher semantic consistency, but reliance on heuristic optimization incurs computational costs. The detection of aforementioned methods depends on diffusion inversion, limiting their function to reversible samplers and is ineffective with irreversible samplers. Our method achieves low-overhead and universally applicable watermark via analytic derivation.
+
+[p. 3 | section: 2. Related Work | type: Caption]
+Figure 2. The ALIEN framework consists of two main stages: (Top) Imperceptible Latent Watermark Generation, where a secret encoder E_s and decoder D_s are trained to embed a message m into a robust latent residual \delta_w while preserving image quality. (Bottom) Analytic SDE Reverse Drift Correction, which applies the time-dependent modulation to the noise prediction. This principled correction steers the generative trajectory to satisfy the watermark constraint in a sampler-agnostic manner.
+
+[p. 3 | section: 3. Methodology | type: Text]
+132133
+
+[p. 3 | section: 3.1. Framework of ALIEN | type: Text]
+We extend to achieve applicability and theoretical controllability of semantic watermarking. As demonstrated in Fig. 2, our ALIEN embeds the watermark in intermediate diffusion states to manipulate the generation trajectory through precise correction of the probability flow. To generate imperceptible watermark residuals, we implement an Imperceptible Latent Watermark Generation module to generate the invisible and robust watermark residual in the latent space. For principled embedding, we propose Analytic SDE Reverse Drift Correction, which analytically derives the necessary modifications to the probability flow required by the diffusion model for watermark embedding under Variance Preserving Stochastic Differential Equation (VP-SDE) (Song et al., 2020b), providing an explicit correction target for noise prediction that is compatible with both stochastic and deterministic sampling processes. This derived target is implemented via the Modulation of Noise Prediction Target module, which specifies the requisite adjustment to the model's noise prediction output, thereby realizing the controlled and imperceptible semantic watermarking.
+
+[p. 3 | section: 3.2. Imperceptible Latent Watermark Generation | type: Text]
+To generate an imperceptible yet robust watermark residual, we jointly train a secret encoder E_s and a watermark decoder D_s . Ideally, the watermarked latent representation z_w should be conditioned on both the input latent z_0 and the
+
+[p. 3 | section: 3.2. Imperceptible Latent Watermark Generation | type: Text]
+message m to enhance imperceptibility. However, utilizing a z_0 -dependent watermark becomes impractical as the intermediate latent states of the diffusion model are not readily accessible for deterministic conditioning. Therefore, we opt to embed a cover-agnostic watermark prominent in the latent space. Specifically, the secret residual \delta_w=E(m) is added to the input latent z_0 , forming the watermarked latent z_w=z_0+\delta_w . The watermarked image x_w is generated as x_w=\mathcal{D}(z_w) , and the message is extracted by applying the decoder D_s to z_w , yielding m'=D_s(z_w) . We employ the Binary Cross-Entropy loss to optimize for the accuracy of message extraction between the original message m and the decoded message m'.
+
+[p. 3 | section: 3.2. Imperceptible Latent Watermark Generation | type: Text]
+To ensure the visual consistency of the watermark, we compute the LPIPS loss (Zhang et al., 2018) and the Mean Squared Error loss between the watermarked image x_w and the reconstructed image x_r , rather than between x_w and the original image x_o . This choice is necessary because the VAE compression and reconstruction already introduce a measurable irrecoverable quality gap between x_o and x_r . Optimizing against x_o would necessitate the watermark training process to compensate for VAE reconstruction errors, which would increase complexity and hinder embedding effectiveness. Our training objective can be summarized below, where \lambda_1 and \lambda_2 are coefficients:
+
+[p. 3 | section: 3.2. Imperceptible Latent Watermark Generation | type: Equation]
+\mathcal{L}_{T} = \mathcal{L}_{BCE}^{(m,m')} + \lambda_{1} \mathcal{L}_{LPIPS}^{(x_{r},x_{w})} + \lambda_{2} \mathcal{L}_{MSE}^{(x_{r},x_{w})}, (1)
+
+[p. 3 | section: 3.2. Imperceptible Latent Watermark Generation | type: Text]
+where \mathcal{L}_{BCE} is the Binary Cross-Entropy loss, \mathcal{L}_{LPIPS} is the Learned Perceptual Image Patch Similarity loss (Zhang
+
+[p. 4 | section: Algorithm 1 ALIEN Watermarking | type: Text]
+17: Return D_s(\mathcal{E}_{VAE}(\mathbf{x}_{wm}))
+
+[p. 4 | section: Algorithm 1 ALIEN Watermarking | type: Code]
+PHASE I: EMBEDDING 2: Input: Pre-trained U-Net \theta, Encoder E_s, Scheduler S, VAE \mathcal{D}_{VAE}, Prompt c, Secret m, Strength \lambda, Interval [T_{start}, T_{end}] 3: Output: Watermarked Image \mathbf{x}_{wm} 4: \delta_{wm} \leftarrow E_s(\mathbf{m}) 5: \mathbf{z}_t \sim \mathcal{N}(\mathbf{0}, \mathbf{I}) 6: for t = T down to 1 do \epsilon_{\theta}^{t} \leftarrow \text{CFG}(\theta, \mathbf{z}_{t}, S.\text{steps}[t], \mathbf{c}) \begin{aligned} & \text{if } T_{start} \leq t \leq T_{end} \text{ then} \\ & \epsilon_{\theta}^t \leftarrow \epsilon_{\theta}^t - \lambda \cdot \left(\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}}\right) \cdot \delta_{wm} \end{aligned} 10: \mathbf{z}_t \leftarrow S.\text{step}(\epsilon_{\theta}^t, t, \mathbf{z}_t).\text{prev\_sample} 11: 12: end for 13: \mathbf{x}_{wm} \leftarrow \mathcal{D}_{VAE}(\mathbf{z}_t) PHASE II: EXTRACTION 15: Input: Image \mathbf{x}_{wm}, \mathcal{E}_{VAE}, Decoder D_s 16: Output: Secret m'
+
+[p. 4 | section: Algorithm 1 ALIEN Watermarking | type: Text]
+et al., 2018), and \mathcal{L}_{MSE} is the Mean Squared Error loss. Existing studies (Wang et al., 2025; Meng et al., 2024) demonstrate that injecting and detecting watermarks in the latent space can inherently resist various common distortions. We follow prior practice by omitting the distortion layer during training (validated in Tab. 4). The effectiveness of watermark remains unaffected even if an adversary finetunes U-Net \theta and \mathcal{D} on clean images and uses a fine-tuned latent decoder \mathcal{D}' to generate images (validated in Fig. 8).
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+To achieve precise watermark embedding over the generative process, we leverage the VP-SDE to analytically derive the exact probability flow correction required for watermark embedding.
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+\mathbf{z}_0 Constraint. Our goal is to embed a predetermined watermark residual \delta_{wm} into the final denoised latent \mathbf{z}_0 , resulting in the \mathbf{z}_0 -space constraint \hat{\mathbf{z}}_0^{wm} = \hat{\mathbf{z}}_0^{orig} + \delta_{wm} , where \hat{\mathbf{z}}_0^{wm} and \hat{\mathbf{z}}_0^{orig} are the clean data estimates predicted by the U-Net for the current latent state \mathbf{z}_t , with and without the watermark, respectively.
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+Score Function. Under the VP-SDE, The diffusion process is defined by a forward SDE that gradually perturbs clean data into noise:
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Equation]
+d\mathbf{z} = \mathbf{f}(\mathbf{z}, t)dt + g(t)d\mathbf{w},
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+where \mathbf{f}(\mathbf{z}, t) : \mathbb{R}^d \to \mathbb{R}^d denotes the drift coefficient, while g(t) \in \mathbb{R} represents the scalar diffusion coefficient, with
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+(b) Injection Strength Schedule
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+Generation Step
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Caption]
+Figure 3. Comparison of ALIEN-R and ALIEN-Q. (a) The L2 norm of noise prediction during the diffusion process. (b) The evolution of injection strength \frac{\sqrt{\alpha_t}}{\sqrt{1-\bar{\alpha}_t}} .
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+\mathbf{w}(t) denoting the standard Wiener process. The reverse generation process of the diffusion model is governed by a reverse-time stochastic differential equation:
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Equation]
+d\mathbf{z} = \underbrace{[\mathbf{f}(\mathbf{z}, t) - g^{2}(t)\nabla_{\mathbf{z}}\log p_{t}(\mathbf{z})]}_{\text{Reverse Drift }\mathbf{F}_{rev}} dt + g(t)d\bar{\mathbf{w}}, \quad (2)
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+where \bar{\mathbf{w}} denotes the standard Wiener process in reverse time. To realize the watermark z_0 constraint, we precisely control the probability flow, which requires determining the necessary correction \Delta \mathbf{F}_{rev} for the reverse SDE drift term. Since \Delta \mathbf{F}_{rev} relies on the score function \nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t) , analytically quantifying the difference in the score function becomes a direct path to derive \Delta \mathbf{F}_{rev} . The score function is exactly and linearly related to the difference between \mathbf{z}_t and its denoised estimate \hat{\mathbf{z}}_0 . This analytical relationship is mathematically described as follows:
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Equation]
+\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t) = -\frac{1}{1 - \bar{\alpha}_t} (\mathbf{z}_t - \sqrt{\bar{\alpha}_t} \hat{\mathbf{z}}_0). (3)
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+Applying the analytical mapping Eq.3 allows us to analytically determine the difference in the score function induced by the \mathbf{z}_0 constraint, thereby translating the watermark residual \delta_{wm} into the required shift in the score function space.
+
+[p. 4 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+Probability Flow Correction. Based on the analytical structure of VP-SDE for the reverse drift term \mathbf{F}_{rev} , we derive
+
+[p. 5 | section: 3.3. Analytic SDE Reverse Drift Correction | type: TableGroup]
+Method G.S. StegaStamp Tree-Ring ROBIN ZoDiac AquaLoRA StableSig. ALIEN-Q ALIEN-R Original Image No Original Watermarked Image Residual (×10) Metrics PSNR:—— SSIM: :—— LPIPS: :—— PSNR:29.26 SSIM:0.909 LPIPS:0.065 PSNR:14.25 SSIM:0.570 LPIPS:0.488 PSNR:24.64 SSIM:0.917 LPIPS:0.091 PSNR:28.46 SSIM:0.921 LPIPS:0.046 SSIM:0.776 PSNR:29.61 SSIM:0.891 LPIPS:0.039 PSNR:33.29 SSIM:0.942 LPIPS:0.020 PSNR:27.24 SSIM:0.855 LPIPS:0.107 Figure 4. Qualitative comparison of watermarked samples and 10 \times magnified residuals. We compare ALIEN with baselines covering post-processing (StegaStamp), latent modification (Tree-Ring), optimization (ROBIN, ZoDiac), and fine-tuning (AquaLoRA, StableSig.).
+
+[p. 5 | section: 3.3. Analytic SDE Reverse Drift Correction | type: TableGroup]
+Table 1. Quantitative Comparison of Visual Quality and Fidelity across Watermarking Schemes. D.S. denotes the Dreamsim (Fu et al., 2023) metric. Method FID CLIP PSNR SSIM SIFID D.S. No WM 24.31 0.3368 _ StegaS. 24.56 0.3363 28.59 0.878 0.189 0.021 ZoDiac _ 28.01 0.922 0.121 0.022 AquaL. 24.79 0.3366 17.07 0.664 0.183 0.139 TreeR. 24.63 0.3370 12.76 0.429 0.741 0.291 G.S. 24.42 0.3378 _ _ ROBIN 24.61 0.3366 22.96 0.756 0.212 0.057 StableS. 24.56 0.3367 29.09 0.878 0.105 0.011 ALIEN-Q 24.29 0.3369 32.41 0.949 0.023 0.003 ALIEN-R 24.74 0.3366 20.42 0.745 0.227 0.061
+
+[p. 5 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+the required reverse SDE drift correction \Delta \mathbf{F}_{rev} to enforce the watermark constraint (Details provided in Appendix A). The resulting correction term \Delta \mathbf{F}_{rev} is analytically defined by the following expression:
+
+[p. 5 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Equation]
+\Delta \mathbf{F}_{rev}(\mathbf{z}_t, t) = -g^2(t) \frac{\sqrt{\bar{\alpha}_t}}{1 - \bar{\alpha}_t} \delta_{wm}. (4)
+
+[p. 5 | section: 3.3. Analytic SDE Reverse Drift Correction | type: Text]
+This analytical derivation Eq.4 provides the theoretical foundation for the ALIEN framework. It precisely quantifies the correction \Delta \mathbf{F}_{rev} required by the watermark objective \delta_{wm} within the SDE probability flow framework. Since this correction targets the score function of the latent distribution, it demonstrates that the watermark is sampler-agnostic.
+
+[p. 5 | section: 3.4. Modulation of Noise Prediction Target | type: Text]
+To achieve the practical implementation of the SDE drift correction \Delta \mathbf{F}_{rev} , we analytically relate the SDE reverse drift correction to the noise prediction offset of U-Net within the VP-SDE framework (Details provided in Appendix A), we derive the required compensation signal \Delta \epsilon_{wm} necessary
+
+[p. 5 | section: 3.4. Modulation of Noise Prediction Target | type: TableGroup]
+Table 2. Stability Evaluation measured by Detection Confidence. We assess robustness across Samplers (DPM++ SDE, Euler a., DPM2 a.), Inference Steps (25, 50), Guidance Scale (10, 20), and Model Versions (v1.5, v2.1). Method Sa ampler Steps Sc ale Model DPM-SDE Eulera DPM2a 25 50 10 20 v1.5 v2.1 StegaS. 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.990 0.999 StableS. 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 TreeR. 0.000 0.000 0.000 0.963 0.963 0.963 0.963 0.958 0.963 G.S. 0.557 0.586 0.552 0.999 0.999 0.999 0.999 0.999 0.999 AquaL. 0.952 0.953 0.939 0.945 0.955 0.940 0.939 0.954 ALIEN-Q 0.989 0.979 0.972 0.985 0.990 0.982 0.975 0.989 0.991 ALIEN-R 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999
+
+[p. 5 | section: 3.4. Modulation of Noise Prediction Target | type: Text]
+to enforce the \mathbf{z}_0 constraint:
+
+[p. 5 | section: 3.4. Modulation of Noise Prediction Target | type: Equation]
+\Delta \epsilon_{wm} = -\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}} \delta_{wm}. (5)
+
+[p. 5 | section: 3.4. Modulation of Noise Prediction Target | type: Text]
+Refer to Eq. (5), to realize a fixed watermark residual \delta_{wm} in the \mathbf{z}_0 space, the U-Net will introduce a time-dependent compensation signal \Delta\epsilon_{wm} proportional to the watermark residual in its noise prediction. As illustrated in Fig. 3, the injection coefficient exhibits a surge approaching \mathbf{z}_0 , implying that late-stage injection yields stronger constraints but risks visual fidelity. We adjust the injection magnitude and timestep range to formulate two configurations: ALIEN-Q (Quality-Oriented) and ALIEN-R (Robustness-Oriented). The procedure is outlined in Alg. 1.
+
+[p. 5 | section: 4.1. Experimental Setup | type: Text]
+Watermarking Baselines. We compare ALIEN with mainstream latent semantic watermarking schemes across three primary categories: the initial latent variable modification
+
+[p. 6 | section: 4.1. Experimental Setup | type: TableGroup]
+Table 3. Robustness Evaluation across variant Regenerative Attacks. Each cell reports performance under three attacks: Regeneration → Rinse-2X → Rinse-4X. Values denote Detection Confidence/ TPR@1%FPR. Method Scheduler (Cell Format: Regen. Data | Rinse-2X Data | Rinse-4X Data) DDIM DPM++ 2M SDE Euler a DPM2 a StegaS. 0.692/0.957 | 0.578/0.347 | 0.531/0.102 0.636/0.575 | 0.562/0.182 | 0.502/0.000 0.624/0.631 | 0.542/0.180 | 0.513/0.000 0.615/0.591 | 0.556/0.120 | 0.495/0.000 ZoDiac 0.938/1.000 | 0.743/0.104 | 0.527/0.032 0.693/0.585 | 0.670/0.431 | 0.562/0.125 0.643/0.315 | 0.643/0.250 | 0.628/0.210 0.833/0.650 | 0.572/0.281 | 0.520/0.152 TreeR. 0.868/1.000 | 0.724/0.861 | 0.408/0.489 0.855/0.918 | 0.824/0.905 | 0.753/0.851 0.821/0.941 | 0.449/0.512 | 0.277/0.306 0.647/0.755 | 0.531/0.656 | 0.326/0.427 G.S. 0.978/1.000 | 0.898/1.000 | 0.845/1.000 0.943/1.000 | 0.953/1.000 | 0.926/1.000 0.946/1.000 | 0.847/1.000 | 0.695/0.905 0.923/1.000 | 0.858/1.000 | 0.711/0.915 AquaL. 0.757/0.742 | 0.627/0.145 | 0.573/0.000 0.879/0.942 | 0.833/0.858 | 0.696/0.486 0.663/0.225 | 0.618/0.078 | 0.551/0.000 0.679/0.371 | 0.604/0.086 | 0.536/0.029 ROBIN —- /0.638 | —- /0.242 | —- /0.153 —- /1.000 | —- /0.728 | —- /0.275 —- /0.980 | —- /0.705 | —- /0.486 —- /0.075 | —- /0.105 | —- /0.100 StableS. 0.496/0.000 | 0.477/0.000 | 0.521/0.000 0.512/0.000 | 0.512/0.000 | 0.510/0.000 0.498/0.000 | 0.520/0.000 | 0.513/0.000 0.506/0.000 | 0.485/0.000 | 0.502/0.000 ALIEN-Q 0.848/1.000 | 0.752/0.865 | 0.618/0.342 0.935/1.000 | 0.898/1.000 | 0.842/0.942 0.866/1.000 | 0.661/0.581 | 0.563/0.163 0.857/1.000 | 0.673/0.636 | 0.581/0.124 ALIEN-R 0.999/1.000 | 0.908/1.000 | 0.829/1.000 0.999/1.000 | 0.989/1.000 | 0.967/1.000 0.988/1.000 | 0.908/1.000 | 0.731/0.727 0.989/1.000 | 0.878/1.000 | 0.742/0.875
+
+[p. 6 | section: 4.1. Experimental Setup | type: TableGroup]
+Gaussian Shading Tree-ring AquaLoRA ALIEN-Q ALIEN-R DDIM Original No Original DDIM Watermarked DPM2 a Watermarked Euler a Watermarked DPM++ 2M SDE Watermarked Figure 5. Visual Comparison under Different Generation Schedulers (DDIM, DPM2 a, Euler a, and DPM++ 2M SDE).
+
+[p. 6 | section: 4.1. Experimental Setup | type: Text]
+method Tree-Ring (Wen et al., 2024) ; the constrained sampling method Gaussian Shading (Yang et al., 2024c) ; and the iterative optimization methods ROBIN (Huang et al., 2024) and Zodiac (Zhang et al., 2024) . Additionally, we select the fine-tuning based method Stable Signature (Fernandez et al., 2023) and Aqualora (Feng et al., 2024) , as well as the post-processing image watermarking technique StegaStamp (Tancik et al., 2020) . Implementation details can be found in Appendix B.2.
+
+[p. 6 | section: 4.1. Experimental Setup | type: Text]
+Models and Tasks. Following existing research (Yang et al., 2024c) , we implement the ALIEN framework on Stable Diffusion v1.5 and Stable Diffusion v2.1. We evaluate our method across two tasks: (1) Detection. All compared methods are configured as single-bit watermarks with a unified pattern. The detection threshold is set individually for each method to achieve a False Positive Rate (FPR) of approximately 1%. (2) Traceability. Multi-bit watermarking methods are evaluated using Bit Accuracy. Single-bit methods, including Tree-ring, Zodiac, and Robin, are excluded due to their lack of watermark capacity. We use prompts
+
+[p. 6 | section: 4.1. Experimental Setup | type: PictureGroup]
+Figure 6. Visual Comparison under Regeneration Attacks (DDIM, DPM2 a, Euler a, and DPM++ 2M SDE).
+
+[p. 6 | section: 4.1. Experimental Setup | type: Text]
+from Stable Diffusion-Prompts (SDP) (Gustavosta, 2023) , setting the Guidance Scale to 7.5 and the number of sampling steps to 50. Both TPR@1%FPR and Bit Accuracy are computed over 350 watermarked images.
+
+[p. 6 | section: 4.2. Comparison to Baselines | type: Text]
+Watermark Fidelity. We employ PSNR (Hore & Ziou, 2010) and SSIM (Wang et al., 2004) for pixel fidelity, LPIPS (Zhang et al., 2018) and DreamSim (Fu et al., 2023) for perceptual similarity, FID (Heusel et al., 2017) and SIFID (Yang et al., 2024a) for realism, and CLIP Score (Radford et al., 2021) for semantic alignment. As shown in Tab. 1, ALIEN-Q achieves state-of-the-art imperceptibility, significantly outperforming all baselines. It yields the highest pixel fidelity of 32.41 dB PSNR and the best perceptual quality of 0.003 DreamSim, while maintaining FID and CLIP scores comparable to non-watermarked images.
+
+[p. 6 | section: 4.2. Comparison to Baselines | type: Text]
+Watermark Stability. We validate watermark stability across three dimensions: Sampler Agnosticism covers both
+
+[p. 7 | section: 4.2. Comparison to Baselines | type: TableGroup]
+Table 4. Comprehensive Comparison of Watermark Robustness. Performance is reported in decimal scale (0-1). Higher values are better (↑). The Avg. column represents the mean performance across all 11 attacks (excluding No Attack). Top section: TPR@1%FPR; Bottom section: Bit Accuracy. Metrics Method No Photo netric De egradati on Ge eometric ; C enerative Avg. Attack Bright. Contr. JPEG Blur Noise ReScale C.C. R.C. VAE-B VAE-C Diff. StegaS. 1.000 0.964 1.000 1.000 1.000 1.000 1.000 0.964 0.975 1.000 1.000 1.000 0.991 StableS. 1.000 0.958 1.000 0.781 0.973 0.042 0.935 1.000 1.000 0.000 0.079 0.000 0.611 AquaL. 1.000 0.289 0.507 1.000 1.000 0.932 1.000 0.127 0.258 0.975 0.958 0.742 0.708 TreeR. 1.000 0.775 0.909 1.000 1.000 0.954 0.968 0.013 0.021 0.954 1.000 1.000 0.778 TPR@ G.S. 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.981 0.979 1.000 1.000 1.000 0.996 Thre1%FPR ROBIN 1.000 0.913 0.684 0.921 1.000 0.013 0.935 1.000 1.000 1.000 1.000 0.638 0.826 ZoDiac 1.000 0.535 0.375 0.959 0.979 0.357 0.965 0.017 0.021 0.660 0.685 1.000 0.592 ALIEN-Q 1.000 0.783 1.000 0.954 1.000 0.645 1.000 0.153 0.311 0.965 0.970 0.945 0.793 ALIEN-R 1.000 1.000 1.000 1.000 1.000 0.979 1.000 0.989 0.988 1.000 1.000 1.000 0.996 StegaS. 0.999 0.811 0.850 0.999 0.999 0.821 0.999 0.667 0.681 0.837 0.816 0.692 0.834 StableS. 0.998 0.892 0.851 0.712 0.845 0.535 0.878 0.991 0.993 0.506 0.541 0.489 0.748 Bit Acc. AquaL. 0.954 0.583 0.672 0.935 0.954 0.810 0.925 0.573 0.648 0.845 0.856 0.757 0.778 Bit Acc. G.S. 0.999 0.939 0.964 0.995 0.999 0.903 0.996 0.657 0.655 0.996 0.997 0.978 0.916 ALIEN-Q 0.989 0.753 0.803 0.889 0.936 0.689 0.903 0.581 0.601 0.834 0.853 0.848 0.790 ALIEN-R 0.999 0.949 0.992 0.999 0.999 0.855 0.999 0.826 0.835 0.979 0.983 0.999 0.947
+
+[p. 7 | section: 4.2. Comparison to Baselines | type: FigureGroup]
+Figure 7. Robustness against VAE embedding attacks. Results are averaged across KLVAE8, KLVAE16, and SDXL variants.
+
+[p. 7 | section: 4.2. Comparison to Baselines | type: FigureGroup]
+Figure 8. Bit accuracy comparison against Stable Signature across VAE fine-tuning and replacement.
+
+[p. 7 | section: 4.2. Comparison to Baselines | type: Text]
+deterministic (DDIM) and irreversible samplers (Euler Ancestral (Karras et al., 2022), DPM++ 2M Ancestral (Karras et al., 2022), DPM++ SDE (Lu et al., 2025)); Component Adaptability involves substituting different VAE and U-Net versions; and Hyperparameter Stability examines sensitivity to Guidance Scale and Inference Steps. As shown in Tab. 2, existing training-free methods exhibit vulnerability to stochastic samplers. Specifically, Tree-Ring and Gaussian Shading fail completely under DPM++ SDE, Euler a., and DPM2 a., where accuracy hovers near the randomguess baseline. ALIEN achieves state-of-the-art sampler agnosticism by maintaining high bit accuracy exceeding 0.97 across all tested schedulers. Our method demonstrates consistent stability across varying inference steps, guidance scales, and model versions.
+
+[p. 7 | section: 4.2. Comparison to Baselines | type: Text]
+Watermark Efficiency. We evaluate the computational overhead across two primary dimensions: Preparation Cost , the one-time offline cost, and Runtime Cost , the online perimage latency for embedding and extraction. The comparative results are detailed in Tab. 7. ALIEN achieves latencies of 0.079 seconds for embedding and 0.023 seconds for ex-
+
+[p. 7 | section: 4.2. Comparison to Baselines | type: Text]
+traction, maintaining speeds comparable to post-processing baselines while being orders of magnitude faster than the optimization-based method Zodiac, which requires over 122 seconds per image.
+
+[p. 7 | section: 4.2. Comparison to Baselines | type: Text]
+Watermark Robustness. We examine watermark's robustness against three typical kinds of adversarial attacks, including image processing attacks (Hore & Ziou, 2010) for transforming generated images, adversarial attacks (An et al., 2024) for disturbing watermark verification, and reconstructive attacks (Zhao et al., 2023) for re-generating nonwatermarked images. Please refer to the Supplementary Materials for detailed parameter settings. As demonstrated in Tab. 4, ALIEN-R achieves state-of-the-art stability against standard distortions by maintaining a True Positive Rate of 0.996. In adversarial embedding scenarios illustrated in Fig. 7, ALIEN-R exhibits exceptional resistance where latent semantic watermarking baselines degrade rapidly. Tab. 3 shows that against reconstructive attacks, ALIEN-R sustains a high confidence exceeding 0.875 even after four re-generation rounds, whereas competitors like StegaStamp and Stable Signature collapse to near-zero.
+
+[p. 8 | section: 4.2. Comparison to Baselines | type: TableGroup]
+Table 5. Quantitative comparison under Forgery Attacks. Lower values indicate better resistance (\downarrow) . Config G.S. Tree-Ring ALIEN (Ours) comig Acc. / PSNR Acc. / PSNR Acc. / PSNR Scenario A: Average Forgery 10 Imgs 0.952 / 12.23 0.882 / 18.86 0.539 / 20.06 50 Imgs 0.969 / 12.79 0.908 / 20.34 0.605 / 25.29 100 Imgs 0.969 / 12.65 0.910 / 20.95 0.708 / 26.48 Scenario B: Reprompt Forgery SD-V2.1 1.000 / 0.931 / 0.533 /
+
+[p. 8 | section: 4.2. Comparison to Baselines | type: FigureGroup]
+Figure 9. Robustness against Imprinting Forgery Attack.
+
+[p. 8 | section: 4.2. Comparison to Baselines | type: Text]
+Forgery Resistance. Following existing research (Müller et al., 2025; Yang et al., 2024b), we evaluate the security of our method against three representative forgery attacks: imprinting forgery, reprompting forgery, and average forgery. Imprinting and reprompting forgeries rely on latent optimization via diffusion inversion. ALIEN exhibits superior resistance to these attacks compared to initial-latent-based watermarks. While baselines like Tree-Ring and Gaussian Shading can be successfully forged using only a single image, ALIEN remains unaffected. Average Forgery involves estimating the watermark pattern by collecting pairs of watermarked and non-watermarked images. While baselines like Tree-Ring exhibit vulnerability with confidence exceeding 0.9, ALIEN maintains a suppressed confidence of 0.711, effectively preventing the rapid extraction of the watermark pattern. The practical challenges in acquiring large-scale specific-user data within real-world API scenarios significantly elevate the security threshold.
+
+[p. 8 | section: 4.2. Comparison to Baselines | type: Text]
+Impact of Timestep Range. As shown in Tab. 6, we conducted an ablation study on the injection interval to investigate the trade-off between imperceptibility and robustness. Injecting the watermark across the full reverse process from step 50 down to 1 ensures perfect detection with 1.000 accuracy but introduces significant perceptual degradation, resulting in a PSNR drop to 20.42 dB under Strength B. Narrowing the window to early diffusion stages such as steps 45 to 20 significantly recovers image quality, where the PSNR
+
+[p. 8 | section: 4.2. Comparison to Baselines | type: TableGroup]
+Table 6. Ablation study on Timestep Range under different Watermark Strengths. We compare Image Quality (PSNR) and Detection Performance (Det./Acc.) across two strength settings. Range Strengt \mathbf{th} \mathbf{A} (\lambda = 0.5) Strength B ( \lambda = 1.0 ) (t_{start} \rightarrow t_{end}) PSNR Det. / Acc. PSNR Det. / Acc. \begin{array}{c} 1 \to 50 \\ 25 \to 50 \\ 25 \to 40 \\ 10 \to 25 \\ 20 \to 45 \end{array} 24.55 30.53 40.94 31.54 33.76 1.000 / 1.000 1.000 / 1.000 0.718 / 0.747 0.614 / 0.421 0.882 / 1.000 20.42 26.27 23.10 26.83 31.10 1.000 / 1.000 1.000 / 1.000 0.852 / 1.000 0.681 / 0.721 0.989 / 1.000 Table 7. Performance Comparison regarding Computational Efficiency. <sup>‡</sup> indicates data estimated from original papers.
+
+[p. 8 | section: 4.2. Comparison to Baselines | type: Table]
+Method P rep. Time ( h) Embed. E 111011101 Pre-train Fine-tune Optimize Time (s) Time (s) T.R. _ _ _ 0.011 3.575 G.S. _ 0.102 4.212 ROBIN _ _ 0.4 0.125 1.248 Zodiac _ 122.4 3.601 StegaS. 30 0.108 0.028 S.S. 48^{\ddagger} 0.1 _ _ 0.014 AquaL. 40^{\ddagger} 15 ‡ _ _ 0.026 ALIEN 22 _ _ 0.079 0.023
+
+[p. 8 | section: 4.2. Comparison to Baselines | type: Text]
+increases to 33.76 dB under Strength A while maintaining a high detection rate.
+
+[p. 8 | section: 4.2. Comparison to Baselines | type: Text]
+Impact of Watermark Strength. As shown in Tab. 6, the injection coefficient \lambda directly modulates the magnitude of the probability flow correction. Increasing the strength from \lambda=0.5 in Strength A to \lambda=1.0 in Strength B consistently improves detection performance across all ranges. we select the range from 45 to 20 combined with moderate strength as the optimal configuration for ALIEN-Q to maximize quality while ensuring reliable detection.
+
+[p. 8 | section: 5. Conclusion | type: Text]
+Unlike prior approaches relying on heuristic latent modifications, sampling constraints, or computationally intensive optimization, we propose ALIEN, which presents the first analytical derivation of the time-dependent modulation coefficient. This principled approach precisely guides the diffusion of watermark residuals via probability flow modulation, achieving sampler-agnostic embedding. ALIEN overcomes the security vulnerabilities associated with diffusion inversion and irreversible samplers while ensuring high fidelity and low inference cost. Experimental results demonstrate that ALIEN outperforms existing methods in both quality and robustness. Future research will focus on developing content-aware latent watermarking to further enhance security against forgery attacks.
+
+[p. 9 | section: 6. Impact Statement | type: Text]
+Ensuring the accountability and intellectual property protection of generative models has become a critical priority. This paper introduces ALIEN, a principled watermarking framework that enables robust and sampler-agnostic provenance tracking for Latent Diffusion Models. By overcoming the vulnerability of existing methods to irreversible samplers and diverse attacks, we believe our approach effectively mitigates risks such as copyright infringement and malicious misuse, thereby contributing to the development of safer and more trustworthy generative AI.

icml26/6b484833-bf42-4409-a685-ed34a504bfa9/paper.md

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+# 006 007
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+## 008 009 010 011 012
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+# ALIEN: Analytic Latent Watermarking for Controllable Generation
+
+## Anonymous Authors<sup>1</sup>
+
+## Abstract
+
+Watermarking is a technical alternative to safeguarding intellectual property and reducing misuse. Existing methods focus on optimizing watermarked latent variables to balance watermark robustness and fidelity, as Latent diffusion models (LDMs) are considered a powerful tool for generative tasks. However, reliance on computationally intensive heuristic optimization for iterative signal refinement results in high training overhead and local optima entrapment. To address these issues, we propose an Analytical Watermarking Framework for Controllable Generation (ALIEN). We develop the first analytical derivation of the timedependent modulation coefficient that guides the diffusion of watermark residuals to achieve controllable watermark embedding pattern. Experimental results show that ALIEN-Q outperforms the state-of-the-art by 33.1% across 5 quality metrics, and ALIEN-R demonstrates 14.0% improved robustness against generative variant and stability threats compared to the state-of-the-art across 15 distinct conditions. Code can be available at https://anonymous.4open.science/r/ALIEN/.
+
+## 1. Introduction
+
+Text-to-image diffusion models, such as Stable Diffusion [\(Rombach et al.,](#page-9-0) [2022\)](#page-9-0) and DALL·E [\(Ramesh et al.,](#page-9-1) [2022\)](#page-9-1), have demonstrated impressive capabilities in generating high-quality images. To safeguard the intellectual property of generative models [\(Gowal & Kohli,](#page-8-0) [2023\)](#page-8-0) and facilitate misuse tracking [\(Barrett,](#page-8-1) [2023\)](#page-8-1), Governments are increasingly calling for regulations [\(European Union,](#page-8-2) [2024;](#page-8-2) [Biden,](#page-8-3) [2023\)](#page-8-3) to mandate watermark adoption. Robust and imperceptible watermarking of generated images has become a critical and urgent research focus. Post-processing watermarking [\(Cox et al.,](#page-8-4) [2007\)](#page-8-4) is applied to the contents gener-
+
+Preliminary work. Under review by the International Conference on Machine Learning (ICML). Do not distribute.
+
+<span id="page-0-0"></span>![](_page_0_Figure_20.jpeg)
+
+*Figure 1.* (a) Latent modification, (b) Constrained sampling, (c) Iterative optimization, (d) Our ALIEN with principled embedding.
+
+ated by the diffusion model, but its robustness is insufficient for reliable detection in real-world applications [\(Ren et al.,](#page-9-2) [2024\)](#page-9-2). Some studies consider model distribution scenarios [\(Rezaei et al.,](#page-9-3) [2024;](#page-9-3) [Ci et al.,](#page-8-5) [2024;](#page-8-5) [Feng et al.,](#page-8-6) [2024;](#page-8-6) [Wang](#page-9-4) [et al.,](#page-9-4) [2025\)](#page-9-4). Diffusion models are fine-tuned to embed watermarks into the model parameters, which inevitably limits efficiency and scalability.
+
+Recent research has concentrated on semantic watermarking [\(Lee & Cho,](#page-9-5) [2025\)](#page-9-5), which aims to embed watermark signals into the semantic or latent features to better resist imageprocessing-based attacks [\(Zhao et al.,](#page-10-0) [2024\)](#page-10-0). Watermarking methods based on initial latent variable modifications [\(Wen et al.,](#page-9-6) [2024;](#page-9-6) [Ci et al.,](#page-8-7) [2025\)](#page-8-7) embed watermarks by directly modifying or adding perturbations to the initial latents (Fig. [1\(](#page-0-0)a)). While the mechanism is intuitive, the mapping between the initial latent space and the final image is highly complex and nonlinear, making direct modifications prone to semantic drift. Furthermore, to maintain invisibility, the amount of modification to the initial latents is strictly limited, making it difficult to increase watermark capacity. To ensure high capacity and lossless watermark embedding, Watermarks based on the Gaussian-Constrained Identifiable Subspace Sampling [\(Yang et al.,](#page-9-7) [2024c;](#page-9-7) [Gunn et al.,](#page-8-8) [2024\)](#page-8-8)
+
+<sup>1</sup>Anonymous Institution, Anonymous City, Anonymous Region, Anonymous Country. Correspondence to: Anonymous Author <anon.email@domain.com>.
+
+{1}------------------------------------------------
+
+combined with cryptography, divide the initial latent space into non-overlapping identifiable subspaces, forcing users to sample from subspaces associated with specific watermark information (Fig. [1\(](#page-0-0)b)). This rigid constraint on the initial latent space limits generative diversity. Watermarking methods based on optimization [\(Huang et al.,](#page-8-9) [2024;](#page-8-9) [Zhang et al.,](#page-9-8) [2024\)](#page-9-8) perform watermark optimization in the latent space to better balance robustness and fidelity (Fig. [1\(](#page-0-0)c)). However, their reliance on computationally intensive heuristic optimization to iteratively find the optimal watermark, leading to substantial training overhead and prone to local optima. Furthermore, detection of semantic watermarking typically depends on diffusion inversion, which limits applicability to reversible samplers [\(Lu et al.,](#page-9-9) [2022\)](#page-9-9) and watermarks become undetectable when images are generated with irreversible samplers [\(Karras et al.,](#page-8-10) [2022\)](#page-8-10). Attackers can exploit this vulnerability to remove watermarks by regenerating images with irreversible schedulers. [\(An et al.,](#page-8-11) [2024\)](#page-8-11).
+
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+106
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+108 109 Despite the progress made by aforementioned semantic watermarking schemes in robust embedding, they circumvent a fundamental issue: the inability to derive a precise and efficient watermark embedding mechanism from the generative principles of diffusion models. Current optimization or constraint-based methods essentially avoid this problem, instead relying on computationally intensive optimization or sampling constraints. These approaches inherently limits the fidelity, efficiency, and diversity.
+
+To address these issues, we propose an Analytical Watermarking Framework for Controllable Generation (ALIEN). As shown in Fig. [1\(](#page-0-0)d), unlike existing methods that rely on computationally intensive heuristic latent variable optimization or constraints on initial latent sampling, we start with the reverse process of the Stochastic Differential Equation of the diffusion model and present the first analytic derivation of the watermark residual propagation mechanism. Specifically, given a target watermark residual, we analytically derive a time-dependent modulation coefficient that transforms this target into a precise correction term for the noise prediction. By injecting this correction at each denoising step, we effectively modify the underlying probability flow of the diffusion model. This imposes a deterministic force that seamlessly guides the generation trajectory toward the watermarked state regardless of the sampling path, thereby eliminating the need for iterative optimization and ensuring compatibility with various samplers. ALIEN achieves a principled watermark embedding pattern, rather than relying on heuristic methods. Without the need for iterative optimization, we inject the precisely modulated watermark into the noise prediction target at each step of the denoising process.
+
+Our contributions are three-fold: (1) We achieve the first analytic derivation of watermark propagation for seamless, low-inference-cost embedding, eliminating the need for iterative optimization. (2) Since the watermark is precisely compensated based on diffusion model, ALIEN preserves semantic consistency and visual fidelity by leveraging precise theoretical compensation for the watermark signal. (3) The ALIEN watermark embedding mechanism is independent of specific initial latent variables and sampler types (including irreversible samplers), solving the issue of strong reliance on reversible samplers of semantic watermarking.
+
+## 2. Related Work
+
+Diffusion models exhibit exceptional performance in image generation [\(Dhariwal & Nichol,](#page-8-12) [2021\)](#page-8-12), leveraging the methodology [\(Ho et al.,](#page-8-13) [2020;](#page-8-13) [Song et al.,](#page-9-10) [2020b\)](#page-9-10) and the sampling techniques [\(Song et al.,](#page-9-11) [2020a;](#page-9-11) [Song & Ermon,](#page-9-12) [2020\)](#page-9-12). LDMs optimize image generation within the latent space of the pretrained Variational Autoencoder (VAE), which further accelerates the practical applications of diffusion models. During the inference phase, LDM first samples an initial latent z<sup>T</sup> ∈ R c×w×h from a standard Gaussian distribution N (0, I), where T denotes the total time step of the diffusion model. Following iterative denoising, the latent vector evolves into the noise-free representation z0. The final image x<sup>0</sup> is reconstructed by the VAE decoder from z0. Safeguarding the intellectual property of generated content and preventing misuse have become critical research priorities. This paper focuses on critical issues of fidelity, efficiency, and controllability in existing approaches for integrating watermarking into the diffusion process.
+
+Watermarking in Latent Diffusion Models aims at tracking the origin and ensuring the accountability of the generated content. For a comprehensive context regarding the taxonomy of existing watermarking methods a detailed review is provided in Appendix [D.](#page-16-0) We specifically focus on prior work integrating watermarking during the diffusion process. Latent modification Watermark such as Tree-Ring [\(Wen et al.,](#page-9-6) [2024\)](#page-9-6) and RingID [\(Ci et al.,](#page-8-7) [2025\)](#page-8-7) embed watermarks in the Fourier space of the initial latent which leads to semantic drift. Constrained sampling watermark such as Gaussian Shading [\(Yang et al.,](#page-9-7) [2024c\)](#page-9-7), GaussMarker [\(Li](#page-9-13) [et al.,](#page-9-13) [2025\)](#page-9-13) and PRC [\(Gunn et al.,](#page-8-8) [2024\)](#page-8-8) utilize cryptographic principles to modify the sampling pattern, but strict constraints limit the sampling range, resulting in reduced controllability. Optimization-based methods such as Zodiac [\(Zhang et al.,](#page-9-8) [2024\)](#page-9-8) and Robin [\(Huang et al.,](#page-8-9) [2024\)](#page-8-9), optimize latent variables for higher semantic consistency, but reliance on heuristic optimization incurs computational costs. The detection of aforementioned methods depends on diffusion inversion, limiting their function to reversible samplers and is ineffective with irreversible samplers. Our method achieves low-overhead and universally applicable watermark via analytic derivation.
+
+{2}------------------------------------------------
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+Figure 2. The ALIEN framework consists of two main stages: (Top) Imperceptible Latent Watermark Generation, where a secret encoder  $E_s$  and decoder  $D_s$  are trained to embed a message m into a robust latent residual  $\delta_w$  while preserving image quality. (Bottom) Analytic SDE Reverse Drift Correction, which applies the time-dependent modulation to the noise prediction. This principled correction steers the generative trajectory to satisfy the watermark constraint in a sampler-agnostic manner.
+
+## 3. Methodology
+
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+#### 3.1. Framework of ALIEN
+
+We extend to achieve applicability and theoretical controllability of semantic watermarking. As demonstrated in Fig. 2, our ALIEN embeds the watermark in intermediate diffusion states to manipulate the generation trajectory through precise correction of the probability flow. To generate imperceptible watermark residuals, we implement an Imperceptible Latent Watermark Generation module to generate the invisible and robust watermark residual in the latent space. For principled embedding, we propose Analytic SDE Reverse Drift Correction, which analytically derives the necessary modifications to the probability flow required by the diffusion model for watermark embedding under Variance Preserving Stochastic Differential Equation (VP-SDE) (Song et al., 2020b), providing an explicit correction target for noise prediction that is compatible with both stochastic and deterministic sampling processes. This derived target is implemented via the Modulation of Noise Prediction Target module, which specifies the requisite adjustment to the model's noise prediction output, thereby realizing the controlled and imperceptible semantic watermarking.
+
+#### 3.2. Imperceptible Latent Watermark Generation
+
+To generate an imperceptible yet robust watermark residual, we jointly train a secret encoder  $E_s$  and a watermark decoder  $D_s$ . Ideally, the watermarked latent representation  $z_w$  should be conditioned on both the input latent  $z_0$  and the
+
+message m to enhance imperceptibility. However, utilizing a  $z_0$ -dependent watermark becomes impractical as the intermediate latent states of the diffusion model are not readily accessible for deterministic conditioning. Therefore, we opt to embed a cover-agnostic watermark prominent in the latent space. Specifically, the secret residual  $\delta_w=E(m)$  is added to the input latent  $z_0$ , forming the watermarked latent  $z_w=z_0+\delta_w$ . The watermarked image  $x_w$  is generated as  $x_w=\mathcal{D}(z_w)$ , and the message is extracted by applying the decoder  $D_s$  to  $z_w$ , yielding  $m'=D_s(z_w)$ . We employ the Binary Cross-Entropy loss to optimize for the accuracy of message extraction between the original message m and the decoded message m'.
+
+To ensure the visual consistency of the watermark, we compute the LPIPS loss (Zhang et al., 2018) and the Mean Squared Error loss between the watermarked image  $x_w$  and the reconstructed image  $x_r$ , rather than between  $x_w$  and the original image  $x_o$ . This choice is necessary because the VAE compression and reconstruction already introduce a measurable irrecoverable quality gap between  $x_o$  and  $x_r$ . Optimizing against  $x_o$  would necessitate the watermark training process to compensate for VAE reconstruction errors, which would increase complexity and hinder embedding effectiveness. Our training objective can be summarized below, where  $\lambda_1$  and  $\lambda_2$  are coefficients:
+
+$$\mathcal{L}_{T} = \mathcal{L}_{BCE}^{(m,m')} + \lambda_{1} \mathcal{L}_{LPIPS}^{(x_{r},x_{w})} + \lambda_{2} \mathcal{L}_{MSE}^{(x_{r},x_{w})},$$
+ (1)
+
+where  $\mathcal{L}_{BCE}$  is the Binary Cross-Entropy loss,  $\mathcal{L}_{LPIPS}$  is the Learned Perceptual Image Patch Similarity loss (Zhang
+
+{3}------------------------------------------------
+
+## <span id="page-3-2"></span>Algorithm 1 ALIEN Watermarking
+
+17: **Return**  $D_s(\mathcal{E}_{VAE}(\mathbf{x}_{wm}))$ 
+
+```
+PHASE I: EMBEDDING
+ 2: Input: Pre-trained U-Net \theta, Encoder E_s, Scheduler S,
+        VAE \mathcal{D}_{VAE}, Prompt c, Secret m, Strength \lambda, Interval
+        [T_{start}, T_{end}]
+ 3: Output: Watermarked Image \mathbf{x}_{wm}
+ 4: \delta_{wm} \leftarrow E_s(\mathbf{m})
+ 5: \mathbf{z}_t \sim \mathcal{N}(\mathbf{0}, \mathbf{I})
+ 6: for t = T down to 1 do
+            \epsilon_{\theta}^{t} \leftarrow \text{CFG}(\theta, \mathbf{z}_{t}, S.\text{steps}[t], \mathbf{c})
+            \begin{aligned} & \text{if } T_{start} \leq t \leq T_{end} \text{ then} \\ & \epsilon_{\theta}^t \leftarrow \epsilon_{\theta}^t - \lambda \cdot \left(\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}}\right) \cdot \delta_{wm} \end{aligned}
+10:
+            \mathbf{z}_t \leftarrow S.\text{step}(\epsilon_{\theta}^t, t, \mathbf{z}_t).\text{prev\_sample}
+11:
+12: end for
+13: \mathbf{x}_{wm} \leftarrow \mathcal{D}_{VAE}(\mathbf{z}_t)
+                        PHASE II: EXTRACTION
+15: Input: Image \mathbf{x}_{wm}, \mathcal{E}_{VAE}, Decoder D_s
+16: Output: Secret m'
+```
+
+et al., 2018), and  $\mathcal{L}_{MSE}$  is the Mean Squared Error loss. Existing studies (Wang et al., 2025; Meng et al., 2024) demonstrate that injecting and detecting watermarks in the latent space can inherently resist various common distortions. We follow prior practice by omitting the distortion layer during training (validated in Tab. 4). The effectiveness of watermark remains unaffected even if an adversary finetunes U-Net  $\theta$  and  $\mathcal{D}$  on clean images and uses a fine-tuned latent decoder  $\mathcal{D}'$  to generate images (validated in Fig. 8).
+
+#### 3.3. Analytic SDE Reverse Drift Correction
+
+To achieve precise watermark embedding over the generative process, we leverage the VP-SDE to analytically derive the exact probability flow correction required for watermark embedding.
+
+ $\mathbf{z}_0$  Constraint. Our goal is to embed a predetermined watermark residual  $\delta_{wm}$  into the final denoised latent  $\mathbf{z}_0$ , resulting in the  $\mathbf{z}_0$ -space constraint  $\hat{\mathbf{z}}_0^{wm} = \hat{\mathbf{z}}_0^{orig} + \delta_{wm}$ , where  $\hat{\mathbf{z}}_0^{wm}$  and  $\hat{\mathbf{z}}_0^{orig}$  are the clean data estimates predicted by the U-Net for the current latent state  $\mathbf{z}_t$ , with and without the watermark, respectively.
+
+**Score Function.** Under the VP-SDE, The diffusion process is defined by a forward SDE that gradually perturbs clean data into noise:
+
+$$d\mathbf{z} = \mathbf{f}(\mathbf{z}, t)dt + g(t)d\mathbf{w},$$
+
+where  $\mathbf{f}(\mathbf{z}, t) : \mathbb{R}^d \to \mathbb{R}^d$  denotes the drift coefficient, while  $g(t) \in \mathbb{R}$  represents the scalar diffusion coefficient, with
+
+<span id="page-3-1"></span>![](_page_3_Figure_10.jpeg)
+
+![](_page_3_Figure_11.jpeg)
+
+(b) Injection Strength Schedule
+
+Generation Step
+
+Figure 3. Comparison of ALIEN-R and ALIEN-Q. (a) The L2 norm of noise prediction during the diffusion process. (b) The evolution of injection strength  $\frac{\sqrt{\alpha_t}}{\sqrt{1-\bar{\alpha}_t}}$ .
+
+ $\mathbf{w}(t)$  denoting the standard Wiener process. The reverse generation process of the diffusion model is governed by a reverse-time stochastic differential equation:
+
+$$d\mathbf{z} = \underbrace{[\mathbf{f}(\mathbf{z}, t) - g^{2}(t)\nabla_{\mathbf{z}}\log p_{t}(\mathbf{z})]}_{\text{Reverse Drift }\mathbf{F}_{rev}} dt + g(t)d\bar{\mathbf{w}}, \quad (2)$$
+
+where  $\bar{\mathbf{w}}$  denotes the standard Wiener process in reverse time. To realize the watermark  $z_0$  constraint, we precisely control the probability flow, which requires determining the necessary correction  $\Delta \mathbf{F}_{rev}$  for the reverse SDE drift term. Since  $\Delta \mathbf{F}_{rev}$  relies on the score function  $\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t)$ , analytically quantifying the difference in the score function becomes a direct path to derive  $\Delta \mathbf{F}_{rev}$ . The score function is exactly and linearly related to the difference between  $\mathbf{z}_t$  and its denoised estimate  $\hat{\mathbf{z}}_0$ . This analytical relationship is mathematically described as follows:
+
+<span id="page-3-0"></span>
+$$\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t) = -\frac{1}{1 - \bar{\alpha}_t} (\mathbf{z}_t - \sqrt{\bar{\alpha}_t} \hat{\mathbf{z}}_0).$$
+ (3)
+
+Applying the analytical mapping Eq.3 allows us to analytically determine the difference in the score function induced by the  $\mathbf{z}_0$  constraint, thereby translating the watermark residual  $\delta_{wm}$  into the required shift in the score function space.
+
+**Probability Flow Correction.** Based on the analytical structure of VP-SDE for the reverse drift term  $\mathbf{F}_{rev}$ , we derive
+
+{4}------------------------------------------------
+
+| Method               | G.S.                               | StegaStamp                              | Tree-Ring                               | ROBIN                                   | ZoDiac                                  | AquaLoRA   | StableSig.                              | ALIEN-Q                                 | ALIEN-R                                 |
+|----------------------|------------------------------------|-----------------------------------------|-----------------------------------------|-----------------------------------------|-----------------------------------------|------------|-----------------------------------------|-----------------------------------------|-----------------------------------------|
+| Original<br>Image    | No<br>Original                     |                                         |                                         |                                         |                                         |            |                                         |                                         |                                         |
+| Watermarked<br>Image |                                    |                                         |                                         |                                         |                                         |            |                                         |                                         |                                         |
+| Residual (×10)       |                                    |                                         |                                         |                                         |                                         |            |                                         |                                         |                                         |
+| Metrics              | PSNR:——<br>SSIM: :——<br>LPIPS: :—— | PSNR:29.26<br>SSIM:0.909<br>LPIPS:0.065 | PSNR:14.25<br>SSIM:0.570<br>LPIPS:0.488 | PSNR:24.64<br>SSIM:0.917<br>LPIPS:0.091 | PSNR:28.46<br>SSIM:0.921<br>LPIPS:0.046 | SSIM:0.776 | PSNR:29.61<br>SSIM:0.891<br>LPIPS:0.039 | PSNR:33.29<br>SSIM:0.942<br>LPIPS:0.020 | PSNR:27.24<br>SSIM:0.855<br>LPIPS:0.107 |
+
+Figure 4. Qualitative comparison of watermarked samples and  $10 \times$  magnified residuals. We compare ALIEN with baselines covering post-processing (StegaStamp), latent modification (Tree-Ring), optimization (ROBIN, ZoDiac), and fine-tuning (AquaLoRA, StableSig.).
+
+<span id="page-4-2"></span>*Table 1.* Quantitative Comparison of Visual Quality and Fidelity across Watermarking Schemes. D.S. denotes the Dreamsim (Fu et al., 2023) metric.
+
+| Method   | FID   | CLIP   | PSNR  | SSIM  | SIFID | D.S.  |
+|----------|-------|--------|-------|-------|-------|-------|
+| No WM    | 24.31 | 0.3368 |       |       | _     |       |
+| StegaS.  | 24.56 | 0.3363 | 28.59 | 0.878 | 0.189 | 0.021 |
+| ZoDiac   | _     |        | 28.01 | 0.922 | 0.121 | 0.022 |
+| AquaL.   | 24.79 | 0.3366 | 17.07 | 0.664 | 0.183 | 0.139 |
+| TreeR.   | 24.63 | 0.3370 | 12.76 | 0.429 | 0.741 | 0.291 |
+| G.S.     | 24.42 | 0.3378 | _     |       | _     |       |
+| ROBIN    | 24.61 | 0.3366 | 22.96 | 0.756 | 0.212 | 0.057 |
+| StableS. | 24.56 | 0.3367 | 29.09 | 0.878 | 0.105 | 0.011 |
+| ALIEN-Q  | 24.29 | 0.3369 | 32.41 | 0.949 | 0.023 | 0.003 |
+| ALIEN-R  | 24.74 | 0.3366 | 20.42 | 0.745 | 0.227 | 0.061 |
+
+the required reverse SDE drift correction  $\Delta \mathbf{F}_{rev}$  to enforce the watermark constraint (Details provided in Appendix A). The resulting correction term  $\Delta \mathbf{F}_{rev}$  is analytically defined by the following expression:
+
+<span id="page-4-0"></span>
+$$\Delta \mathbf{F}_{rev}(\mathbf{z}_t, t) = -g^2(t) \frac{\sqrt{\bar{\alpha}_t}}{1 - \bar{\alpha}_t} \delta_{wm}.$$
+ (4)
+
+This analytical derivation Eq.4 provides the theoretical foundation for the ALIEN framework. It precisely quantifies the correction  $\Delta \mathbf{F}_{rev}$  required by the watermark objective  $\delta_{wm}$  within the SDE probability flow framework. Since this correction targets the score function of the latent distribution, it demonstrates that the watermark is sampler-agnostic.
+
+#### 3.4. Modulation of Noise Prediction Target
+
+To achieve the practical implementation of the SDE drift correction  $\Delta \mathbf{F}_{rev}$ , we analytically relate the SDE reverse drift correction to the noise prediction offset of U-Net within the VP-SDE framework (Details provided in Appendix A), we derive the required compensation signal  $\Delta \epsilon_{wm}$  necessary
+
+<span id="page-4-3"></span>*Table 2.* Stability Evaluation measured by Detection Confidence. We assess robustness across Samplers (DPM++ SDE, Euler a., DPM2 a.), Inference Steps (25, 50), Guidance Scale (10, 20), and Model Versions (v1.5, v2.1).
+
+| Method   | Sa      | ampler |       | Steps |       | Sc    | ale   | Model |       |
+|----------|---------|--------|-------|-------|-------|-------|-------|-------|-------|
+|          | DPM-SDE | Eulera | DPM2a | 25    | 50    | 10    | 20    | v1.5  | v2.1  |
+| StegaS.  | 0.999   | 0.999  | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.990 | 0.999 |
+| StableS. | 0.999   | 0.999  | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |
+| TreeR.   | 0.000   | 0.000  | 0.000 | 0.963 | 0.963 | 0.963 | 0.963 | 0.958 | 0.963 |
+| G.S.     | 0.557   | 0.586  | 0.552 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |
+| AquaL.   | 0.952   | 0.953  | 0.939 | 0.945 | 0.955 | 0.940 | 0.939 | 0.954 |       |
+| ALIEN-Q  | 0.989   | 0.979  | 0.972 | 0.985 | 0.990 | 0.982 | 0.975 | 0.989 | 0.991 |
+| ALIEN-R  | 0.999   | 0.999  | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |
+
+to enforce the  $\mathbf{z}_0$  constraint:
+
+<span id="page-4-1"></span>
+$$\Delta \epsilon_{wm} = -\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}} \delta_{wm}.$$
+ (5)
+
+Refer to Eq. (5), to realize a fixed watermark residual  $\delta_{wm}$  in the  $\mathbf{z}_0$  space, the U-Net will introduce a time-dependent compensation signal  $\Delta\epsilon_{wm}$  proportional to the watermark residual in its noise prediction. As illustrated in Fig. 3, the injection coefficient exhibits a surge approaching  $\mathbf{z}_0$ , implying that late-stage injection yields stronger constraints but risks visual fidelity. We adjust the injection magnitude and timestep range to formulate two configurations: ALIEN-Q (Quality-Oriented) and ALIEN-R (Robustness-Oriented). The procedure is outlined in Alg. 1.
+
+#### 4. Experiments
+
+## 4.1. Experimental Setup
+
+Watermarking Baselines. We compare ALIEN with mainstream latent semantic watermarking schemes across three primary categories: the initial latent variable modification
+
+{5}------------------------------------------------
+
+324
+
+326
+
+328 329
+
+<span id="page-5-0"></span>*Table 3.* Robustness Evaluation across variant Regenerative Attacks. Each cell reports performance under three attacks: Regeneration → Rinse-2X → Rinse-4X. Values denote Detection Confidence/ TPR@1%FPR.
+
+| Method   |                                                                                                                                                                         | Scheduler (Cell Format: Regen. Data   Rinse-2X Data   Rinse-4X Data) |  |                                   |         |  |                                   |  |        |                                   |  |  |
+|----------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------|--|-----------------------------------|---------|--|-----------------------------------|--|--------|-----------------------------------|--|--|
+|          | DDIM                                                                                                                                                                    |                                                                      |  | DPM++ 2M SDE                      | Euler a |  |                                   |  | DPM2 a |                                   |  |  |
+| StegaS.  | 0.692/0.957   0.578/0.347   0.531/0.102 0.636/0.575   0.562/0.182   0.502/0.000 0.624/0.631   0.542/0.180   0.513/0.000 0.615/0.591   0.556/0.120   0.495/0.000         |                                                                      |  |                                   |         |  |                                   |  |        |                                   |  |  |
+| ZoDiac   | 0.938/1.000   0.743/0.104   0.527/0.032 0.693/0.585   0.670/0.431   0.562/0.125 0.643/0.315   0.643/0.250   0.628/0.210 0.833/0.650   0.572/0.281   0.520/0.152         |                                                                      |  |                                   |         |  |                                   |  |        |                                   |  |  |
+| TreeR.   | 0.868/1.000   0.724/0.861   0.408/0.489 0.855/0.918   0.824/0.905   0.753/0.851 0.821/0.941   0.449/0.512   0.277/0.306 0.647/0.755   0.531/0.656   0.326/0.427         |                                                                      |  |                                   |         |  |                                   |  |        |                                   |  |  |
+| G.S.     | 0.978/1.000   0.898/1.000   0.845/1.000 0.943/1.000   0.953/1.000   0.926/1.000 0.946/1.000   0.847/1.000   0.695/0.905 0.923/1.000   0.858/1.000   0.711/0.915         |                                                                      |  |                                   |         |  |                                   |  |        |                                   |  |  |
+| AquaL.   | 0.757/0.742   0.627/0.145   0.573/0.000 0.879/0.942   0.833/0.858   0.696/0.486 0.663/0.225   0.618/0.078   0.551/0.000 0.679/0.371   0.604/0.086   0.536/0.029         |                                                                      |  |                                   |         |  |                                   |  |        |                                   |  |  |
+| ROBIN    | —- /0.638   —- /0.242   —- /0.153                                                                                                                                       |                                                                      |  | —- /1.000   —- /0.728   —- /0.275 |         |  | —- /0.980   —- /0.705   —- /0.486 |  |        | —- /0.075   —- /0.105   —- /0.100 |  |  |
+| StableS. | 0.496/0.000   0.477/0.000   0.521/0.000 0.512/0.000   0.512/0.000   0.510/0.000 0.498/0.000   0.520/0.000   0.513/0.000 0.506/0.000   0.485/0.000   0.502/0.000         |                                                                      |  |                                   |         |  |                                   |  |        |                                   |  |  |
+|          | ALIEN-Q 0.848/1.000   0.752/0.865   0.618/0.342 0.935/1.000   0.898/1.000   0.842/0.942 0.866/1.000   0.661/0.581   0.563/0.163 0.857/1.000   0.673/0.636   0.581/0.124 |                                                                      |  |                                   |         |  |                                   |  |        |                                   |  |  |
+|          | ALIEN-R 0.999/1.000   0.908/1.000   0.829/1.000 0.999/1.000   0.989/1.000   0.967/1.000 0.988/1.000   0.908/1.000   0.731/0.727 0.989/1.000   0.878/1.000   0.742/0.875 |                                                                      |  |                                   |         |  |                                   |  |        |                                   |  |  |
+
+|                             | Gaussian<br>Shading | Tree-ring | AquaLoRA ALIEN-Q | ALIEN-R |
+|-----------------------------|---------------------|-----------|------------------|---------|
+| DDIM<br>Original            | No<br>Original      |           |                  |         |
+| DDIM<br>Watermarked         |                     |           |                  |         |
+| DPM2 a<br>Watermarked       |                     |           |                  |         |
+| Euler a<br>Watermarked      |                     |           |                  |         |
+| DPM++ 2M SDE<br>Watermarked |                     |           |                  |         |
+
+*Figure 5.* Visual Comparison under Different Generation Schedulers (DDIM, DPM2 a, Euler a, and DPM++ 2M SDE).
+
+method Tree-Ring [\(Wen et al.,](#page-9-6) [2024\)](#page-9-6); the constrained sampling method Gaussian Shading [\(Yang et al.,](#page-9-7) [2024c\)](#page-9-7); and the iterative optimization methods ROBIN [\(Huang et al.,](#page-8-9) [2024\)](#page-8-9) and Zodiac [\(Zhang et al.,](#page-9-8) [2024\)](#page-9-8). Additionally, we select the fine-tuning based method Stable Signature [\(Fernandez](#page-8-15) [et al.,](#page-8-15) [2023\)](#page-8-15) and Aqualora [\(Feng et al.,](#page-8-6) [2024\)](#page-8-6), as well as the post-processing image watermarking technique StegaStamp [\(Tancik et al.,](#page-9-15) [2020\)](#page-9-15). Implementation details can be found in Appendix [B.2.](#page-13-0)
+
+Models and Tasks. Following existing research [\(Yang et al.,](#page-9-7) [2024c\)](#page-9-7), we implement the ALIEN framework on Stable Diffusion v1.5 and Stable Diffusion v2.1. We evaluate our method across two tasks: (1) Detection. All compared methods are configured as single-bit watermarks with a unified pattern. The detection threshold is set individually for each method to achieve a False Positive Rate (FPR) of approximately 1%. (2) Traceability. Multi-bit watermarking methods are evaluated using Bit Accuracy. Single-bit methods, including Tree-ring, Zodiac, and Robin, are excluded due to their lack of watermark capacity. We use prompts
+
+![](_page_5_Picture_8.jpeg)
+
+*Figure 6.* Visual Comparison under Regeneration Attacks (DDIM, DPM2 a, Euler a, and DPM++ 2M SDE).
+
+from Stable Diffusion-Prompts (SDP) [\(Gustavosta,](#page-8-16) [2023\)](#page-8-16), setting the Guidance Scale to 7.5 and the number of sampling steps to 50. Both TPR@1%FPR and Bit Accuracy are computed over 350 watermarked images.
+
+#### 4.2. Comparison to Baselines
+
+Watermark Fidelity. We employ PSNR [\(Hore & Ziou,](#page-8-17) [2010\)](#page-8-17) and SSIM [\(Wang et al.,](#page-9-16) [2004\)](#page-9-16) for pixel fidelity, LPIPS [\(Zhang et al.,](#page-10-1) [2018\)](#page-10-1) and DreamSim [\(Fu et al.,](#page-8-14) [2023\)](#page-8-14) for perceptual similarity, FID [\(Heusel et al.,](#page-8-18) [2017\)](#page-8-18) and SIFID [\(Yang et al.,](#page-9-17) [2024a\)](#page-9-17) for realism, and CLIP Score [\(Radford](#page-9-18) [et al.,](#page-9-18) [2021\)](#page-9-18) for semantic alignment. As shown in Tab. [1,](#page-4-2) ALIEN-Q achieves state-of-the-art imperceptibility, significantly outperforming all baselines. It yields the highest pixel fidelity of 32.41 dB PSNR and the best perceptual quality of 0.003 DreamSim, while maintaining FID and CLIP scores comparable to non-watermarked images.
+
+Watermark Stability. We validate watermark stability across three dimensions: *Sampler Agnosticism* covers both
+
+{6}------------------------------------------------
+
+<span id="page-6-0"></span>*Table 4.* Comprehensive Comparison of Watermark Robustness. Performance is reported in decimal scale (0-1). Higher values are better (↑). The **Avg.** column represents the mean performance across all 11 attacks (excluding No Attack). Top section: TPR@1%FPR; Bottom section: Bit Accuracy.
+
+| Metrics   | Method   | No     | Photo   | netric | De    | egradati | on    | Ge      | eometric | ;     | C     | enerative |       | Avg.  |
+|-----------|----------|--------|---------|--------|-------|----------|-------|---------|----------|-------|-------|-----------|-------|-------|
+|           |          | Attack | Bright. | Contr. | JPEG  | Blur     | Noise | ReScale | C.C.     | R.C.  | VAE-B | VAE-C     | Diff. |       |
+|           | StegaS.  | 1.000  | 0.964   | 1.000  | 1.000 | 1.000    | 1.000 | 1.000   | 0.964    | 0.975 | 1.000 | 1.000     | 1.000 | 0.991 |
+|           | StableS. | 1.000  | 0.958   | 1.000  | 0.781 | 0.973    | 0.042 | 0.935   | 1.000    | 1.000 | 0.000 | 0.079     | 0.000 | 0.611 |
+|           | AquaL.   | 1.000  | 0.289   | 0.507  | 1.000 | 1.000    | 0.932 | 1.000   | 0.127    | 0.258 | 0.975 | 0.958     | 0.742 | 0.708 |
+|           | TreeR.   | 1.000  | 0.775   | 0.909  | 1.000 | 1.000    | 0.954 | 0.968   | 0.013    | 0.021 | 0.954 | 1.000     | 1.000 | 0.778 |
+| TPR@      | G.S.     | 1.000  | 1.000   | 1.000  | 1.000 | 1.000    | 1.000 | 1.000   | 0.981    | 0.979 | 1.000 | 1.000     | 1.000 | 0.996 |
+| Thre1%FPR | ROBIN    | 1.000  | 0.913   | 0.684  | 0.921 | 1.000    | 0.013 | 0.935   | 1.000    | 1.000 | 1.000 | 1.000     | 0.638 | 0.826 |
+|           | ZoDiac   | 1.000  | 0.535   | 0.375  | 0.959 | 0.979    | 0.357 | 0.965   | 0.017    | 0.021 | 0.660 | 0.685     | 1.000 | 0.592 |
+|           | ALIEN-Q  | 1.000  | 0.783   | 1.000  | 0.954 | 1.000    | 0.645 | 1.000   | 0.153    | 0.311 | 0.965 | 0.970     | 0.945 | 0.793 |
+|           | ALIEN-R  | 1.000  | 1.000   | 1.000  | 1.000 | 1.000    | 0.979 | 1.000   | 0.989    | 0.988 | 1.000 | 1.000     | 1.000 | 0.996 |
+|           | StegaS.  | 0.999  | 0.811   | 0.850  | 0.999 | 0.999    | 0.821 | 0.999   | 0.667    | 0.681 | 0.837 | 0.816     | 0.692 | 0.834 |
+|           | StableS. | 0.998  | 0.892   | 0.851  | 0.712 | 0.845    | 0.535 | 0.878   | 0.991    | 0.993 | 0.506 | 0.541     | 0.489 | 0.748 |
+| Bit Acc.  | AquaL.   | 0.954  | 0.583   | 0.672  | 0.935 | 0.954    | 0.810 | 0.925   | 0.573    | 0.648 | 0.845 | 0.856     | 0.757 | 0.778 |
+| Bit Acc.  | G.S.     | 0.999  | 0.939   | 0.964  | 0.995 | 0.999    | 0.903 | 0.996   | 0.657    | 0.655 | 0.996 | 0.997     | 0.978 | 0.916 |
+|           | ALIEN-Q  | 0.989  | 0.753   | 0.803  | 0.889 | 0.936    | 0.689 | 0.903   | 0.581    | 0.601 | 0.834 | 0.853     | 0.848 | 0.790 |
+|           | ALIEN-R  | 0.999  | 0.949   | 0.992  | 0.999 | 0.999    | 0.855 | 0.999   | 0.826    | 0.835 | 0.979 | 0.983     | 0.999 | 0.947 |
+
+<span id="page-6-2"></span>![](_page_6_Figure_4.jpeg)
+
+Figure 7. Robustness against VAE embedding attacks. Results are averaged across KLVAE8, KLVAE16, and SDXL variants.
+
+<span id="page-6-1"></span>![](_page_6_Figure_6.jpeg)
+
+Figure 8. Bit accuracy comparison against Stable Signature across VAE fine-tuning and replacement.
+
+deterministic (DDIM) and irreversible samplers (Euler Ancestral (Karras et al., 2022), DPM++ 2M Ancestral (Karras et al., 2022), DPM++ SDE (Lu et al., 2025)); Component Adaptability involves substituting different VAE and U-Net versions; and Hyperparameter Stability examines sensitivity to Guidance Scale and Inference Steps. As shown in Tab. 2, existing training-free methods exhibit vulnerability to stochastic samplers. Specifically, Tree-Ring and Gaussian Shading fail completely under DPM++ SDE, Euler a., and DPM2 a., where accuracy hovers near the randomguess baseline. ALIEN achieves state-of-the-art sampler agnosticism by maintaining high bit accuracy exceeding 0.97 across all tested schedulers. Our method demonstrates consistent stability across varying inference steps, guidance scales, and model versions.
+
+**Watermark Efficiency.** We evaluate the computational overhead across two primary dimensions: *Preparation Cost*, the one-time offline cost, and *Runtime Cost*, the online perimage latency for embedding and extraction. The comparative results are detailed in Tab. 7. ALIEN achieves latencies of 0.079 seconds for embedding and 0.023 seconds for ex-
+
+traction, maintaining speeds comparable to post-processing baselines while being orders of magnitude faster than the optimization-based method Zodiac, which requires over 122 seconds per image.
+
+Watermark Robustness. We examine watermark's robustness against three typical kinds of adversarial attacks, including image processing attacks (Hore & Ziou, 2010) for transforming generated images, adversarial attacks (An et al., 2024) for disturbing watermark verification, and reconstructive attacks (Zhao et al., 2023) for re-generating nonwatermarked images. Please refer to the Supplementary Materials for detailed parameter settings. As demonstrated in Tab. 4, ALIEN-R achieves state-of-the-art stability against standard distortions by maintaining a True Positive Rate of 0.996. In adversarial embedding scenarios illustrated in Fig. 7, ALIEN-R exhibits exceptional resistance where latent semantic watermarking baselines degrade rapidly. Tab. 3 shows that against reconstructive attacks, ALIEN-R sustains a high confidence exceeding 0.875 even after four re-generation rounds, whereas competitors like StegaStamp and Stable Signature collapse to near-zero.
+
+{7}------------------------------------------------
+
+*Table 5.* Quantitative comparison under Forgery Attacks. Lower values indicate better resistance  $(\downarrow)$ .
+
+| Config                       | G.S.          | Tree-Ring     | ALIEN (Ours)  |  |  |  |  |  |  |  |
+|------------------------------|---------------|---------------|---------------|--|--|--|--|--|--|--|
+| comig                        | Acc. / PSNR   | Acc. / PSNR   | Acc. / PSNR   |  |  |  |  |  |  |  |
+| Scenario A: Average Forgery  |               |               |               |  |  |  |  |  |  |  |
+| 10 Imgs                      | 0.952 / 12.23 | 0.882 / 18.86 | 0.539 / 20.06 |  |  |  |  |  |  |  |
+| 50 Imgs                      | 0.969 / 12.79 | 0.908 / 20.34 | 0.605 / 25.29 |  |  |  |  |  |  |  |
+| 100 Imgs                     | 0.969 / 12.65 | 0.910 / 20.95 | 0.708 / 26.48 |  |  |  |  |  |  |  |
+| Scenario B: Reprompt Forgery |               |               |               |  |  |  |  |  |  |  |
+| SD-V2.1                      | 1.000 /       | 0.931 /       | 0.533 /       |  |  |  |  |  |  |  |
+
+![](_page_7_Figure_4.jpeg)
+
+Figure 9. Robustness against Imprinting Forgery Attack.
+
+Forgery Resistance. Following existing research (Müller et al., 2025; Yang et al., 2024b), we evaluate the security of our method against three representative forgery attacks: imprinting forgery, reprompting forgery, and average forgery. Imprinting and reprompting forgeries rely on latent optimization via diffusion inversion. ALIEN exhibits superior resistance to these attacks compared to initial-latent-based watermarks. While baselines like Tree-Ring and Gaussian Shading can be successfully forged using only a single image, ALIEN remains unaffected. Average Forgery involves estimating the watermark pattern by collecting pairs of watermarked and non-watermarked images. While baselines like Tree-Ring exhibit vulnerability with confidence exceeding 0.9, ALIEN maintains a suppressed confidence of 0.711, effectively preventing the rapid extraction of the watermark pattern. The practical challenges in acquiring large-scale specific-user data within real-world API scenarios significantly elevate the security threshold.
+
+Impact of Timestep Range. As shown in Tab. 6, we conducted an ablation study on the injection interval to investigate the trade-off between imperceptibility and robustness. Injecting the watermark across the full reverse process from step 50 down to 1 ensures perfect detection with 1.000 accuracy but introduces significant perceptual degradation, resulting in a PSNR drop to 20.42 dB under Strength B. Narrowing the window to early diffusion stages such as steps 45 to 20 significantly recovers image quality, where the PSNR
+
+<span id="page-7-1"></span>*Table 6.* Ablation study on Timestep Range under different Watermark Strengths. We compare Image Quality (PSNR) and Detection Performance (Det./Acc.) across two strength settings.
+
+| Range                                                                                                             | Strengt                                   | $\mathbf{th} \mathbf{A} (\lambda = 0.5)$                                          | Strength B ( $\lambda = 1.0$ )            |                                                                                   |  |  |
+|-------------------------------------------------------------------------------------------------------------------|-------------------------------------------|-----------------------------------------------------------------------------------|-------------------------------------------|-----------------------------------------------------------------------------------|--|--|
+| $(t_{start} \rightarrow t_{end})$                                                                                 | PSNR                                      | Det. / Acc.                                                                       | PSNR                                      | Det. / Acc.                                                                       |  |  |
+| $ \begin{array}{c}     1 \to 50 \\     25 \to 50 \\     25 \to 40 \\     10 \to 25 \\     20 \to 45 \end{array} $ | 24.55<br>30.53<br>40.94<br>31.54<br>33.76 | 1.000 / 1.000<br>1.000 / 1.000<br>0.718 / 0.747<br>0.614 / 0.421<br>0.882 / 1.000 | 20.42<br>26.27<br>23.10<br>26.83<br>31.10 | 1.000 / 1.000<br>1.000 / 1.000<br>0.852 / 1.000<br>0.681 / 0.721<br>0.989 / 1.000 |  |  |
+
+<span id="page-7-0"></span>*Table 7.* Performance Comparison regarding Computational Efficiency. <sup>‡</sup> indicates data estimated from original papers.
+
+| Method    | P               | rep. Time (     | h)       | Embed. E |          |  |  |  |
+|-----------|-----------------|-----------------|----------|----------|----------|--|--|--|
+| 111011101 | Pre-train       | Fine-tune       | Optimize | Time (s) | Time (s) |  |  |  |
+| T.R.      | _               | _               | _        | 0.011    | 3.575    |  |  |  |
+| G.S.      | _               |                 |          | 0.102    | 4.212    |  |  |  |
+| ROBIN     | _               | _               | 0.4      | 0.125    | 1.248    |  |  |  |
+| Zodiac    | _               |                 |          | 122.4    | 3.601    |  |  |  |
+| StegaS.   | 30              |                 |          | 0.108    | 0.028    |  |  |  |
+| S.S.      | $48^{\ddagger}$ | 0.1             | _        | _        | 0.014    |  |  |  |
+| AquaL.    | $40^{\ddagger}$ | 15 <sup>‡</sup> | _        | _        | 0.026    |  |  |  |
+| ALIEN     | 22              | _               | _        | 0.079    | 0.023    |  |  |  |
+
+increases to 33.76 dB under Strength A while maintaining a high detection rate.
+
+Impact of Watermark Strength. As shown in Tab. 6, the injection coefficient  $\lambda$  directly modulates the magnitude of the probability flow correction. Increasing the strength from  $\lambda=0.5$  in Strength A to  $\lambda=1.0$  in Strength B consistently improves detection performance across all ranges. we select the range from 45 to 20 combined with moderate strength as the optimal configuration for ALIEN-Q to maximize quality while ensuring reliable detection.
+
+#### 5. Conclusion
+
+Unlike prior approaches relying on heuristic latent modifications, sampling constraints, or computationally intensive optimization, we propose ALIEN, which presents the first analytical derivation of the time-dependent modulation coefficient. This principled approach precisely guides the diffusion of watermark residuals via probability flow modulation, achieving sampler-agnostic embedding. ALIEN overcomes the security vulnerabilities associated with diffusion inversion and irreversible samplers while ensuring high fidelity and low inference cost. Experimental results demonstrate that ALIEN outperforms existing methods in both quality and robustness. Future research will focus on developing content-aware latent watermarking to further enhance security against forgery attacks.
+
+{8}------------------------------------------------
+
+## 6. Impact Statement
+
+Ensuring the accountability and intellectual property protection of generative models has become a critical priority. This paper introduces ALIEN, a principled watermarking framework that enables robust and sampler-agnostic provenance tracking for Latent Diffusion Models. By overcoming the vulnerability of existing methods to irreversible samplers and diverse attacks, we believe our approach effectively mitigates risks such as copyright infringement and malicious misuse, thereby contributing to the development of safer and more trustworthy generative AI.
+
+## References
+
+- <span id="page-8-11"></span>An, B., Ding, M., Rabbani, T., Agrawal, A., Xu, Y., Deng, C., Zhu, S., Mohamed, A., Wen, Y., Goldstein, T., et al. Waves: Benchmarking the robustness of image watermarks. *arXiv preprint arXiv:2401.08573*, 2024.
+- <span id="page-8-19"></span>Balle, J., Minnen, D., Singh, S., Hwang, S. J., and Johnston, ´ N. Variational image compression with a scale hyperprior. *arXiv preprint arXiv:1802.01436*, 2018.
+- <span id="page-8-1"></span>Barrett, C. Identifying and mitigating the security risks of generative ai. *arXiv preprint arXiv:2308.14840*, 2023.
+- <span id="page-8-3"></span>Biden, J. R. Executive order on the safe, secure, and trustworthy development and use of artificial intelligence, 2023. URL [https://www.whitehouse.gov](https://www.whitehouse.gov/briefing-room/statements-releases/2023/07/07/fact-sheet-executive-order-on-artificial-intelligence/) [/briefing-room/statements-releases/20](https://www.whitehouse.gov/briefing-room/statements-releases/2023/07/07/fact-sheet-executive-order-on-artificial-intelligence/) [23/07/07/fact-sheet-executive-order-o](https://www.whitehouse.gov/briefing-room/statements-releases/2023/07/07/fact-sheet-executive-order-on-artificial-intelligence/) [n-artificial-intelligence/](https://www.whitehouse.gov/briefing-room/statements-releases/2023/07/07/fact-sheet-executive-order-on-artificial-intelligence/).
+- <span id="page-8-20"></span>Cheng, Z., Sun, H., Takeuchi, M., and Katto, J. Learned image compression with discretized gaussian mixture likelihoods and attention modules. In *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition*, pp. 7939–7948, 2020.
+- <span id="page-8-5"></span>Ci, H., Song, Y., Yang, P., Xie, J., and Shou, M. Z. Wmadapter: Adding watermark control to latent diffusion models. *arXiv preprint arXiv:2406.08337*, 2024.
+- <span id="page-8-7"></span>Ci, H., Yang, P., Song, Y., and Shou, M. Z. Ringid: Rethinking tree-ring watermarking for enhanced multi-key identification. In *European Conference on Computer Vision*, pp. 338–354. Springer, 2025.
+- <span id="page-8-4"></span>Cox, I., Miller, M., Bloom, J., Fridrich, J., and Kalker, T. *Digital watermarking and steganography*. Morgan kaufmann, 2007.
+- <span id="page-8-12"></span>Dhariwal, P. and Nichol, A. Diffusion models beat gans on image synthesis. *Advances in neural information processing systems*, 34:8780–8794, 2021.
+
+- <span id="page-8-2"></span>European Union. Artificial intelligence act: Regulation (eu) 2024/1689 of the european parliament and of the council, June 2024. URL: [https://eur-lex.europa.](https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32024R1689) [eu/legal-content/EN/TXT/?uri=CELEX:](https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32024R1689) [32024R1689](https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32024R1689), Accessed: 2024-09-24.
+- <span id="page-8-6"></span>Feng, W., Zhou, W., He, J., Zhang, J., Wei, T., Li, G., Zhang, T., Zhang, W., and Yu, N. Aqualora: Toward white-box protection for customized stable diffusion models via watermark lora. *arXiv preprint arXiv:2405.11135*, 2024.
+- <span id="page-8-15"></span>Fernandez, P., Couairon, G., Jegou, H., Douze, M., and ´ Furon, T. The stable signature: Rooting watermarks in latent diffusion models. In *Proceedings of the IEEE/CVF International Conference on Computer Vision*, pp. 22466– 22477, 2023.
+- <span id="page-8-14"></span>Fu, S., Tamir, N., Sundaram, S., Chai, L., Zhang, R., Dekel, T., and Isola, P. Dreamsim: Learning new dimensions of human visual similarity using synthetic data. *arXiv preprint arXiv:2306.09344*, 2023.
+- <span id="page-8-0"></span>Gowal, S. and Kohli, P. Identifying ai-generated images with synthid. [https://www.deepmind.com/blo](https://www.deepmind.com/blog/identifying-ai-generated-images-with-synthid) [g/identifying-ai-generated-images-wit](https://www.deepmind.com/blog/identifying-ai-generated-images-with-synthid) [h-synthid](https://www.deepmind.com/blog/identifying-ai-generated-images-with-synthid), 2023. Accessed: 2023-09-23.
+- <span id="page-8-8"></span>Gunn, S., Zhao, X., and Song, D. An undetectable watermark for generative image models. *arXiv preprint arXiv:2410.07369*, 2024.
+- <span id="page-8-16"></span>Gustavosta. Stable diffusion prompts dataset, May 2023. URL [https://huggingface.co/datasets/](https://huggingface.co/datasets/Gustavosta/Stable-Diffusion-Prompts) [Gustavosta/Stable-Diffusion-Prompts](https://huggingface.co/datasets/Gustavosta/Stable-Diffusion-Prompts).
+- <span id="page-8-18"></span>Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., and Hochreiter, S. Gans trained by a two time-scale update rule converge to a local nash equilibrium. *Advances in neural information processing systems*, 30, 2017.
+- <span id="page-8-13"></span>Ho, J., Jain, A., and Abbeel, P. Denoising diffusion probabilistic models. *Advances in neural information processing systems*, 33:6840–6851, 2020.
+- <span id="page-8-17"></span>Hore, A. and Ziou, D. Image quality metrics: Psnr vs. ssim. In *2010 20th international conference on pattern recognition*, pp. 2366–2369. IEEE, 2010.
+- <span id="page-8-9"></span>Huang, H., Wu, Y., and Wang, Q. Robin: Robust and invisible watermarks for diffusion models with adversarial optimization. *Advances in Neural Information Processing Systems*, 37:3937–3963, 2024.
+- <span id="page-8-10"></span>Karras, T., Aittala, M., Aila, T., and Laine, S. Elucidating the design space of diffusion-based generative models. *Advances in neural information processing systems*, 35: 26565–26577, 2022.
+
+{9}------------------------------------------------
+
+<span id="page-9-5"></span>Lee, S. J. and Cho, N. I. Semantic watermarking reinvented: Enhancing robustness and generation quality with fourier integrity. In *Proceedings of the IEEE/CVF International Conference on Computer Vision*, pp. 18759–18769, 2025.
+
+<span id="page-9-22"></span>504
+
+513 514
+
+<span id="page-9-19"></span>516
+
+518 519 520
+
+<span id="page-9-20"></span>524 525 526
+
+528 529 530
+
+534
+
+<span id="page-9-1"></span>536
+
+- <span id="page-9-13"></span>Li, K., Huang, Z., Hou, X., and Hong, C. Gaussmarker: Robust dual-domain watermark for diffusion models. *arXiv preprint arXiv:2506.11444*, 2025.
+- Lin, T.-Y., Maire, M., Belongie, S., Hays, J., Perona, P., Ramanan, D., Dollar, P., and Zitnick, C. L. Microsoft coco: ´ Common objects in context. In *Computer Vision–ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part V 13*, pp. 740– 755. Springer, 2014.
+- <span id="page-9-9"></span>Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J. Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps. *Advances in Neural Information Processing Systems*, 35:5775–5787, 2022.
+- Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J. Dpmsolver++: Fast solver for guided sampling of diffusion probabilistic models. *Machine Intelligence Research*, pp. 1–22, 2025.
+- <span id="page-9-14"></span>Meng, Z., Peng, B., and Dong, J. Latent watermark: Inject and detect watermarks in latent diffusion space. *arXiv preprint arXiv:2404.00230*, 2024.
+- Muller, A., Lukovnikov, D., Thietke, J., Fischer, A., and ¨ Quiring, E. Black-box forgery attacks on semantic watermarks for diffusion models. In *Proceedings of the Computer Vision and Pattern Recognition Conference*, pp. 20937–20946, 2025.
+- <span id="page-9-18"></span>Radford, A., Kim, J. W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., Krueger, G., and Sutskever, I. Learning transferable visual models from natural language supervision. In *ICML*, 2021.
+- Ramesh, A., Dhariwal, P., Nichol, A., Chu, C., and Chen, M. Hierarchical text-conditional image generation with clip latents. *arXiv preprint arXiv:2204.06125*, 1(2):3, 2022.
+- <span id="page-9-2"></span>Ren, K., Yang, Z., Lu, L., Liu, J., Li, Y., Wan, J., Zhao, X., Feng, X., and Shao, S. Sok: On the role and future of aigc watermarking in the era of gen-ai. *arXiv preprint arXiv:2411.11478*, 2024.
+- <span id="page-9-3"></span>Rezaei, A., Akbari, M., Alvar, S. R., Fatemi, A., and Zhang, Y. Lawa: Using latent space for in-generation image watermarking. In *European Conference on Computer Vision*, pp. 118–136. Springer, 2024.
+
+- <span id="page-9-0"></span>Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B. High-resolution image synthesis with latent diffusion models. In *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)*, pp. 10684–10695, June 2022.
+- <span id="page-9-11"></span>Song, J., Meng, C., and Ermon, S. Denoising diffusion implicit models. *arXiv preprint arXiv:2010.02502*, 2020a.
+- <span id="page-9-12"></span>Song, Y. and Ermon, S. Improved techniques for training score-based generative models. *Advances in neural information processing systems*, 33:12438–12448, 2020.
+- <span id="page-9-10"></span>Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. Score-based generative modeling through stochastic differential equations. *arXiv preprint arXiv:2011.13456*, 2020b.
+- <span id="page-9-15"></span>Tancik, M., Mildenhall, B., and Ng, R. Stegastamp: Invisible hyperlinks in physical photographs. In *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition*, pp. 2117–2126, 2020.
+- <span id="page-9-16"></span>Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P. Image quality assessment: from error visibility to structural similarity. *IEEE transactions on image processing*, 13(4):600–612, 2004.
+- <span id="page-9-4"></span>Wang, Z., Guo, J., Zhu, J., Li, Y., Huang, H., Chen, M., and Tu, Z. Sleepermark: Towards robust watermark against fine-tuning text-to-image diffusion models. In *Proceedings of the Computer Vision and Pattern Recognition Conference*, pp. 8213–8224, 2025.
+- <span id="page-9-6"></span>Wen, Y., Kirchenbauer, J., Geiping, J., and Goldstein, T. Tree-rings watermarks: Invisible fingerprints for diffusion images. *Advances in Neural Information Processing Systems*, 36, 2024.
+- <span id="page-9-17"></span>Yang, J., Liu, H., Guo, W., Rao, Z., Xu, Y., and Niu, D. Sifid: Reassess summary factual inconsistency detection with llm. *arXiv preprint arXiv:2403.07557*, 2024a.
+- <span id="page-9-21"></span>Yang, P., Ci, H., Song, Y., and Shou, M. Z. Can simple averaging defeat modern watermarks? *Advances in Neural Information Processing Systems*, 37:56644–56673, 2024b.
+- <span id="page-9-7"></span>Yang, Z., Zeng, K., Chen, K., Fang, H., Zhang, W., and Yu, N. Gaussian shading: Provable performance-lossless image watermarking for diffusion models. In *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition*, pp. 12162–12171, 2024c.
+- <span id="page-9-8"></span>Zhang, L., Liu, X., Martin, A. V., Bearfield, C. X., Brun, Y., and Guan, H. Attack-resilient image watermarking using stable diffusion. *Advances in Neural Information Processing Systems*, 37:38480–38507, 2024.
+
+{10}------------------------------------------------
+
+Zhang, R., Isola, P., Efros, A. A., Shechtman, E., and Wang, O. The unreasonable effectiveness of deep features as a perceptual metric. In *Proceedings of the IEEE conference on computer vision and pattern recognition*, pp. 586–595, 2018.
+
+<span id="page-10-1"></span>
+
+<span id="page-10-2"></span>
+
+- Zhao, X., Zhang, K., Su, Z., Vasan, S., Grishchenko, I., Kruegel, C., Vigna, G., Wang, Y.-X., and Li, L. Invisible image watermarks are provably removable using generative ai. *arXiv preprint arXiv:2306.01953*, 2023.
+- <span id="page-10-0"></span>Zhao, X., Zhang, K., Su, Z., Vasan, S., Grishchenko, I., Kruegel, C., Vigna, G., Wang, Y.-X., and Li, L. Invisible image watermarks are provably removable using generative ai. *Advances in neural information processing systems*, 37:8643–8672, 2024.
+
+{11}------------------------------------------------
+
+# Supplementary Material
+
+| A |     | Theoretical Analysis of ALIEN                  | 12 |
+|---|-----|------------------------------------------------|----|
+|   | A.1 | Watermark Constraint and Score Discrepancy<br> | 12 |
+|   | A.2 | Proof of Reverse SDE Drift Term Correction     | 12 |
+|   | A.3 | Derivation of UNet Target Noise<br>            | 12 |
+| B |     | Implementation Details                         | 13 |
+|   | B.1 | Algorithm Pseudocode<br>                       | 13 |
+|   | B.2 | Hyperparameters and Training Settings<br>      | 13 |
+| C |     | Experimental Setup and Extended Experiments    | 14 |
+|   | C.1 | Dataset Settings                               | 14 |
+|   | C.2 | Robustness Evaluation Settings                 | 15 |
+|   | C.3 | Extended Experiments                           | 15 |
+| D |     | Extended Related Work                          | 16 |
+|   | D.1 | Watermarking Schemes Taxonomy                  | 16 |
+
+{12}------------------------------------------------
+
+## <span id="page-12-0"></span>A. Theoretical Analysis of ALIEN
+
+In this section, we provide a rigorous derivation establishing the analytical link between the watermark constraint in the  $z_0$ -space and the necessary correction to the probability flow drift term. This derivation proves that ALIEN is theoretically grounded in the VP-SDE framework and is inherently sampler-agnostic.
+
+### <span id="page-12-1"></span>A.1. Watermark Constraint and Score Function Discrepancy
+
+1. Watermark Constraint Definition Our objective is to embed a fixed watermark residual  $\delta_{wm}$  into the latent representation. We define this as a geometric constraint on the estimated clean data manifold. Let  $\hat{\mathbf{z}}_0$  denote the original estimate derived from the model  $\theta$ , and  $\hat{\mathbf{z}}_0^{wm}$  denote the target watermarked estimate:
+
+<span id="page-12-4"></span>
+$$\hat{\mathbf{z}}_0^{wm} = \hat{\mathbf{z}}_0 + \delta_{wm}. \tag{6}$$
+
+**2. Derivation of Score Function Difference**  $\Delta$ **Score** Under the VP-SDE framework, Tweedie's formula establishes a linear bijection between the score function  $\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t)$  and the denoised estimate  $\hat{\mathbf{z}}_0$ :
+
+$$\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t) = -\frac{\mathbf{z}_t - \sqrt{\bar{\alpha}_t} \hat{\mathbf{z}}_0}{1 - \bar{\alpha}_t}.$$
+ (7)
+
+To enforce the watermark constraint (Eq. 6), the score function must shift to  $\nabla_{\mathbf{z}_t} \log p_t^{wm}$ . By substituting the constraint  $\hat{\mathbf{z}}_0 - \hat{\mathbf{z}}_0^{wm} = -\delta_{wm}$ , we derive the score discrepancy  $\Delta S$ core:
+
+<span id="page-12-5"></span>
+$$\Delta \text{Score} = \nabla_{\mathbf{z}_{t}} \log p_{t}^{wm} - \nabla_{\mathbf{z}_{t}} \log p_{t}$$
+
+$$= -\frac{1}{1 - \bar{\alpha}_{t}} \left( -\sqrt{\bar{\alpha}_{t}} (\hat{\mathbf{z}}_{0}^{wm} - \hat{\mathbf{z}}_{0}) \right)$$
+
+$$= \frac{\sqrt{\bar{\alpha}_{t}}}{1 - \bar{\alpha}_{t}} \delta_{wm}.$$
+(8)
+
+#### <span id="page-12-2"></span>A.2. Proof of Reverse SDE Drift Term Correction $\Delta \mathbf{F}_{rev}$
+
+**Definition of Reverse Drift**  $\mathbf{F}_{rev}$  The generation trajectory in diffusion models is governed by the reverse-time SDE. The deterministic component of this process, known as the drift term  $\mathbf{F}_{rev}$ , is defined as:
+
+$$\mathbf{F}_{rev}(\mathbf{z}_t, t) = \mathbf{f}(\mathbf{z}_t, t) - g^2(t) \nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t). \tag{9}$$
+
+where  $\mathbf{f}(\mathbf{z}_t, t)$  is the forward drift and g(t) is the diffusion coefficient.
+
+**Derivation of Drift Correction**  $\Delta \mathbf{F}_{rev}$  We calculate the modification to the drift term required to accommodate the watermark. Since the forward physics  $\mathbf{f}(\mathbf{z}_t, t)$  remains invariant, the drift correction depends solely on the score shift:
+
+$$\Delta \mathbf{F}_{rev} = \mathbf{F}_{rev}^{wm} - \mathbf{F}_{rev}^{orig} = -g^2(t) \left(\Delta \text{Score}\right). \tag{10}$$
+
+Substituting Eq. (8) into the expression above, we obtain the explicit form of the Watermark Drift Force:
+
+$$\Delta \mathbf{F}_{rev}(\mathbf{z}_t, t) = -g^2(t) \frac{\sqrt{\bar{\alpha}_t}}{1 - \bar{\alpha}_t} \delta_{wm}. \tag{11}$$
+
+**Theorem:** The spatial constraint  $\delta_{wm}$  imposes a constant, deterministic force  $\Delta \mathbf{F}_{rev}$  on the probability flow. Because  $\mathbf{F}_{rev}$  is the shared driving term for both the stochastic reverse SDE and the deterministic Probability Flow ODE (PF-ODE), this correction guarantees that the watermark embedding is robust across different samplers.
+
+## <span id="page-12-3"></span>A.3. Derivation of Noise Prediction Target $\epsilon^{target}$
+
+To implement the theoretical drift correction  $\Delta \mathbf{F}_{rev}$  in practice, we modulate the output of the U-Net  $\vartheta$ .
+
+**Score-Noise Relationship** The neural network  $\epsilon_{\vartheta}$  approximates the score function via the relation:
+
+$$\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t) = -\frac{\epsilon_{\vartheta}(\mathbf{z}_t, t)}{\sqrt{1 - \bar{\alpha}_t}}.$$
+(12)
+
+{13}------------------------------------------------
+
+## <span id="page-13-3"></span>**Algorithm 2** ALIEN Watermarking
+
+```
+715
+716
+                                                                                     Phase I: Watermark Embedding
+717
+              2: Input: Pre-trained U-Net \theta, Encoder E_s, Scheduler S, VAE Decoder \mathcal{D}_{VAE}, Prompt c, Secret m, Injection Interval
+718
+                   [T_{start}, T_{end}], Strength \lambda
+719
+              3: Output: Watermarked Image \mathbf{x}_{wm}
+720
+              4: \delta_{wm} \leftarrow E_s(\mathbf{m})
+721
+              5: \mathbf{z}_t \sim \mathcal{N}(\mathbf{0}, \mathbf{I})
+              6: for t = T down to 1 do
+                   \mathbf{t} \leftarrow S. \mathsf{timesteps}[t]
+724
+                      \epsilon_{\theta}^{t} \leftarrow \text{CFG}(\theta, \mathbf{z}_{t}, \mathbf{t}, \mathbf{c})
+725
+                      if t \leq T_{end} and t \geq T_{start} then
+726
+                          // Modulate the prediction target
+727
+                          \boldsymbol{\epsilon}_{\theta}^{t} \leftarrow \boldsymbol{\epsilon}_{\theta}^{t} - \lambda \cdot \left(\frac{\sqrt{\bar{\alpha}_{t}}}{\sqrt{1 - \bar{\alpha}_{t}}}\right) \cdot \delta_{wm}
+728
+            12:
+730
+                      \mathbf{z}_t \leftarrow S.\text{step}(\epsilon_{\theta}^t, \mathbf{t}, \mathbf{z}_t).\text{prev\_sample}
+            14: end for
+731
+            15: \mathbf{x}_{wm} \leftarrow \mathcal{D}_{VAE}(\mathbf{z}_t)
+732
+733
+                                                                                     Phase II: Watermark Extraction
+            17: Input: Watermarked Image \mathbf{x}_{wm}, VAE Encoder \mathcal{E}_{VAE}, Watermark Decoder D_s
+734
+735
+            18: Output: Extracted Secret m'
+            19: // Encode image back to watermarked latent
+736
+737
+            20: \mathbf{z}_0 \leftarrow \mathcal{E}_{VAE}(\mathbf{x}_{wm})
+738
+            21: // Extract secret message from latent
+            22: \mathbf{m}' \leftarrow D_s(\mathbf{z}_0)
+739
+```
+
+**Mapping Drift Correction to**  $\epsilon$ **-Space** We equate the score difference derived from the drift requirement to the difference in noise prediction. Using  $\Delta Score = -\frac{1}{\sqrt{1-\bar{\alpha}_t}}(\epsilon^{target} - \epsilon_{\vartheta}) = -\frac{\Delta \epsilon}{\sqrt{1-\bar{\alpha}_t}}$ , we have:
+
+$$-\frac{\Delta \epsilon}{\sqrt{1-\bar{\alpha}_t}} = \frac{\sqrt{\bar{\alpha}_t}}{1-\bar{\alpha}_t} \delta_{wm}. \tag{13}$$
+
+**Final Update Rule** Solving for the correction term  $\Delta \epsilon$ :
+
+$$\Delta \epsilon = -\sqrt{1 - \bar{\alpha}_t} \cdot \frac{\sqrt{\bar{\alpha}_t}}{1 - \bar{\alpha}_t} \delta_{wm} = -\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}} \delta_{wm}. \tag{14}$$
+
+Thus, the final target noise  $\epsilon^{target}$  required to enforce the watermark is:
+
+$$\epsilon^{target} = \epsilon_{\vartheta} + \Delta \epsilon = \epsilon_{\vartheta} - \left(\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}}\right) \delta_{wm}. \tag{15}$$
+
+## <span id="page-13-1"></span>**B.** Implementation Details
+
+#### <span id="page-13-2"></span>**B.1. Algorithm Pseudocode**
+
+740
+
+741 742
+
+743
+
+744 745
+
+746
+
+747 748 749
+
+750
+
+751
+
+752 753
+
+754 755
+
+756
+
+757 758
+
+759 760 761
+
+762
+
+763
+
+764 765
+
+766 767
+
+768
+
+23: **Return** m<sup>2</sup>
+
+The core logic of the ALIEN watermarking framework is detailed in Algorithm 2. This algorithm outlines the complete process of watermark embedding during the reverse diffusion process and the subsequent extraction from the latent space.
+
+#### <span id="page-13-0"></span>**B.2.** Hyperparameters and Training Settings
+
+Watermark Generation Module Training. We train the Imperceptible Latent Watermark Generation module using the AdamW optimizer with a learning rate of  $5 \times 10^{-5}$  and a weight decay of  $1 \times 10^{-5}$ . We construct a synthetic training set of
+
+{14}------------------------------------------------
+
+770 771
+
+*Table 8.* Detailed Robustness Evaluation Settings. We categorize attacks into four distinct groups. Note that Image Processing attacks are grouped by type (Photometry, Geometry, Degradation) to conserve space.
+
+| Category         | Method & Parameters                                                                                                                                                                                                                                     |
+|------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| Image Processing | Photometry: Brightness (×6.0), Contrast (×12.0)<br>Geometry: Resize (s = 0.5), Center Crop(s = 0.4), Random Crop(s = 0.4)<br>Degradation: Gaussian Noise (σ = 0.25), Blur (radius = 1.5), JPEG (Q = 50)                                                 |
+| Reconstructive   | VAE Compression: VAE-B (Balle et al. ´ , 2018) (Q = 1), VAE-C (Cheng et al., 2020) (Q = 1)<br>Generative Attack: Regen-Diff (Zhao et al., 2024) (SD v1.5, Strength S = 0.2), Rinsing (N = 2, 4)                                                         |
+| Adversarial      | Adv-Emb: PGD-based Latent Attack (An et al., 2024)                                                                                                                                                                                                      |
+| Forgery          | Imprinting: Latent optimization via inversion (Muller et al. ¨ , 2025)<br>Reprompting: Inverse the image to initial latent and regeneration (Muller et al. ¨ , 2025)<br>Average: Estimate watermark pattern by averaging residuals (Yang et al., 2024b) |
+
+![](_page_14_Picture_4.jpeg)
+
+*Figure 10.* Visual Robustness Examples. Comparison of the watermarked image under various attacks: (a) Original, (b) Brightness, (c) Contrast, (d) JPEG Compression, (e) Gaussian Blur, (f) Gaussian Noise, (g) Center Crop (C.C.), (h) Random Crop (R.C.), (i) VAE Compression (BMSHJ), and (j) VAE Compression (Cheng).
+
+10,000 images generated based on COCO2014 [\(Lin et al.,](#page-9-22) [2014\)](#page-9-22) prompts. The model is trained for 50,000 steps with a batch size of 16. To ensure training stability and perceptual quality, we impose a maximum gradient norm of 10<sup>−</sup><sup>2</sup> . The total objective combines the secret recovery loss (Lsec), pixel-wise reconstruction loss (Lmse), and perceptual loss (Llpips using AlexNet backbone). The loss weights are set to λsec = 1.0, λmse = 30.0, and λlpips = 0.3. Notably, λmse and λlpips are linearly ramped up from 0 to their peak values over the first 5,000 steps to facilitate stable convergence in the early training phase.
+
+Injection Settings. During the inference phase, ALIEN-Q injects watermarks within the sampling interval of steps 20–45 (with injection strength λ = 0.85), while ALIEN-R extends the injection window to cover steps 0–50 (λ = 1.0) for enhanced robustness.
+
+## <span id="page-14-0"></span>C. Experimental Setup and Extended Experiments
+
+## <span id="page-14-1"></span>C.1. Dataset Settings
+
+Evaluation Datasets. We utilize two distinct datasets to comprehensively evaluate both watermarking performance and image generation quality: For measuring detection accuracy (TPR@1%FPR) and payload capacity (Bit Accuracy), we
+
+{15}------------------------------------------------
+
+<span id="page-15-2"></span>*Table 9.* Breakdown of Performance Gains. We compare ALIEN against the best-performing baseline (Best SOTA) for each metric/condition. Panel A calculates the average relative improvement across 5 quality metrics (33.1%). Panel B highlights the robustness gain across 15 distinct conditions (12 Generative + 3 Stability). The final 14.0% is the weighted average gain over these 15 conditions.
+
+|                                          | Panel A: Quality Improvement (ALIEN-Q vs. Best SOTA)              |                    |                             |         |             |
+|------------------------------------------|-------------------------------------------------------------------|--------------------|-----------------------------|---------|-------------|
+| Metric                                   | Description                                                       | Best SOTA          | Method                      | ALIEN-Q | Improvement |
+| FID ↓                                    | Frechet Inception Distance<br>´                                   | 24.42 (G.S.)       | Lower is better             | 24.29   | +0.5%       |
+| PSNR ↑                                   | Peak Signal-to-Noise Ratio                                        | 29.09 (StableSig.) | Higher is better            | 32.41   | +11.4%      |
+| SSIM ↑                                   | Structural Similarity                                             | 0.922 (ZoDiac)     | Higher is better            | 0.949   | +2.9%       |
+| SIFID ↓                                  | Single Image FID                                                  | 0.105 (StableSig.) | Lower is better             | 0.023   | +78.1%      |
+| DreamSim ↓                               | Perceptual Similarity                                             | 0.011 (StableSig.) | Lower is better             | 0.003   | +72.7%      |
+|                                          |                                                                   |                    | Average Quality Improvement |         | +33.1%      |
+|                                          | Panel B: Robustness Improvement (ALIEN-R vs. Training-free SOTA)  |                    |                             |         |             |
+| Condition Category                       | Specifics                                                         | Best SOTA          | Metric                      | ALIEN-R | Gain        |
+| 1. Generative Variant<br>(12 conditions) | Average Acc. across 12 conditions<br>(4 Schedulers × Regen/Rinse) | ∼0.84              | Acc.                        | ∼0.90   | +6.5%       |
+| 2. Sampler Stability                     | Average Acc. across 3 stochastic samplers                         | ∼0.56              | Acc.                        | ∼1.00   | +44.0%      |
+| (3 conditions)                           | (DPM++ SDE, Euler a, DPM2 a)                                      |                    |                             |         |             |
+
+<span id="page-15-3"></span>*Table 10.* Comparison of Imperceptibility and Robustness. We compare 48-bit and 128-bit payloads. *Fidelity* is reported as Mean ± Std. Dev. *Robustness* is reported as Detection Accuracy. Abbreviations: *No Att.* (No Attack), *Comp.* (Compression), *Comb.* (Combined Attack).
+
+| Payload  |            | Imperceptibility Metrics |            | Robustness (Bit Accuracy)<br>No Att.<br>Blur<br>Noise<br>JPEG<br>Resize<br>Sharp<br>Bright<br>Contr.<br>Sat. |      |      |      |      |      |      |      |      |       |
+|----------|------------|--------------------------|------------|--------------------------------------------------------------------------------------------------------------|------|------|------|------|------|------|------|------|-------|
+|          | PSNR(↑)    | SSIM(↑)                  | LPIPS(↓)   |                                                                                                              |      |      |      |      |      |      |      |      | Comb. |
+| 48 Bits  | 31.17±0.90 | 0.62±0.03                | 0.097±0.01 | 0.99                                                                                                         | 0.99 | 0.92 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.87  |
+| 128 Bits | 30.79±0.85 | 0.59±0.03                | 0.151±0.01 | 0.99                                                                                                         | 0.99 | 0.90 | 0.98 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.82  |
+
+employ the Stable Diffusion-Prompts (SDP) dataset [\(Gustavosta,](#page-8-16) [2023\)](#page-8-16). We randomly select 350 prompts from the dataset to generate image pairs (watermarked vs. clean) for distinct evaluation. For evaluating generative fidelity, specifically Frechet ´ Inception Distance (FID), we utilize the MS-COCO dataset [\(Lin et al.,](#page-9-22) [2014\)](#page-9-22). We randomly sample 5,000 captions from the MS-COCO validation set to generate 5,000 watermarked images and compute the FID score against the corresponding real reference images to ensure standardized quality comparison.
+
+Generation Configuration. We conduct experiments on two representative Latent Diffusion Models: Stable Diffusion v1.5 and Stable Diffusion v2.1. Unless otherwise specified, we use the DDIM sampler with 50 inference steps. The classifier-free guidance scale is set to 7.5. All generated images are of resolution 512 × 512. All experiments were conducted on a single NVIDIA RTX 3090 GPU.
+
+#### <span id="page-15-1"></span><span id="page-15-0"></span>C.2. Robustness Evaluation Settings
+
+#### C.3. Extended Experiments
+
+Detailed Performance Gain Analysis. To substantiate the claims made in the abstract, we provide a detailed breakdown of the performance improvements. Table [9](#page-15-2) illustrates the calculation of the 33.1% quality improvement and 14.0% robustness improvement compared to the state-of-the-art (SOTA) methods.
+
+Impact of Payload Size. We further investigate the impact of payload size on the trade-off between watermark capacity, imperceptibility, and robustness. As demonstrated in Table [10,](#page-15-3) increasing the payload capacity from 48 bits to 128 bits results in only a minor decrease in fidelity metrics, exemplified by a slight PSNR drop from 31.17 dB to 30.79 dB. This result validates that ALIEN effectively supports high-capacity embedding while maintaining visual quality comparable to low-capacity settings.
+
+{16}------------------------------------------------
+
+<span id="page-16-2"></span>*Table 11.* Impact of Fixed Thresholding on False Positive Rates (ROBIN Scheme). Comparison of clean image means (µclean) versus the optimal threshold for Cropping (τcrop) using the ROBIN watermarking method. For both SD v1.5 and v2.1, benign degradations like Blurring and JPEG shift µclean below τcrop (marked with ×).
+
+| Attack       | Stable Diffusion v1.5 (τcrop |        | = 39.45)     | Stable Diffusion v2.1 (τcrop |        | = 55.80)     |
+|--------------|------------------------------|--------|--------------|------------------------------|--------|--------------|
+|              | Clean Mean                   | Opt. τ | Fixed τ Risk | Clean Mean                   | Opt. τ | Fixed τ Risk |
+| No Attack    | 40.08                        | 38.28  | ✓            | 55.90                        | 52.74  | ✓            |
+| Cropping     | 40.25                        | 39.45  | -            | 55.86                        | 55.80  | -            |
+| Blurring     | 32.38                        | 30.31  | ×            | 52.65                        | 50.24  | ×            |
+| JPEG         | 37.22                        | 36.91  | ×            | 55.65                        | 53.57  | ×            |
+| Color Jitter | 36.91                        | 36.85  | ×            | 54.04                        | 51.39  | ×            |
+| Noise        | 41.63                        | 40.02  | ✓            | 57.07                        | 55.62  | ✓            |
+
+Threshold Determination for Distance-Based Methods. We evaluate the impact of distribution shifts caused by image degradations on threshold determination for the distance-based method, ROBIN. As shown in Table [11,](#page-16-2) using a fixed threshold derived from a challenging scenario (Cropping, τ = 39.45) poses risks when applied to other distortions. We observe a clear distribution shift in the metric space for degradations that suppress high-frequency information. For instance, the mean metric of unwatermarked images under Blurring drops to 32.38, falling below the fixed cropping threshold of 39.45. Since detection occurs when the metric is below the threshold, this shift results in increased False Positive Rates (FPR), where benign, low-quality images are misclassified.
+
+## <span id="page-16-0"></span>D. Extended Related Work
+
+This section provides a detailed review and taxonomy of existing watermarking methods for generative models.
+
+#### <span id="page-16-1"></span>D.1. Watermarking Schemes Taxonomy
+
+We categorize existing watermarking methods for generative models into five primary classes based on their embedding stage: Random Seed Modification, U-Net Modification, VAE Modification, Latent Space Modification, and Post-Processing.
+
+Random Seed Modification (Initial Latent). Methods in this category embed watermarks by changing in the sampling process of the initial latent variables. For instance, Tree-Ring [\(Wen et al.,](#page-9-6) [2024\)](#page-9-6) modifies the initial noise vector in the Fourier domain to embed a ring-shaped pattern, which is detectable via diffusion inversion. Gaussian Shading [\(Yang et al.,](#page-9-7) [2024c\)](#page-9-7) employs a constrained sampling strategy to apply specific patterns to the initial latent.
+
+Model Modification. These approaches embed watermarks by fine-tuning specific components of the generative model to ensure watermark preservation during generation. Stable Signature [\(Fernandez et al.,](#page-8-15) [2023\)](#page-8-15) fine-tunes the VAE decoder to embed the watermark into the pixel space during the latent-to-image decoding stage. Aqualora [\(Feng et al.,](#page-8-6) [2024\)](#page-8-6) modifies the U-Net to inject the watermark during the iterative denoising process.
+
+Latent Space Optimization. Unlike static encoding methods, these approaches formulate watermark embedding as an optimization problem within the latent space. Zodiac [\(Zhang et al.,](#page-9-8) [2024\)](#page-9-8) embeds the watermark by iteratively optimizing the *initial* latent variable to ensure high detectability in the generated output. ROBIN [\(Huang et al.,](#page-8-9) [2024\)](#page-8-9) focuses on optimizing the *intermediate* latent representations during the diffusion process. It incorporates learnable prompts to align the watermarked latents with the text condition.
+
+Post-Processing Methods. These techniques apply digital watermarking algorithms to the image after it has been fully generated, operating independently of the generation pipeline. StegaStamp [\(Tancik et al.,](#page-9-15) [2020\)](#page-9-15) is a deep learning-based encoder-decoder framework that embeds invisible hyperlinks or bit-strings into the final image output.

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+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0074", "section": "References", "page_start": 9, "page_end": 9, "type": "ListGroup", "text": "European Union. Artificial intelligence act: Regulation (eu) 2024/1689 of the european parliament and of the council, June 2024. URL: eu/legal-content/EN/TXT/?uri=CELEX: 32024R1689 , Accessed: 2024-09-24. Feng, W., Zhou, W., He, J., Zhang, J., Wei, T., Li, G., Zhang, T., Zhang, W., and Yu, N. Aqualora: Toward white-box protection for customized stable diffusion models via watermark lora. arXiv preprint arXiv:2405.11135 , 2024. Fernandez, P., Couairon, G., Jegou, H., Douze, M., and ´ Furon, T. The stable signature: Rooting watermarks in latent diffusion models. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pp. 22466– 22477, 2023. Fu, S., Tamir, N., Sundaram, S., Chai, L., Zhang, R., Dekel, T., and Isola, P. Dreamsim: Learning new dimensions of human visual similarity using synthetic data. arXiv preprint arXiv:2306.09344 , 2023. Gowal, S. and Kohli, P. Identifying ai-generated images with synthid. g/identifying-ai-generated-images-wit h-synthid , 2023. Accessed: 2023-09-23. Gunn, S., Zhao, X., and Song, D. An undetectable watermark for generative image models. arXiv preprint arXiv:2410.07369 , 2024. Gustavosta. Stable diffusion prompts dataset, May 2023. URL Gustavosta/Stable-Diffusion-Prompts . Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., and Hochreiter, S. Gans trained by a two time-scale update rule converge to a local nash equilibrium. Advances in neural information processing systems , 30, 2017. Ho, J., Jain, A., and Abbeel, P. Denoising diffusion probabilistic models. Advances in neural information process ing systems , 33:6840–6851, 2020. Hore, A. and Ziou, D. Image quality metrics: Psnr vs. ssim. In 2010 20th international conference on pattern recognition , pp. 2366–2369. IEEE, 2010. Huang, H., Wu, Y., and Wang, Q. Robin: Robust and invisible watermarks for diffusion models with adversarial optimization. Advances in Neural Information Processing Systems , 37:3937–3963, 2024. Karras, T., Aittala, M., Aila, T., and Laine, S. Elucidating the design space of diffusion-based generative models. Advances in neural information processing systems , 35: 26565–26577, 2022.", "source": "marker_v2", "marker_block_id": "/page/8/ListGroup/524"}
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+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0076", "section": "References", "page_start": 10, "page_end": 10, "type": "ListGroup", "text": "Li, K., Huang, Z., Hou, X., and Hong, C. Gaussmarker: Robust dual-domain watermark for diffusion models. arXiv preprint arXiv:2506.11444 , 2025. Lin, T.-Y., Maire, M., Belongie, S., Hays, J., Perona, P., Ramanan, D., Dollar, P., and Zitnick, C. L. Microsoft coco: ´ Common objects in context. In Computer Vision–ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part V 13 , pp. 740– 755. Springer, 2014. Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J. Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps. Advances in Neural Information Processing Systems , 35:5775–5787, 2022. Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J. Dpmsolver++: Fast solver for guided sampling of diffusion probabilistic models. Machine Intelligence Research , pp. 1–22, 2025. Meng, Z., Peng, B., and Dong, J. Latent watermark: Inject and detect watermarks in latent diffusion space. arXiv preprint arXiv:2404.00230 , 2024. Muller, A., Lukovnikov, D., Thietke, J., Fischer, A., and ¨ Quiring, E. Black-box forgery attacks on semantic watermarks for diffusion models. In Proceedings of the Computer Vision and Pattern Recognition Conference , pp. 20937–20946, 2025. Radford, A., Kim, J. W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., Krueger, G., and Sutskever, I. Learning transferable visual models from natural language supervision. In ICML , 2021. Ramesh, A., Dhariwal, P., Nichol, A., Chu, C., and Chen, M. Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.06125 , 1(2):3, 2022. Ren, K., Yang, Z., Lu, L., Liu, J., Li, Y., Wan, J., Zhao, X., Feng, X., and Shao, S. Sok: On the role and future of aigc watermarking in the era of gen-ai. arXiv preprint arXiv:2411.11478 , 2024. Rezaei, A., Akbari, M., Alvar, S. R., Fatemi, A., and Zhang, Y. Lawa: Using latent space for in-generation image watermarking. In European Conference on Computer Vision , pp. 118–136. Springer, 2024.", "source": "marker_v2", "marker_block_id": "/page/9/ListGroup/495"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0077", "section": "References", "page_start": 10, "page_end": 10, "type": "ListGroup", "text": "Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , pp. 10684–10695, June 2022. Song, J., Meng, C., and Ermon, S. Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 , 2020a. Song, Y. and Ermon, S. Improved techniques for training score-based generative models. Advances in neural information processing systems , 33:12438–12448, 2020. Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456 , 2020b. Tancik, M., Mildenhall, B., and Ng, R. Stegastamp: Invisible hyperlinks in physical photographs. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pp. 2117–2126, 2020. Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing , 13(4):600–612, 2004. Wang, Z., Guo, J., Zhu, J., Li, Y., Huang, H., Chen, M., and Tu, Z. Sleepermark: Towards robust watermark against fine-tuning text-to-image diffusion models. In Proceed ings of the Computer Vision and Pattern Recognition Conference , pp. 8213–8224, 2025. Wen, Y., Kirchenbauer, J., Geiping, J., and Goldstein, T. Tree-rings watermarks: Invisible fingerprints for diffusion images. Advances in Neural Information Processing Systems , 36, 2024. Yang, J., Liu, H., Guo, W., Rao, Z., Xu, Y., and Niu, D. Sifid: Reassess summary factual inconsistency detection with llm. arXiv preprint arXiv:2403.07557 , 2024a. Yang, P., Ci, H., Song, Y., and Shou, M. Z. Can simple averaging defeat modern watermarks? Advances in Neu ral Information Processing Systems , 37:56644–56673, 2024b. Yang, Z., Zeng, K., Chen, K., Fang, H., Zhang, W., and Yu, N. Gaussian shading: Provable performance-lossless image watermarking for diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pp. 12162–12171, 2024c. Zhang, L., Liu, X., Martin, A. V., Bearfield, C. X., Brun, Y., and Guan, H. Attack-resilient image watermarking using stable diffusion. Advances in Neural Information Processing Systems , 37:38480–38507, 2024.", "source": "marker_v2", "marker_block_id": "/page/9/ListGroup/496"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0078", "section": "References", "page_start": 11, "page_end": 11, "type": "Text", "text": "Zhang, R., Isola, P., Efros, A. A., Shechtman, E., and Wang, O. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition , pp. 586–595, 2018.", "source": "marker_v2", "marker_block_id": "/page/10/Text/193"}
+{"paper_id": "6b484833-bf42-4409-a685-ed34a504bfa9", "chunk_id": "6b484833-bf42-4409-a685-ed34a504bfa9:0079", "section": "References", "page_start": 11, "page_end": 11, "type": "ListGroup", "text": "Zhao, X., Zhang, K., Su, Z., Vasan, S., Grishchenko, I., Kruegel, C., Vigna, G., Wang, Y.-X., and Li, L. Invisible image watermarks are provably removable using generative ai. arXiv preprint arXiv:2306.01953 , 2023. Zhao, X., Zhang, K., Su, Z., Vasan, S., Grishchenko, I., Kruegel, C., Vigna, G., Wang, Y.-X., and Li, L. Invisible image watermarks are provably removable using generative ai. Advances in neural information processing systems , 37:8643–8672, 2024.", "source": "marker_v2", "marker_block_id": "/page/10/ListGroup/192"}

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@@ -0,0 +1,20 @@
+[p. 9 | section: References | type: ListGroup]
+An, B., Ding, M., Rabbani, T., Agrawal, A., Xu, Y., Deng, C., Zhu, S., Mohamed, A., Wen, Y., Goldstein, T., et al. Waves: Benchmarking the robustness of image watermarks. arXiv preprint arXiv:2401.08573 , 2024. Balle, J., Minnen, D., Singh, S., Hwang, S. J., and Johnston, ´ N. Variational image compression with a scale hyperprior. arXiv preprint arXiv:1802.01436 , 2018. Barrett, C. Identifying and mitigating the security risks of generative ai. arXiv preprint arXiv:2308.14840 , 2023. Biden, J. R. Executive order on the safe, secure, and trustworthy development and use of artificial intelligence, 2023. URL /briefing-room/statements-releases/20 23/07/07/fact-sheet-executive-order-o n-artificial-intelligence/ . Cheng, Z., Sun, H., Takeuchi, M., and Katto, J. Learned image compression with discretized gaussian mixture likelihoods and attention modules. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pp. 7939–7948, 2020. Ci, H., Song, Y., Yang, P., Xie, J., and Shou, M. Z. Wmadapter: Adding watermark control to latent diffusion models. arXiv preprint arXiv:2406.08337 , 2024. Ci, H., Yang, P., Song, Y., and Shou, M. Z. Ringid: Rethinking tree-ring watermarking for enhanced multi-key identification. In European Conference on Computer Vision , pp. 338–354. Springer, 2025. Cox, I., Miller, M., Bloom, J., Fridrich, J., and Kalker, T. Digital watermarking and steganography . Morgan kaufmann, 2007. Dhariwal, P. and Nichol, A. Diffusion models beat gans on image synthesis. Advances in neural information processing systems , 34:8780–8794, 2021.
+
+[p. 9 | section: References | type: ListGroup]
+European Union. Artificial intelligence act: Regulation (eu) 2024/1689 of the european parliament and of the council, June 2024. URL: eu/legal-content/EN/TXT/?uri=CELEX: 32024R1689 , Accessed: 2024-09-24. Feng, W., Zhou, W., He, J., Zhang, J., Wei, T., Li, G., Zhang, T., Zhang, W., and Yu, N. Aqualora: Toward white-box protection for customized stable diffusion models via watermark lora. arXiv preprint arXiv:2405.11135 , 2024. Fernandez, P., Couairon, G., Jegou, H., Douze, M., and ´ Furon, T. The stable signature: Rooting watermarks in latent diffusion models. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pp. 22466– 22477, 2023. Fu, S., Tamir, N., Sundaram, S., Chai, L., Zhang, R., Dekel, T., and Isola, P. Dreamsim: Learning new dimensions of human visual similarity using synthetic data. arXiv preprint arXiv:2306.09344 , 2023. Gowal, S. and Kohli, P. Identifying ai-generated images with synthid. g/identifying-ai-generated-images-wit h-synthid , 2023. Accessed: 2023-09-23. Gunn, S., Zhao, X., and Song, D. An undetectable watermark for generative image models. arXiv preprint arXiv:2410.07369 , 2024. Gustavosta. Stable diffusion prompts dataset, May 2023. URL Gustavosta/Stable-Diffusion-Prompts . Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., and Hochreiter, S. Gans trained by a two time-scale update rule converge to a local nash equilibrium. Advances in neural information processing systems , 30, 2017. Ho, J., Jain, A., and Abbeel, P. Denoising diffusion probabilistic models. Advances in neural information process ing systems , 33:6840–6851, 2020. Hore, A. and Ziou, D. Image quality metrics: Psnr vs. ssim. In 2010 20th international conference on pattern recognition , pp. 2366–2369. IEEE, 2010. Huang, H., Wu, Y., and Wang, Q. Robin: Robust and invisible watermarks for diffusion models with adversarial optimization. Advances in Neural Information Processing Systems , 37:3937–3963, 2024. Karras, T., Aittala, M., Aila, T., and Laine, S. Elucidating the design space of diffusion-based generative models. Advances in neural information processing systems , 35: 26565–26577, 2022.
+
+[p. 10 | section: References | type: Text]
+Lee, S. J. and Cho, N. I. Semantic watermarking reinvented: Enhancing robustness and generation quality with fourier integrity. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pp. 18759–18769, 2025.
+
+[p. 10 | section: References | type: ListGroup]
+Li, K., Huang, Z., Hou, X., and Hong, C. Gaussmarker: Robust dual-domain watermark for diffusion models. arXiv preprint arXiv:2506.11444 , 2025. Lin, T.-Y., Maire, M., Belongie, S., Hays, J., Perona, P., Ramanan, D., Dollar, P., and Zitnick, C. L. Microsoft coco: ´ Common objects in context. In Computer Vision–ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part V 13 , pp. 740– 755. Springer, 2014. Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J. Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps. Advances in Neural Information Processing Systems , 35:5775–5787, 2022. Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J. Dpmsolver++: Fast solver for guided sampling of diffusion probabilistic models. Machine Intelligence Research , pp. 1–22, 2025. Meng, Z., Peng, B., and Dong, J. Latent watermark: Inject and detect watermarks in latent diffusion space. arXiv preprint arXiv:2404.00230 , 2024. Muller, A., Lukovnikov, D., Thietke, J., Fischer, A., and ¨ Quiring, E. Black-box forgery attacks on semantic watermarks for diffusion models. In Proceedings of the Computer Vision and Pattern Recognition Conference , pp. 20937–20946, 2025. Radford, A., Kim, J. W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., Krueger, G., and Sutskever, I. Learning transferable visual models from natural language supervision. In ICML , 2021. Ramesh, A., Dhariwal, P., Nichol, A., Chu, C., and Chen, M. Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.06125 , 1(2):3, 2022. Ren, K., Yang, Z., Lu, L., Liu, J., Li, Y., Wan, J., Zhao, X., Feng, X., and Shao, S. Sok: On the role and future of aigc watermarking in the era of gen-ai. arXiv preprint arXiv:2411.11478 , 2024. Rezaei, A., Akbari, M., Alvar, S. R., Fatemi, A., and Zhang, Y. Lawa: Using latent space for in-generation image watermarking. In European Conference on Computer Vision , pp. 118–136. Springer, 2024.
+
+[p. 10 | section: References | type: ListGroup]
+Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , pp. 10684–10695, June 2022. Song, J., Meng, C., and Ermon, S. Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 , 2020a. Song, Y. and Ermon, S. Improved techniques for training score-based generative models. Advances in neural information processing systems , 33:12438–12448, 2020. Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456 , 2020b. Tancik, M., Mildenhall, B., and Ng, R. Stegastamp: Invisible hyperlinks in physical photographs. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pp. 2117–2126, 2020. Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing , 13(4):600–612, 2004. Wang, Z., Guo, J., Zhu, J., Li, Y., Huang, H., Chen, M., and Tu, Z. Sleepermark: Towards robust watermark against fine-tuning text-to-image diffusion models. In Proceed ings of the Computer Vision and Pattern Recognition Conference , pp. 8213–8224, 2025. Wen, Y., Kirchenbauer, J., Geiping, J., and Goldstein, T. Tree-rings watermarks: Invisible fingerprints for diffusion images. Advances in Neural Information Processing Systems , 36, 2024. Yang, J., Liu, H., Guo, W., Rao, Z., Xu, Y., and Niu, D. Sifid: Reassess summary factual inconsistency detection with llm. arXiv preprint arXiv:2403.07557 , 2024a. Yang, P., Ci, H., Song, Y., and Shou, M. Z. Can simple averaging defeat modern watermarks? Advances in Neu ral Information Processing Systems , 37:56644–56673, 2024b. Yang, Z., Zeng, K., Chen, K., Fang, H., Zhang, W., and Yu, N. Gaussian shading: Provable performance-lossless image watermarking for diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pp. 12162–12171, 2024c. Zhang, L., Liu, X., Martin, A. V., Bearfield, C. X., Brun, Y., and Guan, H. Attack-resilient image watermarking using stable diffusion. Advances in Neural Information Processing Systems , 37:38480–38507, 2024.
+
+[p. 11 | section: References | type: Text]
+Zhang, R., Isola, P., Efros, A. A., Shechtman, E., and Wang, O. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition , pp. 586–595, 2018.
+
+[p. 11 | section: References | type: ListGroup]
+Zhao, X., Zhang, K., Su, Z., Vasan, S., Grishchenko, I., Kruegel, C., Vigna, G., Wang, Y.-X., and Li, L. Invisible image watermarks are provably removable using generative ai. arXiv preprint arXiv:2306.01953 , 2023. Zhao, X., Zhang, K., Su, Z., Vasan, S., Grishchenko, I., Kruegel, C., Vigna, G., Wang, Y.-X., and Li, L. Invisible image watermarks are provably removable using generative ai. Advances in neural information processing systems , 37:8643–8672, 2024.

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+## Abstract
+Watermarking is a technical alternative to safeguarding intellectual property and reducing misuse. Existing methods focus on optimizing watermarked latent variables to balance watermark robustness and fidelity, as Latent diffusion models (LDMs) are considered a powerful tool for generative tasks. However, reliance on computationally intensive heuristic optimization for iterative signal refinement results in high training overhead and local optima entrapment. To address these issues, we propose an Analytical Watermarking Framework for Controllable Generation (ALIEN). We develop the first analytical derivation of the timedependent modulation coefficient that guides the diffusion of watermark residuals to achieve controllable watermark embedding pattern. Experimental results show that ALIEN-Q outperforms the state-of-the-art by 33.1% across 5 quality metrics, and ALIEN-R demonstrates 14.0% improved robustness against generative variant and stability threats compared to the state-of-the-art across 15 distinct conditions. Code can be available at
+## 1. Introduction
+Text-to-image diffusion models, such as Stable Diffusion [\(Rombach et al.,](#page-9-0) [2022\)](#page-9-0) and DALL·E [\(Ramesh et al.,](#page-9-1) [2022\)](#page-9-1), have demonstrated impressive capabilities in generating high-quality images. To safeguard the intellectual property of generative models [\(Gowal & Kohli,](#page-8-0) [2023\)](#page-8-0) and facilitate misuse tracking [\(Barrett,](#page-8-1) [2023\)](#page-8-1), Governments are increasingly calling for regulations [\(European Union,](#page-8-2) [2024;](#page-8-2) [Biden,](#page-8-3) [2023\)](#page-8-3) to mandate watermark adoption. Robust and imperceptible watermarking of generated images has become a critical and urgent research focus. Post-processing watermarking [\(Cox et al.,](#page-8-4) [2007\)](#page-8-4) is applied to the contents gener-
+<span id="page-0-0"></span>![](_page_0_Figure_20.jpeg)
+*Figure 1.* (a) Latent modification, (b) Constrained sampling, (c) Iterative optimization, (d) Our ALIEN with principled embedding.
+ated by the diffusion model, but its robustness is insufficient for reliable detection in real-world applications [\(Ren et al.,](#page-9-2) [2024\)](#page-9-2). Some studies consider model distribution scenarios [\(Rezaei et al.,](#page-9-3) [2024;](#page-9-3) [Ci et al.,](#page-8-5) [2024;](#page-8-5) [Feng et al.,](#page-8-6) [2024;](#page-8-6) [Wang](#page-9-4) [et al.,](#page-9-4) [2025\)](#page-9-4). Diffusion models are fine-tuned to embed watermarks into the model parameters, which inevitably limits efficiency and scalability.
+Recent research has concentrated on semantic watermarking [\(Lee & Cho,](#page-9-5) [2025\)](#page-9-5), which aims to embed watermark signals into the semantic or latent features to better resist imageprocessing-based attacks [\(Zhao et al.,](#page-10-0) [2024\)](#page-10-0). Watermarking methods based on initial latent variable modifications [\(Wen et al.,](#page-9-6) [2024;](#page-9-6) [Ci et al.,](#page-8-7) [2025\)](#page-8-7) embed watermarks by directly modifying or adding perturbations to the initial latents (Fig. [1\(](#page-0-0)a)). While the mechanism is intuitive, the mapping between the initial latent space and the final image is highly complex and nonlinear, making direct modifications prone to semantic drift. Furthermore, to maintain invisibility, the amount of modification to the initial latents is strictly limited, making it difficult to increase watermark capacity. To ensure high capacity and lossless watermark embedding, Watermarks based on the Gaussian-Constrained Identifiable Subspace Sampling [\(Yang et al.,](#page-9-7) [2024c;](#page-9-7) [Gunn et al.,](#page-8-8) [2024\)](#page-8-8)
+{1}------------------------------------------------
+combined with cryptography, divide the initial latent space into non-overlapping identifiable subspaces, forcing users to sample from subspaces associated with specific watermark information (Fig. [1\(](#page-0-0)b)). This rigid constraint on the initial latent space limits generative diversity. Watermarking methods based on optimization [\(Huang et al.,](#page-8-9) [2024;](#page-8-9) [Zhang et al.,](#page-9-8) [2024\)](#page-9-8) perform watermark optimization in the latent space to better balance robustness and fidelity (Fig. [1\(](#page-0-0)c)). However, their reliance on computationally intensive heuristic optimization to iteratively find the optimal watermark, leading to substantial training overhead and prone to local optima. Furthermore, detection of semantic watermarking typically depends on diffusion inversion, which limits applicability to reversible samplers [\(Lu et al.,](#page-9-9) [2022\)](#page-9-9) and watermarks become undetectable when images are generated with irreversible samplers [\(Karras et al.,](#page-8-10) [2022\)](#page-8-10). Attackers can exploit this vulnerability to remove watermarks by regenerating images with irreversible schedulers. [\(An et al.,](#page-8-11) [2024\)](#page-8-11).
+108 109 Despite the progress made by aforementioned semantic watermarking schemes in robust embedding, they circumvent a fundamental issue: the inability to derive a precise and efficient watermark embedding mechanism from the generative principles of diffusion models. Current optimization or constraint-based methods essentially avoid this problem, instead relying on computationally intensive optimization or sampling constraints. These approaches inherently limits the fidelity, efficiency, and diversity.
+To address these issues, we propose an Analytical Watermarking Framework for Controllable Generation (ALIEN). As shown in Fig. [1\(](#page-0-0)d), unlike existing methods that rely on computationally intensive heuristic latent variable optimization or constraints on initial latent sampling, we start with the reverse process of the Stochastic Differential Equation of the diffusion model and present the first analytic derivation of the watermark residual propagation mechanism. Specifically, given a target watermark residual, we analytically derive a time-dependent modulation coefficient that transforms this target into a precise correction term for the noise prediction. By injecting this correction at each denoising step, we effectively modify the underlying probability flow of the diffusion model. This imposes a deterministic force that seamlessly guides the generation trajectory toward the watermarked state regardless of the sampling path, thereby eliminating the need for iterative optimization and ensuring compatibility with various samplers. ALIEN achieves a principled watermark embedding pattern, rather than relying on heuristic methods. Without the need for iterative optimization, we inject the precisely modulated watermark into the noise prediction target at each step of the denoising process.
+Our contributions are three-fold: (1) We achieve the first analytic derivation of watermark propagation for seamless, low-inference-cost embedding, eliminating the need for iterative optimization. (2) Since the watermark is precisely compensated based on diffusion model, ALIEN preserves semantic consistency and visual fidelity by leveraging precise theoretical compensation for the watermark signal. (3) The ALIEN watermark embedding mechanism is independent of specific initial latent variables and sampler types (including irreversible samplers), solving the issue of strong reliance on reversible samplers of semantic watermarking.
+## 2. Related Work
+Diffusion models exhibit exceptional performance in image generation [\(Dhariwal & Nichol,](#page-8-12) [2021\)](#page-8-12), leveraging the methodology [\(Ho et al.,](#page-8-13) [2020;](#page-8-13) [Song et al.,](#page-9-10) [2020b\)](#page-9-10) and the sampling techniques [\(Song et al.,](#page-9-11) [2020a;](#page-9-11) [Song & Ermon,](#page-9-12) [2020\)](#page-9-12). LDMs optimize image generation within the latent space of the pretrained Variational Autoencoder (VAE), which further accelerates the practical applications of diffusion models. During the inference phase, LDM first samples an initial latent z<sup>T</sup> ∈ R c×w×h from a standard Gaussian distribution N (0, I), where T denotes the total time step of the diffusion model. Following iterative denoising, the latent vector evolves into the noise-free representation z0. The final image x<sup>0</sup> is reconstructed by the VAE decoder from z0. Safeguarding the intellectual property of generated content and preventing misuse have become critical research priorities. This paper focuses on critical issues of fidelity, efficiency, and controllability in existing approaches for integrating watermarking into the diffusion process.
+Watermarking in Latent Diffusion Models aims at tracking the origin and ensuring the accountability of the generated content. For a comprehensive context regarding the taxonomy of existing watermarking methods a detailed review is provided in Appendix [D.](#page-16-0) We specifically focus on prior work integrating watermarking during the diffusion process. Latent modification Watermark such as Tree-Ring [\(Wen et al.,](#page-9-6) [2024\)](#page-9-6) and RingID [\(Ci et al.,](#page-8-7) [2025\)](#page-8-7) embed watermarks in the Fourier space of the initial latent which leads to semantic drift. Constrained sampling watermark such as Gaussian Shading [\(Yang et al.,](#page-9-7) [2024c\)](#page-9-7), GaussMarker [\(Li](#page-9-13) [et al.,](#page-9-13) [2025\)](#page-9-13) and PRC [\(Gunn et al.,](#page-8-8) [2024\)](#page-8-8) utilize cryptographic principles to modify the sampling pattern, but strict constraints limit the sampling range, resulting in reduced controllability. Optimization-based methods such as Zodiac [\(Zhang et al.,](#page-9-8) [2024\)](#page-9-8) and Robin [\(Huang et al.,](#page-8-9) [2024\)](#page-8-9), optimize latent variables for higher semantic consistency, but reliance on heuristic optimization incurs computational costs. The detection of aforementioned methods depends on diffusion inversion, limiting their function to reversible samplers and is ineffective with irreversible samplers. Our method achieves low-overhead and universally applicable watermark via analytic derivation.
+{2}------------------------------------------------
+Figure 2. The ALIEN framework consists of two main stages: (Top) Imperceptible Latent Watermark Generation, where a secret encoder $E_s$ and decoder $D_s$ are trained to embed a message m into a robust latent residual $\delta_w$ while preserving image quality. (Bottom) Analytic SDE Reverse Drift Correction, which applies the time-dependent modulation to the noise prediction. This principled correction steers the generative trajectory to satisfy the watermark constraint in a sampler-agnostic manner.
+## 3. Methodology
+<span id="page-2-0"></span>110
+132133
+#### 3.1. Framework of ALIEN
+We extend to achieve applicability and theoretical controllability of semantic watermarking. As demonstrated in Fig. 2, our ALIEN embeds the watermark in intermediate diffusion states to manipulate the generation trajectory through precise correction of the probability flow. To generate imperceptible watermark residuals, we implement an Imperceptible Latent Watermark Generation module to generate the invisible and robust watermark residual in the latent space. For principled embedding, we propose Analytic SDE Reverse Drift Correction, which analytically derives the necessary modifications to the probability flow required by the diffusion model for watermark embedding under Variance Preserving Stochastic Differential Equation (VP-SDE) (Song et al., 2020b), providing an explicit correction target for noise prediction that is compatible with both stochastic and deterministic sampling processes. This derived target is implemented via the Modulation of Noise Prediction Target module, which specifies the requisite adjustment to the model's noise prediction output, thereby realizing the controlled and imperceptible semantic watermarking.
+#### 3.2. Imperceptible Latent Watermark Generation
+To generate an imperceptible yet robust watermark residual, we jointly train a secret encoder $E_s$ and a watermark decoder $D_s$ . Ideally, the watermarked latent representation $z_w$ should be conditioned on both the input latent $z_0$ and the
+message m to enhance imperceptibility. However, utilizing a $z_0$ -dependent watermark becomes impractical as the intermediate latent states of the diffusion model are not readily accessible for deterministic conditioning. Therefore, we opt to embed a cover-agnostic watermark prominent in the latent space. Specifically, the secret residual $\delta_w=E(m)$ is added to the input latent $z_0$ , forming the watermarked latent $z_w=z_0+\delta_w$ . The watermarked image $x_w$ is generated as $x_w=\mathcal{D}(z_w)$ , and the message is extracted by applying the decoder $D_s$ to $z_w$ , yielding $m'=D_s(z_w)$ . We employ the Binary Cross-Entropy loss to optimize for the accuracy of message extraction between the original message m and the decoded message m'.
+To ensure the visual consistency of the watermark, we compute the LPIPS loss (Zhang et al., 2018) and the Mean Squared Error loss between the watermarked image $x_w$ and the reconstructed image $x_r$ , rather than between $x_w$ and the original image $x_o$ . This choice is necessary because the VAE compression and reconstruction already introduce a measurable irrecoverable quality gap between $x_o$ and $x_r$ . Optimizing against $x_o$ would necessitate the watermark training process to compensate for VAE reconstruction errors, which would increase complexity and hinder embedding effectiveness. Our training objective can be summarized below, where $\lambda_1$ and $\lambda_2$ are coefficients:
+$$\mathcal{L}_{T} = \mathcal{L}_{BCE}^{(m,m')} + \lambda_{1} \mathcal{L}_{LPIPS}^{(x_{r},x_{w})} + \lambda_{2} \mathcal{L}_{MSE}^{(x_{r},x_{w})},$$
+(1)
+where $\mathcal{L}_{BCE}$ is the Binary Cross-Entropy loss, $\mathcal{L}_{LPIPS}$ is the Learned Perceptual Image Patch Similarity loss (Zhang
+{3}------------------------------------------------
+## <span id="page-3-2"></span>Algorithm 1 ALIEN Watermarking
+17: **Return** $D_s(\mathcal{E}_{VAE}(\mathbf{x}_{wm}))$
+```
+PHASE I: EMBEDDING
+2: Input: Pre-trained U-Net \theta, Encoder E_s, Scheduler S,
+VAE \mathcal{D}_{VAE}, Prompt c, Secret m, Strength \lambda, Interval
+[T_{start}, T_{end}]
+3: Output: Watermarked Image \mathbf{x}_{wm}
+4: \delta_{wm} \leftarrow E_s(\mathbf{m})
+5: \mathbf{z}_t \sim \mathcal{N}(\mathbf{0}, \mathbf{I})
+6: for t = T down to 1 do
+\epsilon_{\theta}^{t} \leftarrow \text{CFG}(\theta, \mathbf{z}_{t}, S.\text{steps}[t], \mathbf{c})
+\begin{aligned} & \text{if } T_{start} \leq t \leq T_{end} \text{ then} \\ & \epsilon_{\theta}^t \leftarrow \epsilon_{\theta}^t - \lambda \cdot \left(\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}}\right) \cdot \delta_{wm} \end{aligned}
+10:
+\mathbf{z}_t \leftarrow S.\text{step}(\epsilon_{\theta}^t, t, \mathbf{z}_t).\text{prev\_sample}
+11:
+12: end for
+13: \mathbf{x}_{wm} \leftarrow \mathcal{D}_{VAE}(\mathbf{z}_t)
+PHASE II: EXTRACTION
+15: Input: Image \mathbf{x}_{wm}, \mathcal{E}_{VAE}, Decoder D_s
+16: Output: Secret m'
+```
+et al., 2018), and $\mathcal{L}_{MSE}$ is the Mean Squared Error loss. Existing studies (Wang et al., 2025; Meng et al., 2024) demonstrate that injecting and detecting watermarks in the latent space can inherently resist various common distortions. We follow prior practice by omitting the distortion layer during training (validated in Tab. 4). The effectiveness of watermark remains unaffected even if an adversary finetunes U-Net $\theta$ and $\mathcal{D}$ on clean images and uses a fine-tuned latent decoder $\mathcal{D}'$ to generate images (validated in Fig. 8).
+#### 3.3. Analytic SDE Reverse Drift Correction
+To achieve precise watermark embedding over the generative process, we leverage the VP-SDE to analytically derive the exact probability flow correction required for watermark embedding.
+$\mathbf{z}_0$ Constraint. Our goal is to embed a predetermined watermark residual $\delta_{wm}$ into the final denoised latent $\mathbf{z}_0$ , resulting in the $\mathbf{z}_0$ -space constraint $\hat{\mathbf{z}}_0^{wm} = \hat{\mathbf{z}}_0^{orig} + \delta_{wm}$ , where $\hat{\mathbf{z}}_0^{wm}$ and $\hat{\mathbf{z}}_0^{orig}$ are the clean data estimates predicted by the U-Net for the current latent state $\mathbf{z}_t$ , with and without the watermark, respectively.
+**Score Function.** Under the VP-SDE, The diffusion process is defined by a forward SDE that gradually perturbs clean data into noise:
+$$d\mathbf{z} = \mathbf{f}(\mathbf{z}, t)dt + g(t)d\mathbf{w},$$
+where $\mathbf{f}(\mathbf{z}, t) : \mathbb{R}^d \to \mathbb{R}^d$ denotes the drift coefficient, while $g(t) \in \mathbb{R}$ represents the scalar diffusion coefficient, with
+<span id="page-3-1"></span>![](_page_3_Figure_10.jpeg)
+![](_page_3_Figure_11.jpeg)
+(b) Injection Strength Schedule
+Generation Step
+Figure 3. Comparison of ALIEN-R and ALIEN-Q. (a) The L2 norm of noise prediction during the diffusion process. (b) The evolution of injection strength $\frac{\sqrt{\alpha_t}}{\sqrt{1-\bar{\alpha}_t}}$ .
+$\mathbf{w}(t)$ denoting the standard Wiener process. The reverse generation process of the diffusion model is governed by a reverse-time stochastic differential equation:
+$$d\mathbf{z} = \underbrace{[\mathbf{f}(\mathbf{z}, t) - g^{2}(t)\nabla_{\mathbf{z}}\log p_{t}(\mathbf{z})]}_{\text{Reverse Drift }\mathbf{F}_{rev}} dt + g(t)d\bar{\mathbf{w}}, \quad (2)$$
+where $\bar{\mathbf{w}}$ denotes the standard Wiener process in reverse time. To realize the watermark $z_0$ constraint, we precisely control the probability flow, which requires determining the necessary correction $\Delta \mathbf{F}_{rev}$ for the reverse SDE drift term. Since $\Delta \mathbf{F}_{rev}$ relies on the score function $\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t)$ , analytically quantifying the difference in the score function becomes a direct path to derive $\Delta \mathbf{F}_{rev}$ . The score function is exactly and linearly related to the difference between $\mathbf{z}_t$ and its denoised estimate $\hat{\mathbf{z}}_0$ . This analytical relationship is mathematically described as follows:
+<span id="page-3-0"></span>
+$$\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t) = -\frac{1}{1 - \bar{\alpha}_t} (\mathbf{z}_t - \sqrt{\bar{\alpha}_t} \hat{\mathbf{z}}_0).$$
+(3)
+Applying the analytical mapping Eq.3 allows us to analytically determine the difference in the score function induced by the $\mathbf{z}_0$ constraint, thereby translating the watermark residual $\delta_{wm}$ into the required shift in the score function space.
+**Probability Flow Correction.** Based on the analytical structure of VP-SDE for the reverse drift term $\mathbf{F}_{rev}$ , we derive
+{4}------------------------------------------------
+| Method | G.S. | StegaStamp | Tree-Ring | ROBIN | ZoDiac | AquaLoRA | StableSig. | ALIEN-Q | ALIEN-R |
+|----------------------|------------------------------------|-----------------------------------------|-----------------------------------------|-----------------------------------------|-----------------------------------------|------------|-----------------------------------------|-----------------------------------------|-----------------------------------------|
+| Original<br>Image | No<br>Original | | | | | | | | |
+| Watermarked<br>Image | | | | | | | | | |
+| Residual (×10) | | | | | | | | | |
+| Metrics | PSNR:——<br>SSIM: :——<br>LPIPS: :—— | PSNR:29.26<br>SSIM:0.909<br>LPIPS:0.065 | PSNR:14.25<br>SSIM:0.570<br>LPIPS:0.488 | PSNR:24.64<br>SSIM:0.917<br>LPIPS:0.091 | PSNR:28.46<br>SSIM:0.921<br>LPIPS:0.046 | SSIM:0.776 | PSNR:29.61<br>SSIM:0.891<br>LPIPS:0.039 | PSNR:33.29<br>SSIM:0.942<br>LPIPS:0.020 | PSNR:27.24<br>SSIM:0.855<br>LPIPS:0.107 |
+Figure 4. Qualitative comparison of watermarked samples and $10 \times$ magnified residuals. We compare ALIEN with baselines covering post-processing (StegaStamp), latent modification (Tree-Ring), optimization (ROBIN, ZoDiac), and fine-tuning (AquaLoRA, StableSig.).
+<span id="page-4-2"></span>*Table 1.* Quantitative Comparison of Visual Quality and Fidelity across Watermarking Schemes. D.S. denotes the Dreamsim (Fu et al., 2023) metric.
+| Method | FID | CLIP | PSNR | SSIM | SIFID | D.S. |
+|----------|-------|--------|-------|-------|-------|-------|
+| No WM | 24.31 | 0.3368 | | | _ | |
+| StegaS. | 24.56 | 0.3363 | 28.59 | 0.878 | 0.189 | 0.021 |
+| ZoDiac | _ | | 28.01 | 0.922 | 0.121 | 0.022 |
+| AquaL. | 24.79 | 0.3366 | 17.07 | 0.664 | 0.183 | 0.139 |
+| TreeR. | 24.63 | 0.3370 | 12.76 | 0.429 | 0.741 | 0.291 |
+| G.S. | 24.42 | 0.3378 | _ | | _ | |
+| ROBIN | 24.61 | 0.3366 | 22.96 | 0.756 | 0.212 | 0.057 |
+| StableS. | 24.56 | 0.3367 | 29.09 | 0.878 | 0.105 | 0.011 |
+| ALIEN-Q | 24.29 | 0.3369 | 32.41 | 0.949 | 0.023 | 0.003 |
+| ALIEN-R | 24.74 | 0.3366 | 20.42 | 0.745 | 0.227 | 0.061 |
+the required reverse SDE drift correction $\Delta \mathbf{F}_{rev}$ to enforce the watermark constraint (Details provided in Appendix A). The resulting correction term $\Delta \mathbf{F}_{rev}$ is analytically defined by the following expression:
+<span id="page-4-0"></span>
+$$\Delta \mathbf{F}_{rev}(\mathbf{z}_t, t) = -g^2(t) \frac{\sqrt{\bar{\alpha}_t}}{1 - \bar{\alpha}_t} \delta_{wm}.$$
+(4)
+This analytical derivation Eq.4 provides the theoretical foundation for the ALIEN framework. It precisely quantifies the correction $\Delta \mathbf{F}_{rev}$ required by the watermark objective $\delta_{wm}$ within the SDE probability flow framework. Since this correction targets the score function of the latent distribution, it demonstrates that the watermark is sampler-agnostic.
+#### 3.4. Modulation of Noise Prediction Target
+To achieve the practical implementation of the SDE drift correction $\Delta \mathbf{F}_{rev}$ , we analytically relate the SDE reverse drift correction to the noise prediction offset of U-Net within the VP-SDE framework (Details provided in Appendix A), we derive the required compensation signal $\Delta \epsilon_{wm}$ necessary
+<span id="page-4-3"></span>*Table 2.* Stability Evaluation measured by Detection Confidence. We assess robustness across Samplers (DPM++ SDE, Euler a., DPM2 a.), Inference Steps (25, 50), Guidance Scale (10, 20), and Model Versions (v1.5, v2.1).
+| Method | Sa | ampler | | Steps | | Sc | ale | Model | |
+|----------|---------|--------|-------|-------|-------|-------|-------|-------|-------|
+| | DPM-SDE | Eulera | DPM2a | 25 | 50 | 10 | 20 | v1.5 | v2.1 |
+| StegaS. | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.990 | 0.999 |
+| StableS. | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |
+| TreeR. | 0.000 | 0.000 | 0.000 | 0.963 | 0.963 | 0.963 | 0.963 | 0.958 | 0.963 |
+| G.S. | 0.557 | 0.586 | 0.552 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |
+| AquaL. | 0.952 | 0.953 | 0.939 | 0.945 | 0.955 | 0.940 | 0.939 | 0.954 | |
+| ALIEN-Q | 0.989 | 0.979 | 0.972 | 0.985 | 0.990 | 0.982 | 0.975 | 0.989 | 0.991 |
+| ALIEN-R | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |
+to enforce the $\mathbf{z}_0$ constraint:
+<span id="page-4-1"></span>
+$$\Delta \epsilon_{wm} = -\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}} \delta_{wm}.$$
+(5)
+Refer to Eq. (5), to realize a fixed watermark residual $\delta_{wm}$ in the $\mathbf{z}_0$ space, the U-Net will introduce a time-dependent compensation signal $\Delta\epsilon_{wm}$ proportional to the watermark residual in its noise prediction. As illustrated in Fig. 3, the injection coefficient exhibits a surge approaching $\mathbf{z}_0$ , implying that late-stage injection yields stronger constraints but risks visual fidelity. We adjust the injection magnitude and timestep range to formulate two configurations: ALIEN-Q (Quality-Oriented) and ALIEN-R (Robustness-Oriented). The procedure is outlined in Alg. 1.
+#### 4. Experiments
+## 4.1. Experimental Setup
+Watermarking Baselines. We compare ALIEN with mainstream latent semantic watermarking schemes across three primary categories: the initial latent variable modification
+{5}------------------------------------------------
+<span id="page-5-0"></span>*Table 3.* Robustness Evaluation across variant Regenerative Attacks. Each cell reports performance under three attacks: Regeneration → Rinse-2X → Rinse-4X. Values denote Detection Confidence/ TPR@1%FPR.
+| Method | | Scheduler (Cell Format: Regen. Data Rinse-2X Data Rinse-4X Data) | | | | | | | | | | |
+|----------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------|--|-----------------------------------|---------|--|-----------------------------------|--|--------|-----------------------------------|--|--|
+| | DDIM | | | DPM++ 2M SDE | Euler a | | | | DPM2 a | | | |
+| StegaS. | 0.692/0.957 0.578/0.347 0.531/0.102 0.636/0.575 0.562/0.182 0.502/0.000 0.624/0.631 0.542/0.180 0.513/0.000 0.615/0.591 0.556/0.120 0.495/0.000 | | | | | | | | | | | |
+| ZoDiac | 0.938/1.000 0.743/0.104 0.527/0.032 0.693/0.585 0.670/0.431 0.562/0.125 0.643/0.315 0.643/0.250 0.628/0.210 0.833/0.650 0.572/0.281 0.520/0.152 | | | | | | | | | | | |
+| TreeR. | 0.868/1.000 0.724/0.861 0.408/0.489 0.855/0.918 0.824/0.905 0.753/0.851 0.821/0.941 0.449/0.512 0.277/0.306 0.647/0.755 0.531/0.656 0.326/0.427 | | | | | | | | | | | |
+| G.S. | 0.978/1.000 0.898/1.000 0.845/1.000 0.943/1.000 0.953/1.000 0.926/1.000 0.946/1.000 0.847/1.000 0.695/0.905 0.923/1.000 0.858/1.000 0.711/0.915 | | | | | | | | | | | |
+| AquaL. | 0.757/0.742 0.627/0.145 0.573/0.000 0.879/0.942 0.833/0.858 0.696/0.486 0.663/0.225 0.618/0.078 0.551/0.000 0.679/0.371 0.604/0.086 0.536/0.029 | | | | | | | | | | | |
+| ROBIN | —- /0.638 —- /0.242 —- /0.153 | | | —- /1.000 —- /0.728 —- /0.275 | | | —- /0.980 —- /0.705 —- /0.486 | | | —- /0.075 —- /0.105 —- /0.100 | | |
+| StableS. | 0.496/0.000 0.477/0.000 0.521/0.000 0.512/0.000 0.512/0.000 0.510/0.000 0.498/0.000 0.520/0.000 0.513/0.000 0.506/0.000 0.485/0.000 0.502/0.000 | | | | | | | | | | | |
+| | ALIEN-Q 0.848/1.000 0.752/0.865 0.618/0.342 0.935/1.000 0.898/1.000 0.842/0.942 0.866/1.000 0.661/0.581 0.563/0.163 0.857/1.000 0.673/0.636 0.581/0.124 | | | | | | | | | | | |
+| | ALIEN-R 0.999/1.000 0.908/1.000 0.829/1.000 0.999/1.000 0.989/1.000 0.967/1.000 0.988/1.000 0.908/1.000 0.731/0.727 0.989/1.000 0.878/1.000 0.742/0.875 | | | | | | | | | | | |
+| | Gaussian<br>Shading | Tree-ring | AquaLoRA ALIEN-Q | ALIEN-R |
+|-----------------------------|---------------------|-----------|------------------|---------|
+| DDIM<br>Original | No<br>Original | | | |
+| DDIM<br>Watermarked | | | | |
+| DPM2 a<br>Watermarked | | | | |
+| Euler a<br>Watermarked | | | | |
+| DPM++ 2M SDE<br>Watermarked | | | | |
+*Figure 5.* Visual Comparison under Different Generation Schedulers (DDIM, DPM2 a, Euler a, and DPM++ 2M SDE).
+method Tree-Ring [\(Wen et al.,](#page-9-6) [2024\)](#page-9-6); the constrained sampling method Gaussian Shading [\(Yang et al.,](#page-9-7) [2024c\)](#page-9-7); and the iterative optimization methods ROBIN [\(Huang et al.,](#page-8-9) [2024\)](#page-8-9) and Zodiac [\(Zhang et al.,](#page-9-8) [2024\)](#page-9-8). Additionally, we select the fine-tuning based method Stable Signature [\(Fernandez](#page-8-15) [et al.,](#page-8-15) [2023\)](#page-8-15) and Aqualora [\(Feng et al.,](#page-8-6) [2024\)](#page-8-6), as well as the post-processing image watermarking technique StegaStamp [\(Tancik et al.,](#page-9-15) [2020\)](#page-9-15). Implementation details can be found in Appendix [B.2.](#page-13-0)
+Models and Tasks. Following existing research [\(Yang et al.,](#page-9-7) [2024c\)](#page-9-7), we implement the ALIEN framework on Stable Diffusion v1.5 and Stable Diffusion v2.1. We evaluate our method across two tasks: (1) Detection. All compared methods are configured as single-bit watermarks with a unified pattern. The detection threshold is set individually for each method to achieve a False Positive Rate (FPR) of approximately 1%. (2) Traceability. Multi-bit watermarking methods are evaluated using Bit Accuracy. Single-bit methods, including Tree-ring, Zodiac, and Robin, are excluded due to their lack of watermark capacity. We use prompts
+![](_page_5_Picture_8.jpeg)
+*Figure 6.* Visual Comparison under Regeneration Attacks (DDIM, DPM2 a, Euler a, and DPM++ 2M SDE).
+from Stable Diffusion-Prompts (SDP) [\(Gustavosta,](#page-8-16) [2023\)](#page-8-16), setting the Guidance Scale to 7.5 and the number of sampling steps to 50. Both TPR@1%FPR and Bit Accuracy are computed over 350 watermarked images.
+#### 4.2. Comparison to Baselines
+Watermark Fidelity. We employ PSNR [\(Hore & Ziou,](#page-8-17) [2010\)](#page-8-17) and SSIM [\(Wang et al.,](#page-9-16) [2004\)](#page-9-16) for pixel fidelity, LPIPS [\(Zhang et al.,](#page-10-1) [2018\)](#page-10-1) and DreamSim [\(Fu et al.,](#page-8-14) [2023\)](#page-8-14) for perceptual similarity, FID [\(Heusel et al.,](#page-8-18) [2017\)](#page-8-18) and SIFID [\(Yang et al.,](#page-9-17) [2024a\)](#page-9-17) for realism, and CLIP Score [\(Radford](#page-9-18) [et al.,](#page-9-18) [2021\)](#page-9-18) for semantic alignment. As shown in Tab. [1,](#page-4-2) ALIEN-Q achieves state-of-the-art imperceptibility, significantly outperforming all baselines. It yields the highest pixel fidelity of 32.41 dB PSNR and the best perceptual quality of 0.003 DreamSim, while maintaining FID and CLIP scores comparable to non-watermarked images.
+Watermark Stability. We validate watermark stability across three dimensions: *Sampler Agnosticism* covers both
+{6}------------------------------------------------
+<span id="page-6-0"></span>*Table 4.* Comprehensive Comparison of Watermark Robustness. Performance is reported in decimal scale (0-1). Higher values are better (↑). The **Avg.** column represents the mean performance across all 11 attacks (excluding No Attack). Top section: TPR@1%FPR; Bottom section: Bit Accuracy.
+| Metrics | Method | No | Photo | netric | De | egradati | on | Ge | eometric | ; | C | enerative | | Avg. |
+|-----------|----------|--------|---------|--------|-------|----------|-------|---------|----------|-------|-------|-----------|-------|-------|
+| | | Attack | Bright. | Contr. | JPEG | Blur | Noise | ReScale | C.C. | R.C. | VAE-B | VAE-C | Diff. | |
+| | StegaS. | 1.000 | 0.964 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.964 | 0.975 | 1.000 | 1.000 | 1.000 | 0.991 |
+| | StableS. | 1.000 | 0.958 | 1.000 | 0.781 | 0.973 | 0.042 | 0.935 | 1.000 | 1.000 | 0.000 | 0.079 | 0.000 | 0.611 |
+| | AquaL. | 1.000 | 0.289 | 0.507 | 1.000 | 1.000 | 0.932 | 1.000 | 0.127 | 0.258 | 0.975 | 0.958 | 0.742 | 0.708 |
+| | TreeR. | 1.000 | 0.775 | 0.909 | 1.000 | 1.000 | 0.954 | 0.968 | 0.013 | 0.021 | 0.954 | 1.000 | 1.000 | 0.778 |
+| TPR@ | G.S. | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.981 | 0.979 | 1.000 | 1.000 | 1.000 | 0.996 |
+| Thre1%FPR | ROBIN | 1.000 | 0.913 | 0.684 | 0.921 | 1.000 | 0.013 | 0.935 | 1.000 | 1.000 | 1.000 | 1.000 | 0.638 | 0.826 |
+| | ZoDiac | 1.000 | 0.535 | 0.375 | 0.959 | 0.979 | 0.357 | 0.965 | 0.017 | 0.021 | 0.660 | 0.685 | 1.000 | 0.592 |
+| | ALIEN-Q | 1.000 | 0.783 | 1.000 | 0.954 | 1.000 | 0.645 | 1.000 | 0.153 | 0.311 | 0.965 | 0.970 | 0.945 | 0.793 |
+| | ALIEN-R | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.979 | 1.000 | 0.989 | 0.988 | 1.000 | 1.000 | 1.000 | 0.996 |
+| | StegaS. | 0.999 | 0.811 | 0.850 | 0.999 | 0.999 | 0.821 | 0.999 | 0.667 | 0.681 | 0.837 | 0.816 | 0.692 | 0.834 |
+| | StableS. | 0.998 | 0.892 | 0.851 | 0.712 | 0.845 | 0.535 | 0.878 | 0.991 | 0.993 | 0.506 | 0.541 | 0.489 | 0.748 |
+| Bit Acc. | AquaL. | 0.954 | 0.583 | 0.672 | 0.935 | 0.954 | 0.810 | 0.925 | 0.573 | 0.648 | 0.845 | 0.856 | 0.757 | 0.778 |
+| Bit Acc. | G.S. | 0.999 | 0.939 | 0.964 | 0.995 | 0.999 | 0.903 | 0.996 | 0.657 | 0.655 | 0.996 | 0.997 | 0.978 | 0.916 |
+| | ALIEN-Q | 0.989 | 0.753 | 0.803 | 0.889 | 0.936 | 0.689 | 0.903 | 0.581 | 0.601 | 0.834 | 0.853 | 0.848 | 0.790 |
+| | ALIEN-R | 0.999 | 0.949 | 0.992 | 0.999 | 0.999 | 0.855 | 0.999 | 0.826 | 0.835 | 0.979 | 0.983 | 0.999 | 0.947 |
+<span id="page-6-2"></span>![](_page_6_Figure_4.jpeg)
+Figure 7. Robustness against VAE embedding attacks. Results are averaged across KLVAE8, KLVAE16, and SDXL variants.
+<span id="page-6-1"></span>![](_page_6_Figure_6.jpeg)
+Figure 8. Bit accuracy comparison against Stable Signature across VAE fine-tuning and replacement.
+deterministic (DDIM) and irreversible samplers (Euler Ancestral (Karras et al., 2022), DPM++ 2M Ancestral (Karras et al., 2022), DPM++ SDE (Lu et al., 2025)); Component Adaptability involves substituting different VAE and U-Net versions; and Hyperparameter Stability examines sensitivity to Guidance Scale and Inference Steps. As shown in Tab. 2, existing training-free methods exhibit vulnerability to stochastic samplers. Specifically, Tree-Ring and Gaussian Shading fail completely under DPM++ SDE, Euler a., and DPM2 a., where accuracy hovers near the randomguess baseline. ALIEN achieves state-of-the-art sampler agnosticism by maintaining high bit accuracy exceeding 0.97 across all tested schedulers. Our method demonstrates consistent stability across varying inference steps, guidance scales, and model versions.
+**Watermark Efficiency.** We evaluate the computational overhead across two primary dimensions: *Preparation Cost*, the one-time offline cost, and *Runtime Cost*, the online perimage latency for embedding and extraction. The comparative results are detailed in Tab. 7. ALIEN achieves latencies of 0.079 seconds for embedding and 0.023 seconds for ex-
+traction, maintaining speeds comparable to post-processing baselines while being orders of magnitude faster than the optimization-based method Zodiac, which requires over 122 seconds per image.
+Watermark Robustness. We examine watermark's robustness against three typical kinds of adversarial attacks, including image processing attacks (Hore & Ziou, 2010) for transforming generated images, adversarial attacks (An et al., 2024) for disturbing watermark verification, and reconstructive attacks (Zhao et al., 2023) for re-generating nonwatermarked images. Please refer to the Supplementary Materials for detailed parameter settings. As demonstrated in Tab. 4, ALIEN-R achieves state-of-the-art stability against standard distortions by maintaining a True Positive Rate of 0.996. In adversarial embedding scenarios illustrated in Fig. 7, ALIEN-R exhibits exceptional resistance where latent semantic watermarking baselines degrade rapidly. Tab. 3 shows that against reconstructive attacks, ALIEN-R sustains a high confidence exceeding 0.875 even after four re-generation rounds, whereas competitors like StegaStamp and Stable Signature collapse to near-zero.
+{7}------------------------------------------------
+*Table 5.* Quantitative comparison under Forgery Attacks. Lower values indicate better resistance $(\downarrow)$ .
+| Config | G.S. | Tree-Ring | ALIEN (Ours) | | | | | | | |
+|------------------------------|---------------|---------------|---------------|--|--|--|--|--|--|--|
+| comig | Acc. / PSNR | Acc. / PSNR | Acc. / PSNR | | | | | | | |
+| Scenario A: Average Forgery | | | | | | | | | | |
+| 10 Imgs | 0.952 / 12.23 | 0.882 / 18.86 | 0.539 / 20.06 | | | | | | | |
+| 50 Imgs | 0.969 / 12.79 | 0.908 / 20.34 | 0.605 / 25.29 | | | | | | | |
+| 100 Imgs | 0.969 / 12.65 | 0.910 / 20.95 | 0.708 / 26.48 | | | | | | | |
+| Scenario B: Reprompt Forgery | | | | | | | | | | |
+| SD-V2.1 | 1.000 / | 0.931 / | 0.533 / | | | | | | | |
+![](_page_7_Figure_4.jpeg)
+Figure 9. Robustness against Imprinting Forgery Attack.
+Forgery Resistance. Following existing research (Müller et al., 2025; Yang et al., 2024b), we evaluate the security of our method against three representative forgery attacks: imprinting forgery, reprompting forgery, and average forgery. Imprinting and reprompting forgeries rely on latent optimization via diffusion inversion. ALIEN exhibits superior resistance to these attacks compared to initial-latent-based watermarks. While baselines like Tree-Ring and Gaussian Shading can be successfully forged using only a single image, ALIEN remains unaffected. Average Forgery involves estimating the watermark pattern by collecting pairs of watermarked and non-watermarked images. While baselines like Tree-Ring exhibit vulnerability with confidence exceeding 0.9, ALIEN maintains a suppressed confidence of 0.711, effectively preventing the rapid extraction of the watermark pattern. The practical challenges in acquiring large-scale specific-user data within real-world API scenarios significantly elevate the security threshold.
+Impact of Timestep Range. As shown in Tab. 6, we conducted an ablation study on the injection interval to investigate the trade-off between imperceptibility and robustness. Injecting the watermark across the full reverse process from step 50 down to 1 ensures perfect detection with 1.000 accuracy but introduces significant perceptual degradation, resulting in a PSNR drop to 20.42 dB under Strength B. Narrowing the window to early diffusion stages such as steps 45 to 20 significantly recovers image quality, where the PSNR
+<span id="page-7-1"></span>*Table 6.* Ablation study on Timestep Range under different Watermark Strengths. We compare Image Quality (PSNR) and Detection Performance (Det./Acc.) across two strength settings.
+| Range | Strengt | $\mathbf{th} \mathbf{A} (\lambda = 0.5)$ | Strength B ( $\lambda = 1.0$ ) | | | |
+|-------------------------------------------------------------------------------------------------------------------|-------------------------------------------|-----------------------------------------------------------------------------------|-------------------------------------------|-----------------------------------------------------------------------------------|--|--|
+| $(t_{start} \rightarrow t_{end})$ | PSNR | Det. / Acc. | PSNR | Det. / Acc. | | |
+| $ \begin{array}{c} 1 \to 50 \\ 25 \to 50 \\ 25 \to 40 \\ 10 \to 25 \\ 20 \to 45 \end{array} $ | 24.55<br>30.53<br>40.94<br>31.54<br>33.76 | 1.000 / 1.000<br>1.000 / 1.000<br>0.718 / 0.747<br>0.614 / 0.421<br>0.882 / 1.000 | 20.42<br>26.27<br>23.10<br>26.83<br>31.10 | 1.000 / 1.000<br>1.000 / 1.000<br>0.852 / 1.000<br>0.681 / 0.721<br>0.989 / 1.000 | | |
+<span id="page-7-0"></span>*Table 7.* Performance Comparison regarding Computational Efficiency. <sup>‡</sup> indicates data estimated from original papers.
+| Method | P | rep. Time ( | h) | Embed. E | | | | |
+|-----------|-----------------|-----------------|----------|----------|----------|--|--|--|
+| 111011101 | Pre-train | Fine-tune | Optimize | Time (s) | Time (s) | | | |
+| T.R. | _ | _ | _ | 0.011 | 3.575 | | | |
+| G.S. | _ | | | 0.102 | 4.212 | | | |
+| ROBIN | _ | _ | 0.4 | 0.125 | 1.248 | | | |
+| Zodiac | _ | | | 122.4 | 3.601 | | | |
+| StegaS. | 30 | | | 0.108 | 0.028 | | | |
+| S.S. | $48^{\ddagger}$ | 0.1 | _ | _ | 0.014 | | | |
+| AquaL. | $40^{\ddagger}$ | 15 <sup>‡</sup> | _ | _ | 0.026 | | | |
+| ALIEN | 22 | _ | _ | 0.079 | 0.023 | | | |
+increases to 33.76 dB under Strength A while maintaining a high detection rate.
+Impact of Watermark Strength. As shown in Tab. 6, the injection coefficient $\lambda$ directly modulates the magnitude of the probability flow correction. Increasing the strength from $\lambda=0.5$ in Strength A to $\lambda=1.0$ in Strength B consistently improves detection performance across all ranges. we select the range from 45 to 20 combined with moderate strength as the optimal configuration for ALIEN-Q to maximize quality while ensuring reliable detection.
+#### 5. Conclusion
+Unlike prior approaches relying on heuristic latent modifications, sampling constraints, or computationally intensive optimization, we propose ALIEN, which presents the first analytical derivation of the time-dependent modulation coefficient. This principled approach precisely guides the diffusion of watermark residuals via probability flow modulation, achieving sampler-agnostic embedding. ALIEN overcomes the security vulnerabilities associated with diffusion inversion and irreversible samplers while ensuring high fidelity and low inference cost. Experimental results demonstrate that ALIEN outperforms existing methods in both quality and robustness. Future research will focus on developing content-aware latent watermarking to further enhance security against forgery attacks.
+{8}------------------------------------------------
+## 6. Impact Statement
+Ensuring the accountability and intellectual property protection of generative models has become a critical priority. This paper introduces ALIEN, a principled watermarking framework that enables robust and sampler-agnostic provenance tracking for Latent Diffusion Models. By overcoming the vulnerability of existing methods to irreversible samplers and diverse attacks, we believe our approach effectively mitigates risks such as copyright infringement and malicious misuse, thereby contributing to the development of safer and more trustworthy generative AI.
+## References
+- <span id="page-8-11"></span>An, B., Ding, M., Rabbani, T., Agrawal, A., Xu, Y., Deng, C., Zhu, S., Mohamed, A., Wen, Y., Goldstein, T., et al. Waves: Benchmarking the robustness of image watermarks. *arXiv preprint arXiv:2401.08573*, 2024.
+- <span id="page-8-19"></span>Balle, J., Minnen, D., Singh, S., Hwang, S. J., and Johnston, ´ N. Variational image compression with a scale hyperprior. *arXiv preprint arXiv:1802.01436*, 2018.
+- <span id="page-8-1"></span>Barrett, C. Identifying and mitigating the security risks of generative ai. *arXiv preprint arXiv:2308.14840*, 2023.
+- <span id="page-8-3"></span>Biden, J. R. Executive order on the safe, secure, and trustworthy development and use of artificial intelligence, 2023. URL [ [/briefing-room/statements-releases/20]( [23/07/07/fact-sheet-executive-order-o]( [n-artificial-intelligence/](
+- <span id="page-8-20"></span>Cheng, Z., Sun, H., Takeuchi, M., and Katto, J. Learned image compression with discretized gaussian mixture likelihoods and attention modules. In *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition*, pp. 7939–7948, 2020.
+- <span id="page-8-5"></span>Ci, H., Song, Y., Yang, P., Xie, J., and Shou, M. Z. Wmadapter: Adding watermark control to latent diffusion models. *arXiv preprint arXiv:2406.08337*, 2024.
+- <span id="page-8-7"></span>Ci, H., Yang, P., Song, Y., and Shou, M. Z. Ringid: Rethinking tree-ring watermarking for enhanced multi-key identification. In *European Conference on Computer Vision*, pp. 338–354. Springer, 2025.
+- <span id="page-8-4"></span>Cox, I., Miller, M., Bloom, J., Fridrich, J., and Kalker, T. *Digital watermarking and steganography*. Morgan kaufmann, 2007.
+- <span id="page-8-12"></span>Dhariwal, P. and Nichol, A. Diffusion models beat gans on image synthesis. *Advances in neural information processing systems*, 34:8780–8794, 2021.
+- <span id="page-8-2"></span>European Union. Artificial intelligence act: Regulation (eu) 2024/1689 of the european parliament and of the council, June 2024. URL: [ [eu/legal-content/EN/TXT/?uri=CELEX:]( [32024R1689]( Accessed: 2024-09-24.
+- <span id="page-8-6"></span>Feng, W., Zhou, W., He, J., Zhang, J., Wei, T., Li, G., Zhang, T., Zhang, W., and Yu, N. Aqualora: Toward white-box protection for customized stable diffusion models via watermark lora. *arXiv preprint arXiv:2405.11135*, 2024.
+- <span id="page-8-15"></span>Fernandez, P., Couairon, G., Jegou, H., Douze, M., and ´ Furon, T. The stable signature: Rooting watermarks in latent diffusion models. In *Proceedings of the IEEE/CVF International Conference on Computer Vision*, pp. 22466– 22477, 2023.
+- <span id="page-8-14"></span>Fu, S., Tamir, N., Sundaram, S., Chai, L., Zhang, R., Dekel, T., and Isola, P. Dreamsim: Learning new dimensions of human visual similarity using synthetic data. *arXiv preprint arXiv:2306.09344*, 2023.
+- <span id="page-8-0"></span>Gowal, S. and Kohli, P. Identifying ai-generated images with synthid. [ [g/identifying-ai-generated-images-wit]( [h-synthid]( 2023. Accessed: 2023-09-23.
+- <span id="page-8-8"></span>Gunn, S., Zhao, X., and Song, D. An undetectable watermark for generative image models. *arXiv preprint arXiv:2410.07369*, 2024.
+- <span id="page-8-16"></span>Gustavosta. Stable diffusion prompts dataset, May 2023. URL [ [Gustavosta/Stable-Diffusion-Prompts](
+- <span id="page-8-18"></span>Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., and Hochreiter, S. Gans trained by a two time-scale update rule converge to a local nash equilibrium. *Advances in neural information processing systems*, 30, 2017.
+- <span id="page-8-13"></span>Ho, J., Jain, A., and Abbeel, P. Denoising diffusion probabilistic models. *Advances in neural information processing systems*, 33:6840–6851, 2020.
+- <span id="page-8-17"></span>Hore, A. and Ziou, D. Image quality metrics: Psnr vs. ssim. In *2010 20th international conference on pattern recognition*, pp. 2366–2369. IEEE, 2010.
+- <span id="page-8-9"></span>Huang, H., Wu, Y., and Wang, Q. Robin: Robust and invisible watermarks for diffusion models with adversarial optimization. *Advances in Neural Information Processing Systems*, 37:3937–3963, 2024.
+- <span id="page-8-10"></span>Karras, T., Aittala, M., Aila, T., and Laine, S. Elucidating the design space of diffusion-based generative models. *Advances in neural information processing systems*, 35: 26565–26577, 2022.
+{9}------------------------------------------------
+<span id="page-9-5"></span>Lee, S. J. and Cho, N. I. Semantic watermarking reinvented: Enhancing robustness and generation quality with fourier integrity. In *Proceedings of the IEEE/CVF International Conference on Computer Vision*, pp. 18759–18769, 2025.
+<span id="page-9-22"></span>504
+<span id="page-9-19"></span>516
+<span id="page-9-20"></span>524 525 526
+<span id="page-9-1"></span>536
+- <span id="page-9-13"></span>Li, K., Huang, Z., Hou, X., and Hong, C. Gaussmarker: Robust dual-domain watermark for diffusion models. *arXiv preprint arXiv:2506.11444*, 2025.
+- Lin, T.-Y., Maire, M., Belongie, S., Hays, J., Perona, P., Ramanan, D., Dollar, P., and Zitnick, C. L. Microsoft coco: ´ Common objects in context. In *Computer Vision–ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part V 13*, pp. 740– 755. Springer, 2014.
+- <span id="page-9-9"></span>Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J. Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps. *Advances in Neural Information Processing Systems*, 35:5775–5787, 2022.
+- Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., and Zhu, J. Dpmsolver++: Fast solver for guided sampling of diffusion probabilistic models. *Machine Intelligence Research*, pp. 1–22, 2025.
+- <span id="page-9-14"></span>Meng, Z., Peng, B., and Dong, J. Latent watermark: Inject and detect watermarks in latent diffusion space. *arXiv preprint arXiv:2404.00230*, 2024.
+- Muller, A., Lukovnikov, D., Thietke, J., Fischer, A., and ¨ Quiring, E. Black-box forgery attacks on semantic watermarks for diffusion models. In *Proceedings of the Computer Vision and Pattern Recognition Conference*, pp. 20937–20946, 2025.
+- <span id="page-9-18"></span>Radford, A., Kim, J. W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., Krueger, G., and Sutskever, I. Learning transferable visual models from natural language supervision. In *ICML*, 2021.
+- Ramesh, A., Dhariwal, P., Nichol, A., Chu, C., and Chen, M. Hierarchical text-conditional image generation with clip latents. *arXiv preprint arXiv:2204.06125*, 1(2):3, 2022.
+- <span id="page-9-2"></span>Ren, K., Yang, Z., Lu, L., Liu, J., Li, Y., Wan, J., Zhao, X., Feng, X., and Shao, S. Sok: On the role and future of aigc watermarking in the era of gen-ai. *arXiv preprint arXiv:2411.11478*, 2024.
+- <span id="page-9-3"></span>Rezaei, A., Akbari, M., Alvar, S. R., Fatemi, A., and Zhang, Y. Lawa: Using latent space for in-generation image watermarking. In *European Conference on Computer Vision*, pp. 118–136. Springer, 2024.
+- <span id="page-9-0"></span>Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B. High-resolution image synthesis with latent diffusion models. In *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)*, pp. 10684–10695, June 2022.
+- <span id="page-9-11"></span>Song, J., Meng, C., and Ermon, S. Denoising diffusion implicit models. *arXiv preprint arXiv:2010.02502*, 2020a.
+- <span id="page-9-12"></span>Song, Y. and Ermon, S. Improved techniques for training score-based generative models. *Advances in neural information processing systems*, 33:12438–12448, 2020.
+- <span id="page-9-10"></span>Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. Score-based generative modeling through stochastic differential equations. *arXiv preprint arXiv:2011.13456*, 2020b.
+- <span id="page-9-15"></span>Tancik, M., Mildenhall, B., and Ng, R. Stegastamp: Invisible hyperlinks in physical photographs. In *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition*, pp. 2117–2126, 2020.
+- <span id="page-9-16"></span>Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P. Image quality assessment: from error visibility to structural similarity. *IEEE transactions on image processing*, 13(4):600–612, 2004.
+- <span id="page-9-4"></span>Wang, Z., Guo, J., Zhu, J., Li, Y., Huang, H., Chen, M., and Tu, Z. Sleepermark: Towards robust watermark against fine-tuning text-to-image diffusion models. In *Proceedings of the Computer Vision and Pattern Recognition Conference*, pp. 8213–8224, 2025.
+- <span id="page-9-6"></span>Wen, Y., Kirchenbauer, J., Geiping, J., and Goldstein, T. Tree-rings watermarks: Invisible fingerprints for diffusion images. *Advances in Neural Information Processing Systems*, 36, 2024.
+- <span id="page-9-17"></span>Yang, J., Liu, H., Guo, W., Rao, Z., Xu, Y., and Niu, D. Sifid: Reassess summary factual inconsistency detection with llm. *arXiv preprint arXiv:2403.07557*, 2024a.
+- <span id="page-9-21"></span>Yang, P., Ci, H., Song, Y., and Shou, M. Z. Can simple averaging defeat modern watermarks? *Advances in Neural Information Processing Systems*, 37:56644–56673, 2024b.
+- <span id="page-9-7"></span>Yang, Z., Zeng, K., Chen, K., Fang, H., Zhang, W., and Yu, N. Gaussian shading: Provable performance-lossless image watermarking for diffusion models. In *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition*, pp. 12162–12171, 2024c.
+- <span id="page-9-8"></span>Zhang, L., Liu, X., Martin, A. V., Bearfield, C. X., Brun, Y., and Guan, H. Attack-resilient image watermarking using stable diffusion. *Advances in Neural Information Processing Systems*, 37:38480–38507, 2024.
+{10}------------------------------------------------
+Zhang, R., Isola, P., Efros, A. A., Shechtman, E., and Wang, O. The unreasonable effectiveness of deep features as a perceptual metric. In *Proceedings of the IEEE conference on computer vision and pattern recognition*, pp. 586–595, 2018.
+<span id="page-10-1"></span>
+<span id="page-10-2"></span>
+- Zhao, X., Zhang, K., Su, Z., Vasan, S., Grishchenko, I., Kruegel, C., Vigna, G., Wang, Y.-X., and Li, L. Invisible image watermarks are provably removable using generative ai. *arXiv preprint arXiv:2306.01953*, 2023.
+- <span id="page-10-0"></span>Zhao, X., Zhang, K., Su, Z., Vasan, S., Grishchenko, I., Kruegel, C., Vigna, G., Wang, Y.-X., and Li, L. Invisible image watermarks are provably removable using generative ai. *Advances in neural information processing systems*, 37:8643–8672, 2024.
+{11}------------------------------------------------
+# Supplementary Material
+| A | | Theoretical Analysis of ALIEN | 12 |
+|---|-----|------------------------------------------------|----|
+| | A.1 | Watermark Constraint and Score Discrepancy<br> | 12 |
+| | A.2 | Proof of Reverse SDE Drift Term Correction | 12 |
+| | A.3 | Derivation of UNet Target Noise<br> | 12 |
+| B | | Implementation Details | 13 |
+| | B.1 | Algorithm Pseudocode<br> | 13 |
+| | B.2 | Hyperparameters and Training Settings<br> | 13 |
+| C | | Experimental Setup and Extended Experiments | 14 |
+| | C.1 | Dataset Settings | 14 |
+| | C.2 | Robustness Evaluation Settings | 15 |
+| | C.3 | Extended Experiments | 15 |
+| D | | Extended Related Work | 16 |
+| | D.1 | Watermarking Schemes Taxonomy | 16 |
+{12}------------------------------------------------
+## <span id="page-12-0"></span>A. Theoretical Analysis of ALIEN
+In this section, we provide a rigorous derivation establishing the analytical link between the watermark constraint in the $z_0$ -space and the necessary correction to the probability flow drift term. This derivation proves that ALIEN is theoretically grounded in the VP-SDE framework and is inherently sampler-agnostic.
+### <span id="page-12-1"></span>A.1. Watermark Constraint and Score Function Discrepancy
+1. Watermark Constraint Definition Our objective is to embed a fixed watermark residual $\delta_{wm}$ into the latent representation. We define this as a geometric constraint on the estimated clean data manifold. Let $\hat{\mathbf{z}}_0$ denote the original estimate derived from the model $\theta$ , and $\hat{\mathbf{z}}_0^{wm}$ denote the target watermarked estimate:
+<span id="page-12-4"></span>
+$$\hat{\mathbf{z}}_0^{wm} = \hat{\mathbf{z}}_0 + \delta_{wm}. \tag{6}$$
+**2. Derivation of Score Function Difference** $\Delta$ **Score** Under the VP-SDE framework, Tweedie's formula establishes a linear bijection between the score function $\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t)$ and the denoised estimate $\hat{\mathbf{z}}_0$ :
+$$\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t) = -\frac{\mathbf{z}_t - \sqrt{\bar{\alpha}_t} \hat{\mathbf{z}}_0}{1 - \bar{\alpha}_t}.$$
+(7)
+To enforce the watermark constraint (Eq. 6), the score function must shift to $\nabla_{\mathbf{z}_t} \log p_t^{wm}$ . By substituting the constraint $\hat{\mathbf{z}}_0 - \hat{\mathbf{z}}_0^{wm} = -\delta_{wm}$ , we derive the score discrepancy $\Delta S$ core:
+<span id="page-12-5"></span>
+$$\Delta \text{Score} = \nabla_{\mathbf{z}_{t}} \log p_{t}^{wm} - \nabla_{\mathbf{z}_{t}} \log p_{t}$$
+$$= -\frac{1}{1 - \bar{\alpha}_{t}} \left( -\sqrt{\bar{\alpha}_{t}} (\hat{\mathbf{z}}_{0}^{wm} - \hat{\mathbf{z}}_{0}) \right)$$
+$$= \frac{\sqrt{\bar{\alpha}_{t}}}{1 - \bar{\alpha}_{t}} \delta_{wm}.$$
+(8)
+#### <span id="page-12-2"></span>A.2. Proof of Reverse SDE Drift Term Correction $\Delta \mathbf{F}_{rev}$
+**Definition of Reverse Drift** $\mathbf{F}_{rev}$ The generation trajectory in diffusion models is governed by the reverse-time SDE. The deterministic component of this process, known as the drift term $\mathbf{F}_{rev}$ , is defined as:
+$$\mathbf{F}_{rev}(\mathbf{z}_t, t) = \mathbf{f}(\mathbf{z}_t, t) - g^2(t) \nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t). \tag{9}$$
+where $\mathbf{f}(\mathbf{z}_t, t)$ is the forward drift and g(t) is the diffusion coefficient.
+**Derivation of Drift Correction** $\Delta \mathbf{F}_{rev}$ We calculate the modification to the drift term required to accommodate the watermark. Since the forward physics $\mathbf{f}(\mathbf{z}_t, t)$ remains invariant, the drift correction depends solely on the score shift:
+$$\Delta \mathbf{F}_{rev} = \mathbf{F}_{rev}^{wm} - \mathbf{F}_{rev}^{orig} = -g^2(t) \left(\Delta \text{Score}\right). \tag{10}$$
+Substituting Eq. (8) into the expression above, we obtain the explicit form of the Watermark Drift Force:
+$$\Delta \mathbf{F}_{rev}(\mathbf{z}_t, t) = -g^2(t) \frac{\sqrt{\bar{\alpha}_t}}{1 - \bar{\alpha}_t} \delta_{wm}. \tag{11}$$
+**Theorem:** The spatial constraint $\delta_{wm}$ imposes a constant, deterministic force $\Delta \mathbf{F}_{rev}$ on the probability flow. Because $\mathbf{F}_{rev}$ is the shared driving term for both the stochastic reverse SDE and the deterministic Probability Flow ODE (PF-ODE), this correction guarantees that the watermark embedding is robust across different samplers.
+## <span id="page-12-3"></span>A.3. Derivation of Noise Prediction Target $\epsilon^{target}$
+To implement the theoretical drift correction $\Delta \mathbf{F}_{rev}$ in practice, we modulate the output of the U-Net $\vartheta$ .
+**Score-Noise Relationship** The neural network $\epsilon_{\vartheta}$ approximates the score function via the relation:
+$$\nabla_{\mathbf{z}_t} \log p_t(\mathbf{z}_t) = -\frac{\epsilon_{\vartheta}(\mathbf{z}_t, t)}{\sqrt{1 - \bar{\alpha}_t}}.$$
+(12)
+{13}------------------------------------------------
+## <span id="page-13-3"></span>**Algorithm 2** ALIEN Watermarking
+```
+Phase I: Watermark Embedding
+2: Input: Pre-trained U-Net \theta, Encoder E_s, Scheduler S, VAE Decoder \mathcal{D}_{VAE}, Prompt c, Secret m, Injection Interval
+[T_{start}, T_{end}], Strength \lambda
+3: Output: Watermarked Image \mathbf{x}_{wm}
+4: \delta_{wm} \leftarrow E_s(\mathbf{m})
+5: \mathbf{z}_t \sim \mathcal{N}(\mathbf{0}, \mathbf{I})
+6: for t = T down to 1 do
+\mathbf{t} \leftarrow S. \mathsf{timesteps}[t]
+\epsilon_{\theta}^{t} \leftarrow \text{CFG}(\theta, \mathbf{z}_{t}, \mathbf{t}, \mathbf{c})
+if t \leq T_{end} and t \geq T_{start} then
+// Modulate the prediction target
+\boldsymbol{\epsilon}_{\theta}^{t} \leftarrow \boldsymbol{\epsilon}_{\theta}^{t} - \lambda \cdot \left(\frac{\sqrt{\bar{\alpha}_{t}}}{\sqrt{1 - \bar{\alpha}_{t}}}\right) \cdot \delta_{wm}
+12:
+\mathbf{z}_t \leftarrow S.\text{step}(\epsilon_{\theta}^t, \mathbf{t}, \mathbf{z}_t).\text{prev\_sample}
+14: end for
+15: \mathbf{x}_{wm} \leftarrow \mathcal{D}_{VAE}(\mathbf{z}_t)
+Phase II: Watermark Extraction
+17: Input: Watermarked Image \mathbf{x}_{wm}, VAE Encoder \mathcal{E}_{VAE}, Watermark Decoder D_s
+18: Output: Extracted Secret m'
+19: // Encode image back to watermarked latent
+20: \mathbf{z}_0 \leftarrow \mathcal{E}_{VAE}(\mathbf{x}_{wm})
+21: // Extract secret message from latent
+22: \mathbf{m}' \leftarrow D_s(\mathbf{z}_0)
+```
+**Mapping Drift Correction to** $\epsilon$ **-Space** We equate the score difference derived from the drift requirement to the difference in noise prediction. Using $\Delta Score = -\frac{1}{\sqrt{1-\bar{\alpha}_t}}(\epsilon^{target} - \epsilon_{\vartheta}) = -\frac{\Delta \epsilon}{\sqrt{1-\bar{\alpha}_t}}$ , we have:
+$$-\frac{\Delta \epsilon}{\sqrt{1-\bar{\alpha}_t}} = \frac{\sqrt{\bar{\alpha}_t}}{1-\bar{\alpha}_t} \delta_{wm}. \tag{13}$$
+**Final Update Rule** Solving for the correction term $\Delta \epsilon$ :
+$$\Delta \epsilon = -\sqrt{1 - \bar{\alpha}_t} \cdot \frac{\sqrt{\bar{\alpha}_t}}{1 - \bar{\alpha}_t} \delta_{wm} = -\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}} \delta_{wm}. \tag{14}$$
+Thus, the final target noise $\epsilon^{target}$ required to enforce the watermark is:
+$$\epsilon^{target} = \epsilon_{\vartheta} + \Delta \epsilon = \epsilon_{\vartheta} - \left(\frac{\sqrt{\bar{\alpha}_t}}{\sqrt{1 - \bar{\alpha}_t}}\right) \delta_{wm}. \tag{15}$$
+## <span id="page-13-1"></span>**B.** Implementation Details
+#### <span id="page-13-2"></span>**B.1. Algorithm Pseudocode**
+23: **Return** m<sup>2</sup>
+The core logic of the ALIEN watermarking framework is detailed in Algorithm 2. This algorithm outlines the complete process of watermark embedding during the reverse diffusion process and the subsequent extraction from the latent space.
+#### <span id="page-13-0"></span>**B.2.** Hyperparameters and Training Settings
+Watermark Generation Module Training. We train the Imperceptible Latent Watermark Generation module using the AdamW optimizer with a learning rate of $5 \times 10^{-5}$ and a weight decay of $1 \times 10^{-5}$ . We construct a synthetic training set of
+{14}------------------------------------------------
+*Table 8.* Detailed Robustness Evaluation Settings. We categorize attacks into four distinct groups. Note that Image Processing attacks are grouped by type (Photometry, Geometry, Degradation) to conserve space.
+| Category | Method & Parameters |
+|------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| Image Processing | Photometry: Brightness (×6.0), Contrast (×12.0)<br>Geometry: Resize (s = 0.5), Center Crop(s = 0.4), Random Crop(s = 0.4)<br>Degradation: Gaussian Noise (σ = 0.25), Blur (radius = 1.5), JPEG (Q = 50) |
+| Reconstructive | VAE Compression: VAE-B (Balle et al. ´ , 2018) (Q = 1), VAE-C (Cheng et al., 2020) (Q = 1)<br>Generative Attack: Regen-Diff (Zhao et al., 2024) (SD v1.5, Strength S = 0.2), Rinsing (N = 2, 4) |
+| Adversarial | Adv-Emb: PGD-based Latent Attack (An et al., 2024) |
+| Forgery | Imprinting: Latent optimization via inversion (Muller et al. ¨ , 2025)<br>Reprompting: Inverse the image to initial latent and regeneration (Muller et al. ¨ , 2025)<br>Average: Estimate watermark pattern by averaging residuals (Yang et al., 2024b) |
+![](_page_14_Picture_4.jpeg)
+*Figure 10.* Visual Robustness Examples. Comparison of the watermarked image under various attacks: (a) Original, (b) Brightness, (c) Contrast, (d) JPEG Compression, (e) Gaussian Blur, (f) Gaussian Noise, (g) Center Crop (C.C.), (h) Random Crop (R.C.), (i) VAE Compression (BMSHJ), and (j) VAE Compression (Cheng).
+10,000 images generated based on COCO2014 [\(Lin et al.,](#page-9-22) [2014\)](#page-9-22) prompts. The model is trained for 50,000 steps with a batch size of 16. To ensure training stability and perceptual quality, we impose a maximum gradient norm of 10<sup>−</sup><sup>2</sup> . The total objective combines the secret recovery loss (Lsec), pixel-wise reconstruction loss (Lmse), and perceptual loss (Llpips using AlexNet backbone). The loss weights are set to λsec = 1.0, λmse = 30.0, and λlpips = 0.3. Notably, λmse and λlpips are linearly ramped up from 0 to their peak values over the first 5,000 steps to facilitate stable convergence in the early training phase.
+Injection Settings. During the inference phase, ALIEN-Q injects watermarks within the sampling interval of steps 20–45 (with injection strength λ = 0.85), while ALIEN-R extends the injection window to cover steps 0–50 (λ = 1.0) for enhanced robustness.
+## <span id="page-14-0"></span>C. Experimental Setup and Extended Experiments
+## <span id="page-14-1"></span>C.1. Dataset Settings
+Evaluation Datasets. We utilize two distinct datasets to comprehensively evaluate both watermarking performance and image generation quality: For measuring detection accuracy (TPR@1%FPR) and payload capacity (Bit Accuracy), we
+{15}------------------------------------------------
+<span id="page-15-2"></span>*Table 9.* Breakdown of Performance Gains. We compare ALIEN against the best-performing baseline (Best SOTA) for each metric/condition. Panel A calculates the average relative improvement across 5 quality metrics (33.1%). Panel B highlights the robustness gain across 15 distinct conditions (12 Generative + 3 Stability). The final 14.0% is the weighted average gain over these 15 conditions.
+| | Panel A: Quality Improvement (ALIEN-Q vs. Best SOTA) | | | | |
+|------------------------------------------|-------------------------------------------------------------------|--------------------|-----------------------------|---------|-------------|
+| Metric | Description | Best SOTA | Method | ALIEN-Q | Improvement |
+| FID ↓ | Frechet Inception Distance<br>´ | 24.42 (G.S.) | Lower is better | 24.29 | +0.5% |
+| PSNR ↑ | Peak Signal-to-Noise Ratio | 29.09 (StableSig.) | Higher is better | 32.41 | +11.4% |
+| SSIM ↑ | Structural Similarity | 0.922 (ZoDiac) | Higher is better | 0.949 | +2.9% |
+| SIFID ↓ | Single Image FID | 0.105 (StableSig.) | Lower is better | 0.023 | +78.1% |
+| DreamSim ↓ | Perceptual Similarity | 0.011 (StableSig.) | Lower is better | 0.003 | +72.7% |
+| | | | Average Quality Improvement | | +33.1% |
+| | Panel B: Robustness Improvement (ALIEN-R vs. Training-free SOTA) | | | | |
+| Condition Category | Specifics | Best SOTA | Metric | ALIEN-R | Gain |
+| 1. Generative Variant<br>(12 conditions) | Average Acc. across 12 conditions<br>(4 Schedulers × Regen/Rinse) | ∼0.84 | Acc. | ∼0.90 | +6.5% |
+| 2. Sampler Stability | Average Acc. across 3 stochastic samplers | ∼0.56 | Acc. | ∼1.00 | +44.0% |
+| (3 conditions) | (DPM++ SDE, Euler a, DPM2 a) | | | | |
+<span id="page-15-3"></span>*Table 10.* Comparison of Imperceptibility and Robustness. We compare 48-bit and 128-bit payloads. *Fidelity* is reported as Mean ± Std. Dev. *Robustness* is reported as Detection Accuracy. Abbreviations: *No Att.* (No Attack), *Comp.* (Compression), *Comb.* (Combined Attack).
+| Payload | | Imperceptibility Metrics | | Robustness (Bit Accuracy)<br>No Att.<br>Blur<br>Noise<br>JPEG<br>Resize<br>Sharp<br>Bright<br>Contr.<br>Sat. | | | | | | | | | |
+|----------|------------|--------------------------|------------|--------------------------------------------------------------------------------------------------------------|------|------|------|------|------|------|------|------|-------|
+| | PSNR(↑) | SSIM(↑) | LPIPS(↓) | | | | | | | | | | Comb. |
+| 48 Bits | 31.17±0.90 | 0.62±0.03 | 0.097±0.01 | 0.99 | 0.99 | 0.92 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.87 |
+| 128 Bits | 30.79±0.85 | 0.59±0.03 | 0.151±0.01 | 0.99 | 0.99 | 0.90 | 0.98 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.82 |
+employ the Stable Diffusion-Prompts (SDP) dataset [\(Gustavosta,](#page-8-16) [2023\)](#page-8-16). We randomly select 350 prompts from the dataset to generate image pairs (watermarked vs. clean) for distinct evaluation. For evaluating generative fidelity, specifically Frechet ´ Inception Distance (FID), we utilize the MS-COCO dataset [\(Lin et al.,](#page-9-22) [2014\)](#page-9-22). We randomly sample 5,000 captions from the MS-COCO validation set to generate 5,000 watermarked images and compute the FID score against the corresponding real reference images to ensure standardized quality comparison.
+Generation Configuration. We conduct experiments on two representative Latent Diffusion Models: Stable Diffusion v1.5 and Stable Diffusion v2.1. Unless otherwise specified, we use the DDIM sampler with 50 inference steps. The classifier-free guidance scale is set to 7.5. All generated images are of resolution 512 × 512. All experiments were conducted on a single NVIDIA RTX 3090 GPU.
+#### <span id="page-15-1"></span><span id="page-15-0"></span>C.2. Robustness Evaluation Settings
+#### C.3. Extended Experiments
+Detailed Performance Gain Analysis. To substantiate the claims made in the abstract, we provide a detailed breakdown of the performance improvements. Table [9](#page-15-2) illustrates the calculation of the 33.1% quality improvement and 14.0% robustness improvement compared to the state-of-the-art (SOTA) methods.
+Impact of Payload Size. We further investigate the impact of payload size on the trade-off between watermark capacity, imperceptibility, and robustness. As demonstrated in Table [10,](#page-15-3) increasing the payload capacity from 48 bits to 128 bits results in only a minor decrease in fidelity metrics, exemplified by a slight PSNR drop from 31.17 dB to 30.79 dB. This result validates that ALIEN effectively supports high-capacity embedding while maintaining visual quality comparable to low-capacity settings.
+{16}------------------------------------------------
+<span id="page-16-2"></span>*Table 11.* Impact of Fixed Thresholding on False Positive Rates (ROBIN Scheme). Comparison of clean image means (µclean) versus the optimal threshold for Cropping (τcrop) using the ROBIN watermarking method. For both SD v1.5 and v2.1, benign degradations like Blurring and JPEG shift µclean below τcrop (marked with ×).
+| Attack | Stable Diffusion v1.5 (τcrop | | = 39.45) | Stable Diffusion v2.1 (τcrop | | = 55.80) |
+|--------------|------------------------------|--------|--------------|------------------------------|--------|--------------|
+| | Clean Mean | Opt. τ | Fixed τ Risk | Clean Mean | Opt. τ | Fixed τ Risk |
+| No Attack | 40.08 | 38.28 | ✓ | 55.90 | 52.74 | ✓ |
+| Cropping | 40.25 | 39.45 | - | 55.86 | 55.80 | - |
+| Blurring | 32.38 | 30.31 | × | 52.65 | 50.24 | × |
+| JPEG | 37.22 | 36.91 | × | 55.65 | 53.57 | × |
+| Color Jitter | 36.91 | 36.85 | × | 54.04 | 51.39 | × |
+| Noise | 41.63 | 40.02 | ✓ | 57.07 | 55.62 | ✓ |
+Threshold Determination for Distance-Based Methods. We evaluate the impact of distribution shifts caused by image degradations on threshold determination for the distance-based method, ROBIN. As shown in Table [11,](#page-16-2) using a fixed threshold derived from a challenging scenario (Cropping, τ = 39.45) poses risks when applied to other distortions. We observe a clear distribution shift in the metric space for degradations that suppress high-frequency information. For instance, the mean metric of unwatermarked images under Blurring drops to 32.38, falling below the fixed cropping threshold of 39.45. Since detection occurs when the metric is below the threshold, this shift results in increased False Positive Rates (FPR), where benign, low-quality images are misclassified.
+## <span id="page-16-0"></span>D. Extended Related Work
+This section provides a detailed review and taxonomy of existing watermarking methods for generative models.
+#### <span id="page-16-1"></span>D.1. Watermarking Schemes Taxonomy
+We categorize existing watermarking methods for generative models into five primary classes based on their embedding stage: Random Seed Modification, U-Net Modification, VAE Modification, Latent Space Modification, and Post-Processing.
+Random Seed Modification (Initial Latent). Methods in this category embed watermarks by changing in the sampling process of the initial latent variables. For instance, Tree-Ring [\(Wen et al.,](#page-9-6) [2024\)](#page-9-6) modifies the initial noise vector in the Fourier domain to embed a ring-shaped pattern, which is detectable via diffusion inversion. Gaussian Shading [\(Yang et al.,](#page-9-7) [2024c\)](#page-9-7) employs a constrained sampling strategy to apply specific patterns to the initial latent.
+Model Modification. These approaches embed watermarks by fine-tuning specific components of the generative model to ensure watermark preservation during generation. Stable Signature [\(Fernandez et al.,](#page-8-15) [2023\)](#page-8-15) fine-tunes the VAE decoder to embed the watermark into the pixel space during the latent-to-image decoding stage. Aqualora [\(Feng et al.,](#page-8-6) [2024\)](#page-8-6) modifies the U-Net to inject the watermark during the iterative denoising process.
+Latent Space Optimization. Unlike static encoding methods, these approaches formulate watermark embedding as an optimization problem within the latent space. Zodiac [\(Zhang et al.,](#page-9-8) [2024\)](#page-9-8) embeds the watermark by iteratively optimizing the *initial* latent variable to ensure high detectability in the generated output. ROBIN [\(Huang et al.,](#page-8-9) [2024\)](#page-8-9) focuses on optimizing the *intermediate* latent representations during the diffusion process. It incorporates learnable prompts to align the watermarked latents with the text condition.
+Post-Processing Methods. These techniques apply digital watermarking algorithms to the image after it has been fully generated, operating independently of the generation pipeline. StegaStamp [\(Tancik et al.,](#page-9-15) [2020\)](#page-9-15) is a deep learning-based encoder-decoder framework that embeds invisible hyperlinks or bit-strings into the final image output.