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+# A3: Few-shot Prompt Learning of Unlearnable Examples with Cross-Modal Adversarial Feature Alignment
+
+Xuan Wang*
+
+Anhui Key Lab of CSSAE, National University of Defense Technology wangxuan21d@nudt.edu.cn
+
+Tianrui Qin
+
+OPPO Research Institute qintianrui123@gmail.com
+
+Xitong Gao*†
+
+Shenzhen Institutes of Advanced Technology, CAS; Shenzhen University of Advanced Technology xt.gao@siat.ac.cn
+
+Yu-liang Lu†
+
+Anhui Key Lab of CSSAE, National University of Defense Technology publicLuYL@126.com
+
+Dongping Liao
+
+State Key Lab of IoTSC, CIS Dept, University of Macau yb97428@um.edu.mo
+
+Cheng-zhong Xu
+
+State Key Lab of IoTSC, CIS Dept, University of Macau czxu@um.edu, mo
+
+# Abstract
+
+In the age of pervasive machine learning applications, protecting digital content from unauthorized use has become a pressing concern. Unlearnable examples (UEs)—data modified with imperceptible perturbations to inhibit model training while preserving human usability—have emerged as a promising approach. However, existing UE methods assume unauthorized trainers have extensive exposure to UEs or that models are trained from scratch, which may not hold in practical scenarios. This paper investigates the effectiveness of UEs under the few-shot learning paradigm, pitching it against prompt learning (PL) models that leverage pretrained vision-language models (VLMs), like CLIP, capable of generalizing to new classes with minimal data. To address this, we introduce an adaptive UE framework to generate unlearnable examples that specifically target the PL process. In addition, we propose a novel UE countermeasure,  $A^3$ , with cross-modal adversarial feature alignment, specifically designed to circumvent UEs under few-shot PL. Experimental evaluations on 7 datasets show that  $A^3$  outperforms existing PL methods, achieving up to  $33\%$  higher performance in learning from UEs. For example, in the scenario involving  $\ell_{\infty}$ -bounded EM perturbations,  $A^3$  has an average harmonic mean accuracy across 7 datasets of  $82.43\%$ , compared to CoCoOp's baseline of  $65.47\%$ . Our findings highlight the limitations of existing UEs against PL and lay the foundation for future data protection mechanisms.
+
+# 1. Introduction
+
+In the era of pervasive machine learning applications, protecting digital content from unauthorized use is an escalating concern. An emerging solution involves unlearnable ex
+
+amples (UEs) [9, 11, 29, 36, 40]. — data modified with imperceptible perturbations that prevent machine learning models from effectively learning and generalizing from it, while preserving its utility for human observers. Unlike traditional data poisoning attacks intended for malicious use, UEs serve content creators by providing a way to inhibit unauthorized model training. Beyond this, UEs can also be used to shed light on vulnerabilities and learning preferences [36] of deep learning models, and prevent unlawful use of personal features [24]. However, existing UE methods are primarily designed for models trained from scratch, and make strong assumptions where all or a large proportion of training data is used unknowingly by unauthorized trainers. These assumptions may not hold in the wilderness, for several reasons: (a) Creators may release limited data. (b) Unauthorized trainers may have limited exposure to the UEs: they may curate their training data from various sources and may only use a small fraction of the creator's data. (c) Trainers may leverage pretrained models to improve training efficiency, and to generalize well to new classes and contexts.
+
+In this paper, we found that recent advances in prompt learning (PL) with pretrained vision-language models (VLMs) can indeed challenge the robustness of UEs. VLMs use contrastive learning to align images and text features, enabling strong zero-shot and downstream tasks [15, 30, 32, 35]. PL further adapts CLIP by fine-tuning prompts instead of model weights, making it ideal for data-limited scenarios, and novel tasks and classes. This paper thus investigates a central question: Are UEs effective in protecting data against PL-enabled models? This question has profound implications from both the content creator's and the unauthorized trainer's perspectives.
+
+For content creators, understanding this question is crucial for several reasons: (a) To effectively prevent unauthorized usage, creators need to know the minimum amount of modified data required to maintain protection. (b) Content
+
+creators typically control and release a limited quantity of data, making it impractical to assume access to large datasets. This constraint naturally leads to a few-shot scenario, which is the focus of this study.
+
+For unauthorized trainers, PL represents an appealing tool to bypass UEs, as PL exploits the generalization strengths of VLMs: (a) The pretrained encoders of VLMs enables it to generalize well to novel classes, potentially circumventing perturbations that would normally deter training from scratch. (b) While existing methods to circumvent UEs typically involve adversarial training [19], or image augmentations [16, 25], which affect only the image seen by the model. PL may be able to enhance its robustness by incorporating text augmentations, offering a broader strategy to bypass unlearnability protections.
+
+To address these challenges, we propose an adaptive framework that targets UEs in the few-shot PL setting. The contributions of this paper are as follows:
+
+- We introduced a scenario designed to examine the effectiveness of UEs against prompt learning, particularly in a few-shot context where data availability is constrained. Beyond existing UE methods, we introduced an adaptive UE framework that incorporates PL-specific considerations for surrogate-based UEs, generating stronger UEs that are more effective against PL.  
+- We propose a novel method,  $\mathrm{A}^3$ , which employs cross-modal adversarial augmented feature alignment to enhance PL's ability to generalize when learned from UEs. This method adversarially aligns diversely-augmented image and text augmentations to make PL robust against UEs.  
+- Experimental results demonstrate that  $\mathrm{A}^3$  achieves significant performance gains over existing methods, proving more effective against other UE methods in few-shot scenarios, even when faced with larger perturbations, and partial poisoning.  $\mathrm{A}^3$  also generalizes well to novel classes.
+
+This work offers new insights into the capabilities and limitations of UEs against PL, laying a foundation for more robust data protection strategies in the era of knowledge transfer with large pretrained models and multimodal machine learning.
+
+# 2. Related Work & Preliminaries
+
+# 2.1. Unlearnable Examples
+
+The primary goal of unlearnable examples [9, 11, 29, 33, 36, 40] is to safeguard the privacy and copyright of content providers by adding small, human-imperceptible perturbations to data. These perturbations prevent machine learning models from effectively generalizing to the data's original distribution. Unlike traditional data poisoning attacks [10], which aim to introduce backdoor patterns into a model, unlearnable examples are not intended for malicious purposes but solely to protect data from unauthorized use.
+
+Definition of Unlearnable Examples Consider a dataset with  $N$  clean samples  $\mathcal{D}_{\mathrm{clean}} = \{(x_i,y_i)\}_{i = 1}^N$ , where  $\mathbf{x}_i\in \mathcal{X} = [0,1]^{C\times H\times W}$  and  $y_{i}\in \mathcal{V} = \{1,\dots ,K\}$  represent the  $i^{\mathrm{th}}$  input sample with  $C$  channels and  $H\times W$  spatial dimensions, and its corresponding true label. Each sample is drawn from a distribution  $\mathcal{S}$ . The content provider aims to add small perturbations  $\delta_{i}\in \mathcal{B}_{p}(\mathbf{x}_{i},\epsilon)$  to the clean samples in  $\mathbf{x}_i\in \mathcal{D}_{\mathrm{clean}}$  to generate unlearnable examples  $\mathcal{D}_{\mathrm{ue}}(\boldsymbol {\delta})\triangleq \{(\mathbf{x}_i + \boldsymbol {\delta}_i,y_i)\mid (\mathbf{x}_i,y_i)\in \mathcal{D}_{\mathrm{clean}}\}$ . The set  $\mathcal{B}_p(\mathbf{x}_i,\epsilon)$  is:
+
+$$
+\mathcal {B} _ {p} \left(\mathbf {x} _ {i}, \epsilon\right) \triangleq \left\{\mathbf {d} \mid \| \mathbf {d} \| _ {p} \leq \epsilon , \mathbf {x} _ {i} + \mathbf {d} \in \mathcal {X} \right\}. \tag {1}
+$$
+
+It bounds the noise  $\delta_{i}$  of each sample  $\mathbf{x}_i$  within the  $\epsilon$ -ball of  $\ell_p$ -distance with respect to the sample, and the perturbed sample  $\mathbf{x}_i + \delta_i$  remain within the input domain  $\mathcal{X}$ . A small  $\epsilon$  is crucial to ensure that the perturbations do not significantly alter the original content, thus preserving the data's utility, and typically  $p \in \{0,2,\infty\}$ .
+
+When this perturbed dataset is used for training, the goal is for the resulting model to generalize poorly to the original distribution  $S$ . The optimization for the noise can be formulated as the following bi-level optimization problem to solve for the bounded perturbations  $\delta \triangleq \{\delta_i \in \mathcal{B}_p(\mathbf{x}_i, \epsilon)\}_{i=1}^N$ :
+
+$$
+\max  _ {\delta} \mathbb {E} _ {\left(\mathbf {x} _ {i}, y _ {i}\right) \sim \mathcal {S}} \left[ \mathcal {L} \left(f _ {\boldsymbol {\theta} ^ {*} (\delta)} \left(\mathbf {x} _ {i}\right), y _ {i}\right) \right], \tag {2}
+$$
+
+where  $f_{\theta}:\mathcal{X}\to \mathbb{R}^{K}$  denotes the model with parameters  $\pmb{\theta}$ ,  $\mathcal{L}:\mathbb{R}^K\times \mathcal{V}\rightarrow \mathbb{R}$  is the loss function (typically cross-entropy), and  $\pmb{\theta}^{\star}$  represents the model parameters optimized on the perturbed images:
+
+$$
+\boldsymbol {\theta} ^ {\star} (\boldsymbol {\delta}) = \operatorname {a r g m i n} _ {\boldsymbol {\theta}} \mathbb {E} _ {(\mathbf {x} _ {i}, y _ {i}) \sim \mathcal {D} _ {\text {c l e a n}}} [ \mathcal {L} (f _ {\boldsymbol {\theta}} (\mathbf {x} _ {i} + \boldsymbol {\delta} _ {i}), y _ {i}) ]. \tag {3}
+$$
+
+As the above problem is intractable, many works have proposed alternative methods to approximate the solution, commonly involving surrogate models:
+
+- Hypocritical perturbations (HYPO) [33] assumes a surrogate model  $g_{\theta} : \mathcal{X} \to \mathbb{R}^{K}$  with pretrained weights  $\theta$  learned on samples from  $S$ , and directly finds the perturbations  $\delta$  that makes the model easily produce correct predictions for  $\mathcal{D}_{\mathrm{clean}}$  images.  
+- Error maximization (EM) [11] further considers a randomly-initialized surrogate  $g_{\theta}$ , and optimizes the noise  $\delta$ , and the surrogate model  $g_{\theta}$  simultaneously.  
+- Robust error maximization (REM) [9] extends EM to optimize the surrogate  $g_{\theta}$  under adversarial training [19], where the adversarial noise is also bounded within the  $\epsilon$ -ball of  $\ell_p$ -norm, and optimized via projected gradient descent (PGD) [19]. This helps to improve the effectiveness of the perturbations even under adversarial training.
+
+Interestingly, recent works have shown that unlearnable examples can also be curated without the need for optimization, where the perturbations form a linearly-separable subspace that can be learned easily by the model. This bias is so strong that it makes the underlying features less learnable by model training algorithms:
+
+- Linearly-separable perturbations (LSP) [40] generates random color patches as perturbations, and apply them to the images while ensuring the added noise is bounded within a small  $\ell_2$ -distance from the original image. This simple method can enable strong unlearnable examples without the expensive optimization process and the need for surrogate models.  
+- Autoregressive Poisoning (AR) [29] Similar to LSP, AR prescribes a simple perturbation strategy which first fills all channels of the first 2 rows and columns of the image with Gaussian noise, then uses an autoregressive process to fill the remaining pixels with a  $3 \times 3$  sliding window. It then re-scales the perturbations to be within the noise bound  $\mathcal{B}_p(\mathbf{x}_i, \epsilon)$ , before adding them to the image  $\mathbf{x}_i$ .  
+- One-pixel Shortcuts (OPS) [36] For each image belonging to a specific class, OPS searches for an optimal pixel and color value for the class, such that it results in the largest change in the pixel's color value for all perturbed images. This constitutes a simple  $\ell_0$ -bounded perturbation where only one pixel is modified for each image. Surprisingly, when training models from scratch, OPS can generate even stronger unlearnable examples than EM with a 8/255 noise budget [25, 36]. It also resists even  $\ell_{\{2,\infty\}}$ -bounded adversarial training, as the noise added by adversarial training cannot effectively perturb the pixel values for the erasure of  $\ell_0$ -perturbations.
+
+As  $\mathsf{A}^3$  considers the problem of learning from unlearnable examples from the perspective of few-shot learning with prompt learning (PL), we provide a framework that adapts the above methods to this setting, by making the surrogate models  $g$  our prompt learners. It also shows that PL can be in a certain degree effective against unlearnable examples produced by these methods.
+
+# 2.2. Learning from Unlearnable Examples
+
+The emergence of unlearnable examples prompts investigation into the mechanisms that unauthorized trainers might exploit to extract useful features.
+
+Adversarial Training (AT) [2, 19] involves the generation of adversarial examples [4, 12, 41] specifically tailored to the model under training, which are in turn used to train the model to enhance the model's robustness. It also has been known to be an effective approach to improve the model generalization when trained on unlearnable examples [11]. However, adversarial training is known to be computationally expensive, and also affects the model's performance on clean data [38], especially when the sample size is small [5].
+
+For this reason, Image Shortcut Squeezing (ISS) [16] introduces a suite of simple image processing methods can show surprising effectiveness in mitigating the impact of unlearnable examples, without the costs associated with adversarial training. Grayscale removes the color information from the training images, and JPEG Compression
+
+(JPEG) instead performs a lossy JPEG with high compression rate on the training images. However, it was recently discovered [26] that simple image processing is much less effective against adaptively-optimized unlearnable examples. Building upon this idea, UEraser [25] further proposes a stochastic augmentation pipeline with a wider range of transformations, and uses a simple adversarial augmentation to optimize models only on augmented images with the maximum loss. This allows the model to learn the underlying features without being affected by the easily learnable shortcuts in unlearnable examples. While all these methods have shown effectiveness against unlearnable examples, they consider the problem of training models from scratch rather than leveraging pretrained models.
+
+# 2.3. Prompt Learning
+
+Vision-language pretrained models (VLMs), such as CLIP [27] and ALIGN [13], represent a significant advancement in multi-modal learning. Trained on extensive image-text pair datasets, The VLM have two main components: an image encoder  $f_{\mathrm{im}}: \mathcal{X} \to \mathbb{R}^d$  and a text encoder  $f_{\mathrm{tx}}: \mathcal{W} \to \mathbb{R}^d$ , where  $\mathcal{X}$  and  $\mathcal{W}$  are the input image and text, respectively, and learn a shared embedding space  $\mathbb{R}^d$  for images and texts. Image and text pairs that are semantically similar will have similar embeddings in this space, and vice versa. This makes them versatile for a wide range of downstream tasks, including image classification [27], captioning [1], retrieval [18], and providing guidance for image generation [7, 28]. Notably, VLMs show impressive zero-shot performance, where they can perform well on new tasks without task-specific training, showcasing their generalization capabilities.
+
+Prompt Engineering for VLMs seeks to use VLMs for image classification tasks by constructing class-specific text prompts, e.g., "a photo of a c1s" for the class c1s, and comparing the model's similarity scores between the features of these prompts and the target image. The class yielding the highest similarity score is selected as the predicted class for the image. Formally, prompt engineering creates  $M$  text prompts, embedded as a tensor  $\mathbf{V} = \{\mathbf{v}_m\}_{m=1}^M \in \mathbb{R}^{M \times T \times h}$ , where  $\mathbf{v}_m$  denotes an embedded prompt prefix sequence of  $T$  tokens. By appending each prefix  $\mathbf{v}_i$  with  $\mathbf{c}_k \in \mathbb{R}^h$ , the constant embedding vector of the  $k^{\text{th}}$  class, the model can thus construct a holistic classifier  $h_\phi: \mathcal{X} \to \mathbb{R}^K$  by averaging the similarity scores across all  $M$  prompts, where  $\phi = \{\theta, \mathbf{V}, \ldots\}$  denotes all parameters in  $h_\phi$ , consisting of the pretrained CLIP weights  $\pmb{\theta}$ , a manually-designed prompt embedding  $\mathbf{V}$ , and other potential parameters used by the prompt learning algorithm. For the  $k^{\text{th}}$  class, we can obtain its logit as follows:
+
+$$
+h _ {\phi} (\mathbf {x}) _ {k} = \frac {1}{M} \sum_ {m = 1} ^ {M} \operatorname {s i m} \left(f _ {\mathrm {i m}} (\mathbf {x}), f _ {\mathrm {t x}} \left(\left[ \mathbf {v} _ {m}, \mathbf {c} _ {k} \right]\right)\right). \tag {4}
+$$
+
+Here, sim denotes the similarity function used to compute the closeness between the image and text features, typically
+
+the cosine similarity. The  $k^{\mathrm{th}}$  class probabilities can thus be computed using the softmax function, where  $\tau$  is the softmax temperature and is usually set to 1:
+
+$$
+p (y = k \mid \mathbf {x}, \phi) = e ^ {h _ {\phi} (\mathbf {x}) _ {k} / \tau} / \sum_ {j = 1} ^ {K} e ^ {h _ {\phi} (x) _ {j} / \tau}. \quad (5)
+$$
+
+Prompt Learning (PL) While the above zero-shot method is effective for many tasks, it is limited by the quality of the manually-designed prompts and may require extensive labor and expert knowledge to construct. In contrast, PL aims to automatically learn the prompt embeddings  $\mathbf{V}$ , and possibly other parameters in  $\phi$ , by optimizing them during training. To improve downstream task performance, CoOp [43] learns the prompt embeddings  $\mathbf{V}$ , show that even with few-shot examples, can generate better prompts than manual designs, and generalize well to unseen tasks. CoCoOp [42] builds upon CoOp by introducing a trainable meta-net to learn to generate prompt embeddings from the extracted image features, in order to improve the model's performance on unseen tasks. KgCoOp [39] further regularizes the prompt embeddings to be close to the initial handcrafted prompts, showing that by retaining proximity to the original prompts, unseen tasks can be generalized better. Finally, ProDA [17] uses Gaussian to model the prompt embedding distribution, and encourages orthogonality among the prompt embeddings. This paper presents the first work to highlight that prompt learning can be effective in learning useful features from unlearnable examples, even under few-shot scenarios.
+
+# 3. The  $\mathbf{A}^3$  Method
+
+# 3.1. Adaptive UEs Targeting PL
+
+Surrogate-based methods (EM [11], REM [9], and HYPO [33]) for synthesizing UEs typically train models from scratch, and do not assume low data availability, which makes them an unsuitable choice for affecting the PL process of the pretrained CLIP model (Table 1). To address this limitation, we first introduce an adaptive approach for all methods that uses the PL process as the surrogate model. To make the UEs stronger, we also assume that the UEs are synthesized with the same PL method using the same pretrained CLIP model. We implemented adaptive-variations of EM, REM, and HYPO. As they are stronger UEs than the original methods, our experiments by default use these adaptive variants. Recall REM [9] in Section 2, we adapt its objective to PL, specifically CoCoOp [42] in this paper, by using the holistic classifier  $h_{\phi}$  in (4) as the surrogate model. The REM objective to seek  $\delta$  under PL is thus:
+
+$$
+\min  _ {(\boldsymbol {\delta}, \mathbf {V}, \dots)} \max  _ {\boldsymbol {\eta}} \mathbb {E} _ {(\mathbf {x} _ {i}, y _ {i}) \sim \mathcal {D} _ {\text {c l e a n}}} [ \mathcal {L} (h _ {\phi} (\mathbf {x} _ {i} + \boldsymbol {\delta} _ {i} + \boldsymbol {\eta}), y _ {i}) ], \tag {6}
+$$
+
+where  $\pmb {\eta}\in \mathcal{B}_p(\mathbf{x}_i,\epsilon)$  is the  $\epsilon$  -bounded  $\ell_p$  -norm noise.
+
+In this adaptive context, EM [11] simplifies the above REM objective by removing the inner maximization over  $\pmb{\eta}$
+
+and  $\eta = 0$ . Similarly, HYPO [33] further assumes that  $\mathbf{V}$  is kept constant to its initial manual design, and searches for the perturbations  $\delta$  directly.
+
+Surrogate-free methods such as LSP [40], AR [29] and OPS [36] do not rely on a surrogate model training process and directly prescribe the perturbations for a given set of clean examples. Therefore, they do not have an adaptive counterpart. In our experiments, we examine the performance of these methods by directly applying them to the training data used by the prompt learning process.
+
+# 3.2. An Overview of  $\mathbf{A}^3$
+
+Figure 1 provides an overview of  $\mathrm{A}^3$ . The overall algorithm is in Algorithm 1 of Appendix A.3.  $\mathrm{A}^3$  provides a pool of diverse image and text augmentation strategies  $\mathcal{A}_{\mathrm{im}}$  and  $\mathcal{A}_{\mathrm{tx}}$ . For each image-class training pair, it first samples  $K_{\mathrm{im}}$  and  $K_{\mathrm{tx}}$  different image and text augmentation strategies, and applies them to the image and text sample respectively. This results in  $K_{\mathrm{im}} \times K_{\mathrm{tx}}$  distinct augmented pairs for each training sample. Following the prompt learning technique of CoCoOp [42], it then optimizes the prompt embeddings  $\mathbf{V}$  and the meta-net weights  $\psi$  to align the pair of augmented samples with the minimum similarity. Intuitively, training prompts with the most dissimilar augmented pairs of image and text features forces the model to learn from the underlying features rather than fixating on spurious correlations typically exploited by UEs.
+
+# 3.3. Augmentations for Image and Text Modalities
+
+Image Augmentations As noted by Qin et al. [26], the effectiveness of simple augmentation strategies, such as Grayscale and JPEG compression, is greatly diminished in the context of adaptively synthesized UEs. To address this, we follow the approach of UEraser [25], which proposes an extensive set of image augmentation strategies, including not only standard techniques (e.g., random cropping, rotation, etc.), and more complex strategies including fractal-based transformations [21], and TrivialAugment [20].
+
+Text Augmentations Since CLIP models can leverage not only image features but also text embeddings, which makes it particularly effective in zero-shot classification tasks, and few-shot learning facilitated by PL algorithms. In our context of using PL as an effective defense against UEs, we also introduce a set of text augmentation strategies, which include techniques such as random token masking and reordering that operates in the discrete token space of the text input, and small random rotations of the text embeddings.
+
+For the details of the augmentation strategies used in  $\mathrm{A}^3$  for both image and text, please refer to Appendix A.2.
+
+# 3.4. Cross-modal Adversarial Feature Alignment
+
+Given an image  $\mathbf{x}$  and its corresponding label  $y$ , we can use the above augmentation strategies to find  $K_{\mathrm{im}}$  augmented
+
+![](images/55935ae4039ef7df53c264ca9a4b6db363a90b7a5a54779c9db26691094a1d0e.jpg)  
+Figure 1. An overview of  $A^3$ . For each image-class training pair,  $A^3$  respectively sample  $K_{\mathrm{im}}$  and  $K_{\mathrm{tx}}$  different image and text augmentation strategies ( $a_{\mathrm{im}} \sim \mathcal{A}_{\mathrm{im}}$  and  $a_{\mathrm{tx}} \sim \mathcal{A}_{\mathrm{tx}}$ ). It then optimizes the prompt embeddings  $\mathbf{V}$  and the meta-net  $m_{\psi}$  for empirical risk minimization by aligning pairs of augmented samples with the minimum similarity (i.e., maximum loss) between the image and text features.
+
+images and  $K_{\mathrm{tx}}$  text embeddings, by drawing from the sets of image  $a_{\mathrm{im}} \sim \mathcal{A}_{\mathrm{im}}$  and text  $a_{\mathrm{tx}} \sim \mathcal{A}_{\mathrm{tx}}$  augmentation strategies, and applying them to the image and text embeddings respectively, forming a set of augmented images  $\tilde{\mathbf{x}} \triangleq \{\tilde{\mathbf{x}}_i\}_{i=1}^{K_{\mathrm{im}}}$  and a set of text embeddings  $\tilde{\mathbf{t}} \triangleq \{\tilde{\mathbf{t}}_j\}_{j=1}^{K_{\mathrm{tx}}}$ :
+
+$$
+\tilde {\mathbf {x}} _ {i} = a _ {\mathrm {i m}} (\mathbf {x}), \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad a _ {\mathrm {i m}} \sim \mathcal {A} _ {\mathrm {i m}}, \text {f o r} i \in [ 1, \dots , K _ {\mathrm {i m}} ],
+$$
+
+$$
+\tilde {\mathbf {t}} _ {j} = a _ {\mathrm {t x}} \left(\left[ \mathbf {v} _ {j \bmod M}, \mathbf {c} _ {y} \right]\right), a _ {\mathrm {t x}} \sim \mathcal {A} _ {\mathrm {t x}}, \quad \text {f o r} j \in [ 1, \dots , K _ {\mathrm {t x}} ], \tag {7}
+$$
+
+Here, we note that the text embedding before augmentation  $[\mathbf{v}_{j\mathrm{mod}M},\mathbf{c}_y]$  is a concatenation of the prompt embedding  $\mathbf{v}_{j\mathrm{mod}M}$  and the class embedding  $\mathbf{c}_y$ . Recall that  $M$  is the number of prompt embeddings, and the modulus operation  $j\mathrm{mod}M$  is to ensure that the prompt embedding is selected cyclically, if  $K_{\mathrm{tx}}$  exceeds  $M$ .
+
+Using the augmented samples, we can compute the similarity between the image and text features for each pair of augmented samples, assuming  $S(\tilde{\mathbf{x}},\tilde{\mathbf{t}})\in [-1,1]^{K_{\mathrm{im}}\times K_{\mathrm{tx}}}$  is the (cosine) similarity matrix containing the similarity between each image-text pair of augmented samples. Namely, for the  $\tilde{\mathbf{x}}_i$  and  $\tilde{\mathbf{t}}_j$  pair, we have:
+
+$$
+\mathcal {S} (\tilde {\mathbf {x}}, \tilde {\mathbf {t}}) _ {i j} = \operatorname {s i m} \left(f _ {\mathrm {i m}} \left(\tilde {\mathbf {x}} _ {i}\right), f _ {\mathrm {t x}} \left(\tilde {\mathbf {t}} _ {j}\right)\right), \tag {8}
+$$
+
+and we optimize the trainable weights in  $\phi$  by maximizing the similarity alignment between the least similar image and text augmented features. Putting it all together, we have the following min-max problem, which can be optimized using mini-batch stochastic gradient descent (SGD):
+
+$$
+\min  _ {\phi} \mathbb {E} _ {(\mathbf {x}, y) \sim \mathcal {D} _ {\mathrm {u e}}} \left[ \max  _ {(i, j)} \mathcal {L} \left(\mathcal {S} (\tilde {\mathbf {x}}, \tilde {\mathbf {t}}) _ {i j}, y\right) \right], \tag {9}
+$$
+
+where  $\mathcal{L}$  is the softmax cross-entropy loss, and  $\mathcal{D}_{\mathrm{ue}}$  is the set of unlearnable training examples.
+
+# 3.5. More Augmentation Diversity with Meta-Net
+
+To further enhance the diversity of the augmented samples, we introduce a meta-net  $m_{\psi}:\mathbb{R}^d\to \mathbb{R}^{M\times (T - 1)\times h}$  with trainable weights  $\psi$  , which is a small neural network that learns to predict prompt embeddings  $\mathbf{V}$  from  $f_{\mathrm{im}}(\tilde{\mathbf{x}})$  , i.e., the feature extracted from an augmented image by the image encoder. This allows us to generate more diverse augmented text embeddings in addition to the text augmentation strategies. While this can yield  $K_{\mathrm{im}}\times K_{\mathrm{tx}}$  different augmented prompt features, with the computational cost of CLIP's feature extraction, we only use the meta-net for a random augmented image for each augmented text embedding. Using the meta-net, the similarity matrix in (8) thus becomes:
+
+$$
+\mathcal {S} (\tilde {\mathbf {x}}, \tilde {\mathbf {t}}) _ {i j} = \operatorname {s i m} \left(\mathbf {p} _ {i}, \mathbf {q} _ {j}\right),
+$$
+
+where  $\mathbf{p}_i = f_{\mathrm{im}}(\tilde{\mathbf{x}}_i)$  (10)
+
+$$
+\mathbf {q} _ {j} = f _ {\mathrm {t x}} \left(\tilde {\mathbf {t}} _ {j} + m _ {\psi} \left(\mathbf {p} _ {k}\right)\right), k \sim \mathcal {U} \{1, K _ {\mathrm {i m}} \}.
+$$
+
+# 4. Experiments
+
+Datasets For the main experiments, We evaluate  $A^3$  under 7 datasets, including ImageNet [6] Caltech-101 [8], Oxford Flowers-102 [22], Food-101 [3], Oxford-Pets [23], and UCF-101 [31]. These datasets cover various recognition tasks, including classification of generic objects, fine-grained classification, and action recognition. We also proportionally resized and cropped all images to  $224 \times 224$ , the input size for the image encoder  $f_{\mathrm{im}}$ .
+
+Models In our experiments, unless otherwise specified, we use either the ViT-B/16 or ResNet-50 as the backbone for the image encoder  $f_{\mathrm{im}}$ , and the text encoder  $f_{\mathrm{tx}}$  is a Transformer-based model [34]. All pretrained models are obtained from the official CLIP repository [27].
+
+Evaluation For all experiments in this section, unless otherwise specified, we consider a common few-shot learning setup with  $S$  labeled training examples per class, i.e.,  $S$ -shot learning, where  $S = 16$  by default. We used a context length  $T$  of 4, and  $M = 1$  number of prompt embeddings. For all surrogate-based attacks we optimized perturbations  $\delta$  for 15 epochs with the cosine annealing scheduler and a learning rate 0.002. For learning, we adopted the SGD optimizer with a momentum of 0.9 and a weight decay of  $5 \times 10^{-4}$ . We consider the following dataset split protocols:
+
+- Standard We used the standard train-test splits from [42, 43] to ensure reproducibility. In this setting, all classes are included in the training phase, where each class contains  $S$  labeled examples.  
+- Base-to-Novel To better evaluate the model's generalization ability in few-shot scenarios, we also followed [42] to divide each datasets into two equal and non-overlapping groups of classes, where the first group (base) is used for training the prompt learning model and validation, and the second group (novel) which contains unseen classes is also used for performance testing. For this protocol, we reported the test accuracies on the base classes  $\alpha_{\mathrm{b}}$ , the novel classes  $\alpha_{\mathrm{n}}$ , and also their harmonic mean  $\alpha_{\mathrm{h}} = 2 / (\alpha_{\mathrm{b}}^{-1} + \alpha_{\mathrm{n}}^{-1})$ .
+
+Unlearnable Example Methods Different methods consider distinct perturbation types and perturbation budgets:
+
+- Surrogate-based methods such as EM [11], REM [9], and HYPO [33], consider  $\ell_{\infty}$ -bounded perturbations, with a perturbation budget of  $8/255$ . As these methods require surrogate models, we used Section 3.1 to adapt them to the prompt learning setting.  
+- LSP [40] and AR [29] both use the  $\ell_2$ -norm perturbations, but their perturbation budgets are different due to their original setups. LSP assumes a perturbation budget of 1.30, while AR uses 1.00.  
+- OPS [36] is model-agnostic, and uses the  $\ell_0$ -norm perturbations with a perturbation budget of 1 by default.
+
+For additional details regarding the experimental setup, please refer to Appendix B. We will now present the results and main findings of our experiments below. Appendix C provides additional results including sensitivity analysis of the hyperparameters, and more adaptive variants.
+
+# 4.1. Prompt Learning under UEs
+
+Prompt learning generalizes well to existing UEs. Table 1 compares EM-0 and EM, where EM-0 synthesizes UEs by training ResNet-18 surrogate models from scratch on the Caltech-101 dataset, and EM adapts the EM method to prompt learning using Section 3.1. Notably, we found that UE methods that can effectively thwart [26] supervised learning of small models (e.g., ResNet-18) on small datasets (e.g., CIFAR-10 [14]) are much less effective when transferred to CLIP-based prompt learning algorithms.
+
+Prompt learning generalizes better with increasing number of shots  $S$ . Table 1 also shows that the performance of all prompt learning algorithms increases with the number of shots  $S$ , even when all shots are UEs. This trend can be observed across all UE methods, but the adaptive EM method consistently suppresses the performance gains from increasing  $S$  the most.
+
+CoCoOp and ProDA show increased robustness against UEs, while KgCoOp is the most fragile in Table 1. We speculate that this is because the meta-net used in CoCoOp may be able to absorb the shortcut present in the UEs, and ProDA models the Gaussian distribution of prompt embeddings, making it more robust to input-side perturbations. While trained on clean data, KgCoOp [42] exhibits the best performance, as shown in the "Clean" row of Table 1. However, it is notably prone to UEs, showing the largest performance drop when UEs are introduced, especially when using the adaptive EM method. This suggests that KgCoOp, guided by the regularization to be in close proximity to the initial manual prompts, cannot effectively evade crafted UEs by EM based on the initial prompts. Because of the robustness of CoCoOp under our default number of shots ( $S = 16$ ), we chose it as the baseline algorithm for the subsequent experiments.
+
+Without proper defenses, it is better off not learning from UEs. It is interesting to note that usually, the performance of CoCoOp when trained with UEs is worse than the zero-shot performance. This suggests that UEs can indeed be harmful to the model's performance. This behavior can be observed in Tables 1 and 2.
+
+# 4.2. Prompt Learning with  $\mathbf{A}^3$
+
+$\mathbf{A}^3$  is very effective (up to  $33\%$  better than CoCoOp) in mitigating UEs. In Table 2, we observe that  $\mathrm{A}^3$  consistently outperforms CoCoOp across all datasets, producing  $15\%$  to  $33\%$  higher  $\alpha_{\mathrm{h}}$  than CoCoOp for surrogate-based methods (EM, REM, HYPO), and  $6\%$  to  $30\%$  higher for surrogate-free methods (LSP, AR, OPS).
+
+The image and text augmentations in  $\mathbf{A}^3$  are both crucial for its effectiveness. Table 3 performs an ablation study on the individual contributions of image and text augmentations. We note that using either image-only or text-only augmentations can improve the model's performance, but the combination of both is the most effective, giving large accuracy gains over CoCoOp.
+
+Simple augmentation strategies fall short of  $\mathbf{A}^3$ 's performance. We also highlight in Table 3 that applying simple augmentation strategies such as Grayscale and JPEG compression on CoCoOp can certainly gain improvement over the CoCoOp baseline. However, they are still outperformed by  $\mathbf{A}^3$ , sometimes with a large margin ( $\geq 25\%$ ).
+
+A large arsenal of image augmentation strategies also fall short of  $\mathrm{A}^3$ 's performance. Table 3 also shows that while
+
+Table 1. Test accuracies  $(\%)$  of prompt learning algorithms on an unlearnability-poisoned Caltech-101 dataset under varying number of shots  $S$ . Note that "EM-0" is the original EM [11] method, and "EM" is our adaptive variant (Section 3.1). The image encoder of the CLIP model is ResNet-50, and the zero-shot accuracy is  $86.00\%$ . We also report the average accuracy across unlearnability methods (the "Avg." rows) and prompt learning algorithms (the "Avg." column). We highlight the best prompt learning algorithm against each unlearnability method in bold, and underline the strongest unlearnability methods for each prompt learning algorithm.  
+
+<table><tr><td>S</td><td>Method</td><td>CoOp</td><td>CoCoOp</td><td>ProDA</td><td>KgCoOp</td><td>Avg.</td></tr><tr><td rowspan="5">2</td><td>EM-0</td><td>78.23</td><td>80.45</td><td>81.91</td><td>77.86</td><td>79.61</td></tr><tr><td>EM</td><td>61.78</td><td>64.13</td><td>65.05</td><td>59.26</td><td>62.56</td></tr><tr><td>OPS</td><td>74.40</td><td>76.91</td><td>75.75</td><td>73.10</td><td>75.04</td></tr><tr><td>AR</td><td>80.63</td><td>81.83</td><td>80.74</td><td>79.89</td><td>80.77</td></tr><tr><td>Avg.</td><td>73.76</td><td>75.83</td><td>75.86</td><td>72.53</td><td>74.50</td></tr><tr><td rowspan="5">4</td><td>EM-0</td><td>83.29</td><td>85.19</td><td>86.02</td><td>80.83</td><td>83.83</td></tr><tr><td>EM</td><td>68.41</td><td>70.45</td><td>70.14</td><td>64.91</td><td>68.48</td></tr><tr><td>OPS</td><td>78.80</td><td>80.88</td><td>80.15</td><td>78.07</td><td>79.48</td></tr><tr><td>AR</td><td>82.54</td><td>83.70</td><td>84.41</td><td>82.66</td><td>83.33</td></tr><tr><td>Avg.</td><td>78.26</td><td>80.06</td><td>80.18</td><td>76.62</td><td>78.78</td></tr><tr><td rowspan="5">8</td><td>EM-0</td><td>86.18</td><td>89.44</td><td>90.64</td><td>85.42</td><td>87.92</td></tr><tr><td>EM</td><td>70.50</td><td>72.28</td><td>73.03</td><td>67.07</td><td>70.72</td></tr><tr><td>OPS</td><td>80.74</td><td>83.35</td><td>82.63</td><td>79.31</td><td>81.51</td></tr><tr><td>AR</td><td>85.81</td><td>88.41</td><td>88.50</td><td>83.77</td><td>86.62</td></tr><tr><td>Avg.</td><td>80.81</td><td>83.37</td><td>83.70</td><td>78.89</td><td>81.69</td></tr><tr><td rowspan="5">16</td><td>EM-0</td><td>90.76</td><td>90.85</td><td>90.48</td><td>89.60</td><td>90.42</td></tr><tr><td>EM</td><td>71.42</td><td>72.83</td><td>72.10</td><td>69.34</td><td>71.42</td></tr><tr><td>OPS</td><td>82.40</td><td>84.09</td><td>84.43</td><td>80.02</td><td>82.74</td></tr><tr><td>AR</td><td>88.63</td><td>90.74</td><td>90.08</td><td>86.46</td><td>88.98</td></tr><tr><td>Avg.</td><td>83.30</td><td>84.63</td><td>84.27</td><td>81.36</td><td>83.39</td></tr><tr><td>16</td><td>Clean</td><td>91.20</td><td>91.70</td><td>91.60</td><td>91.80</td><td>91.58</td></tr></table>
+
+UEraser [25] is the most effective strategy to learn from UEs among all tested existing methods, the performance of UEraser is still inferior to  $\mathrm{A}^3$ , particularly on HYPO, LSP and AR, with increased perturbation budgets. To preserve image semantics while maximizing augmentation diversity, such image augmentation strategies are often designed with a balance between the two. This trade-off choice may limit the ability to suppress UE perturbations in images. While this is also true for  $\mathrm{A}^3$ , but the additional text augmentation strategies of  $\mathrm{A}^3$  can help to work around this limitation.
+
+Adversarial training (AT) may not be the most effective defense against UEs. As the settings of AT in Table 3 assume  $\ell_{\infty}$ -bounded perturbations with  $\epsilon = 8 / 255$ , it notably struggles against large  $\ell_{\infty}$  perturbation budgets ( $\epsilon = 16 / 255$ ), and other types of perturbation norm-bounds ( $\ell_{2}$  and  $\ell_{0}$ ), as it is not designed to handle them. There may also be an intricate balance between accuracy and robustness [38], which could result in a seesaw effect in the performance as the perturbation budget increases.
+
+Increasing the number of shots  $S$  improves  $\mathbf{A}^3$ 's performance. In Table 4, we found that while CoCoOp's performance metrics continue to improve with increasing  $S$ , it never surpassed the performance of zero-shot CLIP. This echoes the findings in Table 1. On the other hand,  $\mathbf{A}^3$  im
+
+Table 2. Base-to-novel prompt learning accuracies (\%) for CoCoOp and  $\mathrm{A}^3$  trained with unlearnable examples under  $\ell_{\infty}$ -bounded attacks. Rows with "+" indicate when  $\mathrm{A}^3$  is applied.  $\alpha_{\mathrm{b}}$  refers to the model accuracy on poisoned data, while  $\alpha_{\mathrm{n}}$  refers to the model accuracy on novel classes, excluding the poisoned classes. We also report the harmonic mean  $\alpha_{\mathrm{h}} = 2 / (\alpha_{\mathrm{b}}^{-1} + \alpha_{\mathrm{n}}^{-1})$ . For the "Δ" column, we report the test accuracy drop for the CoCoOp baseline from the clean training setting, and accuracy gain for  $\mathrm{A}^3$  over CoCoOp. The backbone is VIT-B/16.  
+
+<table><tr><td></td><td>ImNet</td><td>Caltech</td><td>Pets</td><td>Flowers</td><td>Food</td><td>SUN</td><td>UCF</td><td>Avg.</td><td>Δ</td></tr><tr><td colspan="10">Zero-Shot [27]</td></tr><tr><td>αb</td><td>67.50</td><td>92.60</td><td>87.40</td><td>67.90</td><td>82.90</td><td>64.80</td><td>66.10</td><td>75.60</td><td>—</td></tr><tr><td>αn</td><td>60.20</td><td>87.40</td><td>83.70</td><td>60.80</td><td>75.50</td><td>56.90</td><td>59.50</td><td>69.14</td><td>—</td></tr><tr><td>αh</td><td>63.64</td><td>89.00</td><td>85.52</td><td>64.80</td><td>79.05</td><td>60.60</td><td>62.81</td><td>72.20</td><td>—</td></tr><tr><td colspan="10">Baseline (CoCoOp [42])</td></tr><tr><td>αb</td><td>75.25</td><td>96.30</td><td>94.35</td><td>92.86</td><td>90.18</td><td>78.38</td><td>80.53</td><td>86.84</td><td>—</td></tr><tr><td>αn</td><td>69.43</td><td>93.23</td><td>96.88</td><td>70.17</td><td>90.80</td><td>74.72</td><td>73.28</td><td>81.22</td><td>—</td></tr><tr><td>αh</td><td>72.39</td><td>94.74</td><td>95.58</td><td>79.74</td><td>90.34</td><td>76.28</td><td>76.61</td><td>83.67</td><td>—</td></tr><tr><td>+αb</td><td>76.03</td><td>97.95</td><td>94.06</td><td>92.41</td><td>90.68</td><td>77.59</td><td>80.25</td><td>87.00</td><td></td></tr><tr><td>+αn</td><td>70.47</td><td>93.80</td><td>93.18</td><td>70.29</td><td>91.29</td><td>74.83</td><td>71.89</td><td>80.82</td><td></td></tr><tr><td>+αh</td><td>73.09</td><td>95.73</td><td>93.63</td><td>79.74</td><td>90.98</td><td>76.14</td><td>75.88</td><td>83.60</td><td></td></tr><tr><td colspan="10">EM [11] (l∞, ε = 8/255)</td></tr><tr><td>αb</td><td>56.47</td><td>80.68</td><td>78.44</td><td>74.40</td><td>79.93</td><td>58.90</td><td>63.71</td><td>70.36</td><td>-16.48</td></tr><tr><td>αn</td><td>43.27</td><td>74.90</td><td>76.38</td><td>51.66</td><td>78.15</td><td>53.33</td><td>52.09</td><td>61.40</td><td>-19.82</td></tr><tr><td>αh</td><td>48.77</td><td>77.54</td><td>77.40</td><td>61.03</td><td>79.04</td><td>56.01</td><td>57.38</td><td>65.31</td><td>-18.36</td></tr><tr><td>+αb</td><td>73.48</td><td>95.49</td><td>93.71</td><td>91.84</td><td>89.38</td><td>77.65</td><td>79.34</td><td>85.82</td><td>15.46</td></tr><tr><td>+αn</td><td>67.85</td><td>93.07</td><td>93.53</td><td>68.08</td><td>88.00</td><td>73.17</td><td>71.69</td><td>79.30</td><td>17.90</td></tr><tr><td>+αh</td><td>70.41</td><td>94.34</td><td>93.74</td><td>78.20</td><td>88.87</td><td>75.18</td><td>75.12</td><td>82.27</td><td>16.96</td></tr><tr><td colspan="10">REM [9] (l∞, ε = 8/255)</td></tr><tr><td>αb</td><td>43.51</td><td>62.63</td><td>64.60</td><td>61.98</td><td>60.21</td><td>48.29</td><td>50.53</td><td>55.94</td><td>-30.90</td></tr><tr><td>αn</td><td>30.49</td><td>54.77</td><td>60.12</td><td>46.64</td><td>58.08</td><td>44.30</td><td>41.98</td><td>48.05</td><td>-33.16</td></tr><tr><td>αh</td><td>35.74</td><td>58.39</td><td>62.25</td><td>53.17</td><td>59.06</td><td>46.18</td><td>46.02</td><td>51.54</td><td>-32.12</td></tr><tr><td>+αb</td><td>72.76</td><td>94.52</td><td>93.28</td><td>91.00</td><td>88.06</td><td>76.94</td><td>78.46</td><td>85.00</td><td>29.06</td></tr><tr><td>+αn</td><td>66.42</td><td>92.16</td><td>91.94</td><td>66.74</td><td>87.34</td><td>71.98</td><td>71.22</td><td>78.26</td><td>30.21</td></tr><tr><td>+αh</td><td>69.37</td><td>93.69</td><td>92.74</td><td>76.73</td><td>87.54</td><td>74.43</td><td>74.94</td><td>81.35</td><td>29.80</td></tr><tr><td colspan="10">HYPO [33] (l∞, ε = 8/255)</td></tr><tr><td>αb</td><td>40.08</td><td>58.59</td><td>59.83</td><td>57.33</td><td>56.50</td><td>44.11</td><td>47.66</td><td>52.01</td><td>-34.83</td></tr><tr><td>αn</td><td>30.64</td><td>54.82</td><td>57.11</td><td>44.76</td><td>56.90</td><td>41.25</td><td>43.58</td><td>47.01</td><td>-34.21</td></tr><tr><td>αh</td><td>34.68</td><td>56.57</td><td>58.46</td><td>50.30</td><td>56.55</td><td>42.47</td><td>45.45</td><td>49.21</td><td>-34.46</td></tr><tr><td>+αb</td><td>71.80</td><td>94.28</td><td>93.59</td><td>90.75</td><td>88.55</td><td>77.67</td><td>78.92</td><td>85.08</td><td>33.07</td></tr><tr><td>+αn</td><td>65.29</td><td>90.37</td><td>92.01</td><td>65.25</td><td>84.93</td><td>70.04</td><td>69.85</td><td>76.82</td><td>29.81</td></tr><tr><td>+αh</td><td>68.39</td><td>92.13</td><td>93.05</td><td>76.20</td><td>86.69</td><td>73.73</td><td>74.43</td><td>80.66</td><td>31.45</td></tr><tr><td colspan="10">LSP [40] (l2, ε = 1.30)</td></tr><tr><td>αb</td><td>49.72</td><td>68.49</td><td>65.99</td><td>63.33</td><td>61.88</td><td>50.69</td><td>51.47</td><td>58.80</td><td>-28.04</td></tr><tr><td>αn</td><td>36.04</td><td>56.29</td><td>63.35</td><td>50.62</td><td>59.41</td><td>46.20</td><td>48.88</td><td>51.54</td><td>-29.67</td></tr><tr><td>αh</td><td>41.79</td><td>61.84</td><td>64.47</td><td>56.18</td><td>60.53</td><td>48.43</td><td>50.04</td><td>54.75</td><td>-28.91</td></tr><tr><td>+αb</td><td>72.53</td><td>94.97</td><td>94.02</td><td>91.29</td><td>88.64</td><td>77.04</td><td>78.17</td><td>85.24</td><td>26.44</td></tr><tr><td>+αn</td><td>67.37</td><td>92.44</td><td>93.80</td><td>67.52</td><td>87.40</td><td>72.21</td><td>71.11</td><td>78.84</td><td>27.30</td></tr><tr><td>+αh</td><td>69.97</td><td>93.74</td><td>94.27</td><td>77.09</td><td>87.77</td><td>74.47</td><td>74.54</td><td>81.69</td><td>26.94</td></tr><tr><td colspan="10">AR [29] (l2, ε = 1.00)</td></tr><tr><td>αb</td><td>42.33</td><td>61.73</td><td>60.58</td><td>59.01</td><td>57.20</td><td>46.23</td><td>49.06</td><td>53.73</td><td>-33.11</td></tr><tr><td>αn</td><td>31.67</td><td>56.42</td><td>58.08</td><td>44.54</td><td>55.96</td><td>43.30</td><td>42.69</td><td>47.52</td><td>-33.69</td></tr><tr><td>αh</td><td>36.29</td><td>59.00</td><td>59.27</td><td>50.63</td><td>56.52</td><td>44.74</td><td>45.67</td><td>50.30</td><td>-33.37</td></tr><tr><td>+αb</td><td>71.68</td><td>94.38</td><td>92.55</td><td>90.82</td><td>87.77</td><td>76.67</td><td>77.58</td><td>84.49</td><td>30.76</td></tr><tr><td>+αn</td><td>66.09</td><td>91.59</td><td>91.67</td><td>66.06</td><td>86.25</td><td>71.19</td><td>70.86</td><td>77.67</td><td>30.15</td></tr><tr><td>+αh</td><td>68.74</td><td>92.98</td><td>92.10</td><td>78.40</td><td>87.00</td><td>73.93</td><td>74.21</td><td>81.05</td><td>30.75</td></tr><tr><td colspan="10">OPS [36] (l0, ε = 1)</td></tr><tr><td>αb</td><td>68.28</td><td>88.60</td><td>86.20</td><td>81.59</td><td>85.65</td><td>65.60</td><td>68.98</td><td>77.84</td><td>-9.00</td></tr><tr><td>αn</td><td>54.50</td><td>80.21</td><td>80.83</td><td>58.70</td><td>79.06</td><td>60.49</td><td>60.32</td><td>67.73</td><td>-13.49</td></tr><tr><td>αh</td><td>60.57</td><td>84.05</td><td>83.45</td><td>68.28</td><td>82.24</td><td>62.89</td><td>64.39</td><td>72.37</td><td>-11.40</td></tr><tr><td>+αb</td><td>73.08</td><td>95.10</td><td>93.39</td><td>91.50</td><td>89.56</td><td>76.97</td><td>78.13</td><td>83.96</td><td>7.55</td></tr><tr><td>+αn</td><td>67.20</td><td>92.63</td><td>93.88</td><td>68.03</td><td>88.01</td><td>72.64</td><td>71.28</td><td>79.10</td><td>11.37</td></tr><tr><td>+αh</td><td>70.06</td><td>93.86</td><td>93.63</td><td>78.05</td><td>88.87</td><td>74.69</td><td>74.50</td><td>81.42</td><td>9.68</td></tr></table>
+
+Table 3. Clean test accuracies (\%) on Caltech-101 datasets (16-shots, standard protocol). "UEr" means UEraser. Baseline and compared methods are adapted to CoCoOp [42]. Image encoder backbone is ResNet-50. "Text" and "Image" refer to the augmented modalities, "Full" includes both.  
+
+<table><tr><td></td><td colspan="2">Baseline</td><td>Gray</td><td>JPEG</td><td>AT</td><td>UEr</td><td>Text</td><td>Image</td><td>Full</td></tr><tr><td rowspan="2">EM</td><td>8/255</td><td>75.53</td><td>74.28</td><td>79.21</td><td>82.84</td><td>90.37</td><td>84.69</td><td>92.51</td><td>94.28</td></tr><tr><td>16/255</td><td>59.36</td><td>60.96</td><td>64.58</td><td>77.03</td><td>88.79</td><td>82.45</td><td>90.40</td><td>91.86</td></tr><tr><td rowspan="2">REM</td><td>8/255</td><td>52.33</td><td>63.71</td><td>70.22</td><td>78.96</td><td>90.73</td><td>86.89</td><td>92.32</td><td>93.88</td></tr><tr><td>16/255</td><td>37.97</td><td>59.54</td><td>66.78</td><td>74.10</td><td>86.96</td><td>83.33</td><td>89.35</td><td>90.25</td></tr><tr><td rowspan="2">HYPO</td><td>8/255</td><td>47.36</td><td>50.02</td><td>64.56</td><td>78.89</td><td>87.74</td><td>84.07</td><td>91.47</td><td>93.21</td></tr><tr><td>16/255</td><td>27.18</td><td>34.67</td><td>59.11</td><td>72.26</td><td>82.48</td><td>79.27</td><td>86.09</td><td>89.33</td></tr><tr><td rowspan="2">LSP</td><td>1.30</td><td>43.23</td><td>64.70</td><td>80.01</td><td>81.58</td><td>90.66</td><td>83.37</td><td>92.83</td><td>94.02</td></tr><tr><td>1.74</td><td>25.41</td><td>42.58</td><td>68.30</td><td>76.29</td><td>83.05</td><td>80.77</td><td>87.24</td><td>91.62</td></tr><tr><td rowspan="2">AR</td><td>1.00</td><td>50.18</td><td>53.24</td><td>81.40</td><td>76.73</td><td>90.12</td><td>84.96</td><td>91.63</td><td>93.41</td></tr><tr><td>1.30</td><td>32.65</td><td>35.57</td><td>69.26</td><td>64.22</td><td>82.89</td><td>81.17</td><td>86.61</td><td>90.06</td></tr><tr><td rowspan="2">OPS</td><td>1</td><td>86.17</td><td>86.52</td><td>89.73</td><td>83.16</td><td>88.61</td><td>89.93</td><td>90.50</td><td>93.86</td></tr><tr><td>4</td><td>73.24</td><td>73.34</td><td>80.23</td><td>69.59</td><td>80.12</td><td>81.37</td><td>84.07</td><td>87.10</td></tr></table>
+
+Table 4. Base-to-novel metrics for different number of shots  $S \in  \{ 0,2,4,8,{16}\}$  . The image encoder backbone is ResNet-50.  
+
+<table><tr><td colspan="2">S</td><td colspan="2">Caltech</td><td colspan="2">Food</td><td colspan="2">ImageNet</td></tr><tr><td colspan="2">A3</td><td>-</td><td>+</td><td>-</td><td>+</td><td>-</td><td>+</td></tr><tr><td rowspan="3">0</td><td>αb</td><td colspan="2">86.7</td><td colspan="2">78.1</td><td colspan="2">62.7</td></tr><tr><td>αn</td><td colspan="2">78.4</td><td colspan="2">74.9</td><td colspan="2">52.8</td></tr><tr><td>αh</td><td colspan="2">82.6</td><td colspan="2">76.4</td><td colspan="2">57.2</td></tr><tr><td rowspan="3">2</td><td>αb</td><td>69.34</td><td>88.51</td><td>66.11</td><td>84.34</td><td>44.04</td><td>66.04</td></tr><tr><td>αn</td><td>61.78</td><td>83.45</td><td>60.29</td><td>81.77</td><td>30.9</td><td>60.03</td></tr><tr><td>αh</td><td>65.34</td><td>85.91</td><td>63.07</td><td>83.04</td><td>36.32</td><td>62.89</td></tr><tr><td rowspan="3">4</td><td>αb</td><td>76.09</td><td>91.23</td><td>75.21</td><td>87.81</td><td>50.43</td><td>68.1</td></tr><tr><td>αn</td><td>67.51</td><td>87.93</td><td>66.19</td><td>86.15</td><td>36.61</td><td>62.9</td></tr><tr><td>αh</td><td>71.54</td><td>89.55</td><td>70.41</td><td>86.97</td><td>42.42</td><td>65.4</td></tr><tr><td rowspan="3">8</td><td>αb</td><td>77.86</td><td>92.89</td><td>75.85</td><td>88.03</td><td>51.65</td><td>69.01</td></tr><tr><td>αn</td><td>70.19</td><td>89.11</td><td>70.09</td><td>86.44</td><td>39.22</td><td>64.58</td></tr><tr><td>αh</td><td>73.83</td><td>90.96</td><td>72.86</td><td>87.23</td><td>44.58</td><td>66.72</td></tr><tr><td rowspan="3">16</td><td>αb</td><td>77.52</td><td>93.36</td><td>76.67</td><td>88.52</td><td>53.72</td><td>71.08</td></tr><tr><td>αn</td><td>72.43</td><td>91.02</td><td>73.34</td><td>87.76</td><td>40.74</td><td>64.95</td></tr><tr><td>αh</td><td>74.89</td><td>92.18</td><td>74.97</td><td>88.14</td><td>46.34</td><td>67.88</td></tr></table>
+
+![](images/3e63b6b5e9254872d7c39ebffcb88b9b4640ae4b812eb8255b8919a5c846b150.jpg)  
+αoriginal αunlearn 01 αtest αtrain
+
+![](images/cd91b39d42053d417575a3e791bbf2c683504123f56e5f0e61be118cd4fe24c9.jpg)
+
+![](images/0e966e46ae20f2d8b7aafbc0fd37033660a7ccc32b79ee38a6907e2f24abd3a5.jpg)  
+(a)  $\mathrm{EM} + \mathrm{CoCoOp}$  
+(c)  $\mathrm{REM} + \mathrm{CoCoOp}$
+
+![](images/13a94f1e41a87b7f18ea40d518aa2cd3057bf3ccb934147e291bfc18ae11ba04.jpg)  
+(b)  $\mathrm{EM} + \mathrm{A}^3$  
+(d)  $\mathrm{REM} + \mathrm{A}^3$
+
+![](images/81616334ed89d10775a3865fa15e1d3ed0af05dedecca17cf98b084e1cdb7d74.jpg)
+
+![](images/a6ad827e2de157735f90f2d0d34f9bc8deb05ba662f5c66c99a57b3fa52a03e9.jpg)  
+(f)  $\mathrm{AR} + \mathrm{A}^3$
+
+![](images/2a809476949a81417905ada8d5f012a84bf314fba9e658888963850b1dcbf5e6.jpg)  
+(e)  $\mathrm{AR} + \mathrm{CoCoOp}$  
+(g)  $\mathrm{LSP} + \mathrm{CoCoOp}$  
+Figure 2. CoCoOp vs. A<sup>3</sup> under partial poisoning with rates  $R \in \{\frac{1}{8}, \frac{1}{4}, \frac{1}{2}, 1\}$  (x-axis, %). Accuracy metrics (y-axis, %):  $\alpha_{\text{unlearn}} = \text{UEs}$  in the training set;  $\alpha_{\text{original}} = \text{original clean images of the UEs}$ ;  $\alpha_{\text{test}} = \text{clean images in the test set}$ ;  $\alpha_{\text{train}} = \text{clean images in the training set}$ . The image encoder backbone is ResNet-50.
+
+![](images/9c16c1e3695b1908ad6ede841fafda072772a77904d57be754a7105f372b4987.jpg)  
+(h)  $\mathrm{LSP} + \mathrm{A}^3$
+
+proves notably with increasing  $S$ , where CoCoOp falls behind while  $A^3$  leads by a large margin.
+
+With partially poisoned datasets,  $\mathbf{A}^3$  learns the underlying features while CoCoOp likely does not. In practice, model trainers may curate datasets from a variety of sources,
+
+and only a portion of the data may contain UE perturbations. Training on such partially poisoned datasets typically result in minimal performance loss over the clean dataset, and is not indicative of the model's ability to learn the underlying features of the UEs. In Figure 2, we thus investigate whether CoCoOp and  $\mathbf{A}^3$  can learn such features when trained on partially poisoned datasets. It evaluates the accuracy metrics of the unlearnable part ( $\alpha_{\mathrm{unlearn}}$ ), the original images of the unlearnable part ( $\alpha_{\mathrm{original}}$ , i.e., before perturbation), the samples from the test set ( $\alpha_{\mathrm{test}}$ ), and the clean part of the train set ( $\alpha_{\mathrm{train}}$ ). Importantly, if the model can learn the underlying features, then the  $\alpha_{\mathrm{original}}$  should be close to  $\alpha_{\mathrm{train}}$ , otherwise, it should be close to  $\alpha_{\mathrm{test}}$ . It is evident that CoCoOp actually struggles to learn useful features from the UEs, as  $\alpha_{\mathrm{original}}$  closely tracks  $\alpha_{\mathrm{test}}$ , while  $\alpha_{\mathrm{unlearn}}$  is higher than  $\alpha_{\mathrm{train}}$ . This suggests that CoCoOp is likely overfitting to the UE perturbations, even more so than the clean training data. In contrast,  $\mathbf{A}^3$  shows that  $\alpha_{\mathrm{original}}$  follows  $\alpha_{\mathrm{train}}$  closely, and  $\alpha_{\mathrm{unlearn}}$  is close to  $\alpha_{\mathrm{test}}$ , hinting that  $\mathbf{A}^3$  is learning the underlying features instead of the UE-crafted perturbations.
+
+# 5. Conclusion
+
+First, PLs' generalization combined with  $A^3$  make them challenging adversaries for traditional UEs. Second, Augmenting PL with diverse image and text perturbations significantly improves their resilience against UEs, pointing to the need for multimodal considerations in both UEs and countermeasures. Third, compared to simpler augmentations or adversarial training,  $A^3$ 's cross-modal feature alignment proved especially effective in mitigating PL's adaptation to UEs than preexisting learning methods. Finally, we emphasize the need for adaptive, multimodal approaches in UEs and open pathways toward more sophisticated protections against unauthorized training in an era of large multimodal and pretrained models.
+
+# Acknowledgment
+
+This work is supported in part by National Natural Science Foundation of China (62376263, 62372443 and 62271496), Guangdong Basic and Applied Basic Research Foundation (2023B1515130002), Natural Science Foundation of Guangdong (2024A1515030209 and 2024A1515011970), Shenzhen Science and Technology Innovation Commission (JCYJ20230807140507015 and JCYJ20220531100804009), and Yu-Liang Lu's Project Team Development Funding (KY23A102). This work was carried out in part at SICC, which is supported by SKL-IOTSC, University of Macau.
+
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+# A4A: Adapter for Adapter Transfer via All-for-All Mapping for Cross-Architecture Models
+
+Keyu Tu, Mengqi Huang, Zhuowei Chen, Zhendong Mao*  
+University of Science and Technology of China
+
+{kytu,huangmq,chenzw01}@mail.ustc.edu.cn，{zdmao}@ustc.edu.cn
+
+# Abstract
+
+Large-scale text-to-image models evolve rapidly in size and architecture. The existing adapters struggle to keep pace with these models, requiring extensive retraining. This paper proposes a novel adapter transfer framework, A4A (Adapter for Adapter), which uses an all-for-all mapping approach to seamlessly transfer attention-based adapters across different model architectures (e.g., U-Net to transformer). The framework consists of Coupling Space Projection and Upgraded Space Mapping. During Coupling Space Projection, all attention features of the pretrained adapter are aggregated to fully capture the coupling relationship before being projected into a unified space. The unified space maintains coupling features in a consistent dimension, effectively and efficiently addressing feature scale discrepancies arising from the base model's architecture. In the Upgraded Space Mapping Module, randomly initialized learnable features are introduced to connect the unified and upgraded spaces by integrating reference features via the attention mechanism. The learned features are adaptively injected into the upgrade model through the Alignment module, which bridges the discrepancies between the models using the all-for-all mapping. Experimental results on personalized image generation tasks demonstrate that A4A outperforms previous methods in transferring adapters while being the first to achieve adapter transfer across model architectures.
+
+# 1. Introduction
+
+Recent advancements in large-scale text-to-image diffusion models [5, 11, 23, 26] have significantly improved their ability to generate high-quality, realistic images based on user-friendly textual prompts. Building on these generative capabilities, numerous adapters have been developed upon these pretrained models to further endow them with new control conditions, such as pose and human identity control,
+
+thereby fostering the growth of downstream real-world applications like personalized image creation. As pretrained models rapidly evolve, with increasing parameters (e.g., from SD1.5's 860M to SDXL's 2600M) and developing architectures (e.g., from the convolution U-Net [27] to the transformer [22]), the original adapters built on base models require substantial resources for retraining and significant effort for redesign to accommodate upgraded models. This leads to a lag in adapter development compared to the progression of upgraded models<sup>1</sup>. Therefore, the adapter transfer task, i.e., effectively and efficiently transferring existing adapters from base models to upgraded models to leverage the strong control capabilities of the original well-developed adapters and the superior generative abilities of the upgraded models, has become an increasingly important and urgent requirement in both academia and industry.
+
+Given the substantial potential benefits of adapter transfer, several prior studies have been conducted in this field. For instance, Ctrl-Adapter [19] has been proposed to transfer the ControlNet [41] architecture by fusing the output of the zero-convolution from the pretrained ControlNet into the corresponding layer in the upgraded model. Concurrently, X-Adapter [25] has been explored for mapping the latent from the base model's decoder block and adding them to the corresponding location within the upgraded model's decoder. In summary, existing adapter transfer methods primarily focus on addition-based adapters (i.e., the control conditions are injected into the pretrained models by simple addition, typically, ControlNet), through a layer-by-layer mapping, i.e., the output of each layer in the base model's adapters are mapped to the semantically equivalent layer in the upgraded model.
+
+However, in this study, we argue that the existing layer-by-layer mapping fails to fully exploit the coupling between original adapters and base models to effectively bridge the
+
+discrepancies between base models and upgraded models. Here, coupling refers to the already well-trained compatibility between the original adapters and base models, while differences refer to the architectural discrepancies between base models and upgraded models. The reason behind this is that the original adapters and base models function as an integrated whole, and the layer-by-layer mapping disrupts this holistic consistency by isolating the output of each layer. Consequently, during the subsequent mapping to the upgraded models, this overall consistency cannot be effectively utilized. As a result, existing adapter transfer methods suffer from limited transfer scopes. On the one hand, they can only transfer addition-based adapters (typically, ControlNet) but fail to generalize to the attention-based adapters, which are more widely used. This is technically more challenging because attention-based adapters (i.e. the control conditions are injected into pretrained models by attention mechanisms) involve more complex interactions and dependencies across different layers of the model. On the other hand, these methods are limited to transferring between similar pretrained model architectures (e.g., from a U-Net model to another U-Net model) but fail when transferring from a U-Net model to a transformer model. This limitation is particularly critical, as the latest state-of-the-art pretrained text-to-image models [1, 6] are predominantly transformer-based, while the current most mature adapters remain developed on the U-Net architecture.
+
+To address this challenge, we propose a novel adapter transfer framework, A4A (Adapter for Adapter), which utilizes an innovative all-for-all mapping approach to seamlessly transfer the intrinsic coupling between all layers of the original adapters and base models to all layers of the upgraded models, thereby enabling the transfer of more difficult and widely used attention-based adapters and facilitating cross-architecture model transfers. Specifically, A4A achieves all-for-all mapping through the Coupling Space Projection and Upgraded Space Mapping. In the Coupling Space Projection phase, all attention features of the pretrained adapter are collected, capturing the complete coupling relationship between the adapter and the base model, and then projected into a unified space. The coupling relationship treats the features of all layers of the adapter as a unified whole, conveying a continuous representation of the new control conditions throughout the generation process, distinguishing it from isolated layer mappings. Upgraded space refers to the coupled feature space that corresponds to the upgraded model, where we randomly initialize learnable attention features to transfer the coupling relationship from the base model to the upgraded model. By integrating the reference features through the attention mechanism and aligning them with the upgraded architecture, the learnable features bridge the discrepancies between the models.
+
+The contributions of this work are as follows:
+
+1. To alleviate the limited transfer scopes, we introduce a novel all-for-all mapping approach that enables the transfer of attention-based adapters and facilitates cross-architecture model transfers.  
+2. A4A projects the adapter's complete features into the unified coupling space and bridges it with the upgraded space by fusing these features with randomly initialized learnable features through the attention mechanism.  
+3. Experiments in various types of personalized image creation demonstrate that A4A is an effective attention-based adapter transfer approach for cross-architecture models, achieving better performance than the pretrained adapter from the upgraded model with minimal training costs.
+
+# 2. Related work
+
+# 2.1. Latent Diffusion Models
+
+Recent diffusion-based text-to-image models [11, 23, 26, 29] have received wide acclaim for their outstanding image fidelity and diversity. Ho et al. [11] introduce the denoising diffusion process into generation models in the seminal work DDPM. Diffusion models learn the generation process through iterative denoising steps. Latent Diffusion Model (LDM) [26] proposed to perform the diffusion process in the latent space of a Variational Autoencoder [31]. Under the LDM architecture, two primary backbone models are employed: the convolutional U-Net [27] and the transformer [22]. While these models share a similar generation process, there are significant differences between the two models. The most notable example of U-Net models is the StableDiffusion [23, 26] series, excluding SDv3.0 [6], which consists of the symmetric encoder and decoder. The encoder is composed of multiple blocks of diverse dimensions, interconnected by down-sampling layers. Each block incorporates several attention layers [32] to fuse latents and conditions. Another series of models [4, 6, 9, 28] adopts DiT blocks [22] for denoising. The transformer model has been widely used in recent video generation tasks [20], where it has achieved state-of-the-art results. After patchification, the resulting features are progressively processed through a series of DiT blocks. In the DiT blocks, the features are scaled and shifted using AdaLN, maintaining the same dimension, which distinguishes them from U-Net-based models. Transformer-based models, with their flexible structure and impressive generative capabilities, have garnered significant attention due to their great potential.
+
+# 2.2. Adapters for Text-to-Image Diffusion Models
+
+Given the inefficiencies of fine-tuning large pretrained models, an alternative strategy is to utilize adapters, which introduce a limited number of trainable parameters while keeping the pretrained model frozen. Due to their flexibility and
+
+greater efficiency compared to fine-tuning, adapters have gained significant interest. By designing conditional modules, an adapter can introduce new control conditions, such as personalized characters, objects, layouts, and style information, to a pretrained text-to-image model. Downstream tasks for these adapters include personalized character generation (ID customization) [7, 34, 40, 42, 44], personalized object generation (IP customization) [2, 7, 13, 21, 30, 36, 37, 40, 42], attribute and layout control [3, 16, 18, 35, 38, 43], and stylization [10, 39]. As discussed in Sec. 1, these adapters can be categorized into two main types: attention-based and addition-based. In the addition-based adapter (typically, ControlNet [41]), the encoded new conditions are directly added to the output of the sub-blocks of the generation model. In contrast, the attention-based adapter processes the encoded conditions through attention layers, modifying the original attention values based on both the new conditions and the text prompts. Attention-based adapters [7, 10, 30, 34, 36-40, 42-44] have received widespread attention due to their efficient and precise condition control capabilities, dominating the field of adapters.
+
+# 2.3. Adapter Transferring
+
+The rapid evolution and diverse architectures of text-to-image generation models place constraints on transferring the aforementioned adapters. Consequently, to accommodate new models, adapters often require retraining from scratch on these pretrained diffusion models. X-Adapter [25] designates models equipped with the well-trained adapter as base models, with the upgraded version referred to as the upgraded model. It establishes manual connections between decoder blocks of the same dimensions in both the base and upgraded models. Specifically, the decoder of SD1.5 and SDXL consists of blocks with dimensions 1280, 640, and 320. X-Adapter [25] maps the output of the base model's blocks to the corresponding blocks of identical dimensions in the upgraded model. As a result, X-Adapter is specifically suited for SD-series models and faces challenges when transferring to transformer-based models [4, 6, 9, 22, 28]. Ctrl-Adapter [19] aims to transfer the addition-based adapter, ControlNet [41], for video generation models or upgraded image generation models. It connects the output of the zero-convolutional layers of both models through mappers to transfer the ControlNet.
+
+# 3. Method
+
+We propose a novel framework for transferring well-trained adapters from the base model to the upgraded model with architectural discrepancies, specifically U-Net model and transformer model. For the sake of brevity, we define PTA as the Pre-Trained Adapter. Specifically, pretrained refers to the version that has been officially published. Additionally, we denote  $M_{base}$  and  $M_{up}$  as the previously mentioned
+
+base model and upgraded model. A4A first projects the extracted attention features into the unified coupling to maintain the coupling relationship between PTAs and  $M_{base}$ . Then, the coupling space is mapped to the upgraded space, where learnable features integrate the reference coupling features with attention layers. These learned features are then adaptively aligned with  $M_{up}$  through the Alignment component.
+
+# 3.1. Preliminaries
+
+Before presenting our method, we introduce the diffusion model with various backbones. The Latent Diffusion Model (LDM), which perform noise addition and denoising in the latent space  $z$  of the VAE encoder, is the most prominent open-source community for text-to-image generation. The objective of training LDMs is:
+
+$$
+\min  _ {\theta} \mathcal {L} _ {L D M} = \mathbb {E} _ {z, \epsilon \sim \mathcal {N} (0, I), t} | | \epsilon - \epsilon_ {\theta} (z _ {t}, t, E _ {t} (y _ {t})) | | _ {2} ^ {2}, \tag {1}
+$$
+
+where  $t$  is uniformly sampled from the time steps  $\{1, \dots, T\}$ ,  $y_{t}$  denotes the conditional text prompt, and  $E_{t}$  represents the text encoder. The parameterized denoising network denoted as  $\epsilon_{\theta}$ , may take the form of either a U-Net model or a transformer model. The U-Net architecture consists of blocks with varying dimensions. Each U-Net block includes down-sampling or up-sampling layers along with attention layers. The transformer model primarily consists of multiple DiT blocks grounded on the transformer architecture. Since our method aims to transfer the widely used attention-based adapters, we define the cross-attention process and its associated signals as follows:
+
+$$
+\boldsymbol {q} = \boldsymbol {W} ^ {q} \cdot \boldsymbol {i}, \quad \boldsymbol {k} = \boldsymbol {W} ^ {k} \cdot \boldsymbol {c}, \quad a n d \quad \boldsymbol {v} = \boldsymbol {W} ^ {v} \cdot \boldsymbol {c} \tag {2}
+$$
+
+where  $i$  denotes the latents of the image, and  $c$  signifies the embeddings of the condition, such as the text prompt in the original model. Additionally,  $W$  represents the weights for attention projection. Attention is conducted as follows:
+
+$$
+\operatorname {A t t e n t i o n} (\boldsymbol {q}, \boldsymbol {k}, \boldsymbol {v}) = \operatorname {S o f t m a x} \left(\frac {\boldsymbol {q} \cdot \boldsymbol {k} ^ {T}}{\sqrt {d}}\right) \boldsymbol {v} \tag {3}
+$$
+
+where  $d$  represents the dimensions of  $\pmb{k}$  and  $\pmb{v}$ . Through cross-attention, the image latents and condition embeddings are comprehensively integrated.
+
+# 3.2. Coupling Space Projection
+
+Condition Encoder of PTA. For new control conditions  $y_{n}$  beyond the original text prompt, adapters typically incorporate a condition encoder as illustrated in Fig. 1. We denote  $E_{n}$  to distinguish it from the original text encoder  $E_{t}$  of the pretrained large-scale T2I models:
+
+$$
+\boldsymbol {c} _ {n} = E _ {n} \left(y _ {n}\right), \tag {4}
+$$
+
+![](images/a86d0fff88187fdbf456d2a9bebc8d42078a61a7a43735c068e5321b344f0df4.jpg)  
+Figure 1. The illustration of the Adapter for Adapter (A4A) framework. Both the base model and the upgraded model are kept frozen. (a) Coupling Space Projection: The pretrained Adapter, consisting of the condition encoder and attention layers (highlighted in pink), is loaded. The adapter features  $k_{i}$  and  $v_{i}$  are projected into a unified coupling space, reshaping them as  $K$  and  $V$ . (b) Upgraded Space Mapping: Randomly initialized learnable upgraded features,  $\bar{K}$  and  $\bar{V}$ , are concatenated with  $K$  and  $V$  as references. The learning process of  $\bar{K}$  and  $\bar{V}$  bridges the discrepancy between the base model and the upgraded model. These features are then aligned with the original cross-attention layers of the upgraded model through Alignment, which can be a U-Net or Transformer model. Best viewed in color.
+
+where  $c_{n}$  denotes the new condition embeddings. Taking IP-Adapter [40] as an example, the Image Encoder external to the original generation model serves as the condition encoder. And we directly integrate the pretrained condition encoder  $E_{n}$  from the adapter to efficiently transfer the well-trained adapter to the upgraded model.
+
+Attention Layers of PTA. As illustrated in Fig. 1, the encoded new condition embeddings  $c_{n}$  are processed through the attention mechanism coupling with the base model. We explicitly depict the attention layers associated with the pretrained adapter in the figure, denoting the weights of the  $i$ -th attention layer of the adapter as  $W_{A,i}$ , distinguishing them from the original attention weights  $W$  in the base model. Subscript  $A$  represents the adapter, and  $i$  represents the  $i$ -th adapter attention layer. For instance, the fine-tuned cross-attention layers in the Decoupled Cross-Attention module of IP-Adapter [40] exemplify this.  $c_{n}$  are sequentially fed into the aforementioned adapter's attention layers  $W_{A,i}$ :
+
+$$
+\boldsymbol {k} _ {i} = \boldsymbol {W} _ {A, i} ^ {k} \left(\boldsymbol {c} _ {n}\right), \quad \boldsymbol {k} _ {i} \in \mathbb {R} ^ {N \times d _ {i}}, \tag {5}
+$$
+
+$$
+\boldsymbol {v} _ {i} = \boldsymbol {W} _ {A, i} ^ {v} \left(\boldsymbol {c} _ {n}\right), \quad \boldsymbol {v} _ {i} \in \mathbb {R} ^ {N \times d _ {i}}, \tag {6}
+$$
+
+where  $d_{i}$  is the dimension of the feature, and  $\mathbf{N}$  denotes the number of tokens for feature  $k_{i}$  and  $\boldsymbol{v}_{i}$ . To extract the attention features from  $\boldsymbol{c}_{n}$ , we employ the attention layers of the adapter rather than utilizing the entire base model.
+
+Projection onto the Coupling Space. The features obtained from multiple layers form a sequence of length  $l$ ,  $[k_1, k_2, \dots, k_l]$  and  $[v_1, v_2, \dots, v_l]$ , where  $l$  represents the number of attention layers of PTA. The dimensions  $d_i$  of the features vary, as shown in Fig. 1. To achieve the all-for-all mapping for the attention-based adapter from  $M_{base}$  to  $M_{up}$ , the features of all cross-attention layers need to be
+
+projected into a unified coupling space  $S_{co}$  which is defined by the smallest common multiple  $d_{scm}$  of all dimensions  $d_{i}$ :
+
+$$
+\boldsymbol {K} = \operatorname {P r o j} ([ \boldsymbol {k} _ {1}, \boldsymbol {k} _ {2}, \dots , \boldsymbol {k} _ {l} ]), \quad \boldsymbol {K} \in \mathbb {R} ^ {l \times N \times d _ {s c m}}, \quad (7)
+$$
+
+$$
+\pmb {V} = \mathrm {P r o j} ([ \pmb {v} _ {1}, \pmb {v} _ {2}, \dots , \pmb {v} _ {l} ]), \quad \pmb {V} \in \mathbb {R} ^ {l \times N \times d _ {s c m}}. \quad (8)
+$$
+
+The projection module consists of several linear layers designed to map dimensions  $d_{i}$  to  $d_{scm}$ . After the sequences are projected to  $S_{co}$ , they are reshaped into matrices  $K$ , and  $V$ . Mapping to  $S_{co}$  defined by  $d_{scm}$  strikes the best balance between efficiency and effectiveness. Sec. 7.3 in the supplementary material demonstrates this through experiments. It reduces computational complexity by aligning features to a common dimension, avoiding the overhead of larger spaces. At the same time, it maintains sufficient representational capacity, preventing the loss of important information, which can happen with smaller spaces. This ensures effective feature alignment without excessive resource usage, making it an optimal choice for both computational efficiency and model performance.
+
+# 3.3. Upgraded Space Mapping
+
+Similarly, we define the number of the cross-attention layers in the upgraded model as  $\bar{l}$ , and the space for upgraded models as  $S_{up}$ . To transfer the unified adapter features to the upgraded space, inspired by BLIP-2 [17], we randomly initialize two learnable parameters  $\bar{K} \in \mathbb{R}^{\bar{l} \times N \times d_{\text{scm}}}$  and  $\bar{V} \in \mathbb{R}^{\bar{l} \times N \times d_{\text{scm}}}$ . Given that the attention layer is effective for integrating features, we adopt this architecture to learn the aforementioned parameters. Consider the learning of  $\bar{K}$  as an example. To enhance the robustness, we first
+
+normalize  $\bar{\pmb{K}}$  and  $\pmb{K}$  using layer normalization. And then, the following operation is performed:
+
+$$
+\begin{array}{l} \bar {\boldsymbol {K}} = \operatorname {F F N} \left[ \boldsymbol {W} ^ {o u t} \cdot \text {A t t e n t i o n} \left(\bar {\boldsymbol {K}} \boldsymbol {W} _ {1} ^ {k}, \right. \right. \tag {9} \\ [ \boldsymbol {K}, \bar {\boldsymbol {K}} ] W _ {2} ^ {k}, [ \boldsymbol {K}, \bar {\boldsymbol {K}} ] W _ {3} ^ {k}) ]. \\ \end{array}
+$$
+
+where  $[\pmb{K},\bar{\pmb{K}} ]$  denotes the concatenation of  $\pmb{K}$  and  $\bar{\pmb{K}}$  along dimension  $N$ . The projection weights  $\pmb{W}_1^k,\pmb{W}_2^k,\pmb{W}_3^k\in \mathbb{R}^{d_{scm}\times d_{in}}$  map  $\bar{\pmb{K}}$  and  $\pmb{K}$ , respectively, to the intermediate space with dimension  $d_{in}$ . Following the processing of features using the Attention as described in Eq. (3), they are subsequently transformed back to the original space via the  $\pmb{W}^{out}$ . The Feed Forward Network (FFN) is composed of layers arranged sequentially, including layer normalization, linear transformations, GELU activation, and additional linear layers. The aforementioned process of Eq. (9) is iterated  $\mathbf{R}$  times, with  $\mathbf{R}$  serving as a hyperparameter. The learning process of  $\bar{\pmb{V}}$  is similar to  $\bar{\pmb{K}}$ :
+
+$$
+\bar {\boldsymbol {V}} = \operatorname {F F N} \left[ \boldsymbol {W} ^ {\text {o u t}} \cdot \text {A t t e n t i o n} \left(\bar {\boldsymbol {V}} \boldsymbol {W} _ {1} ^ {v}, \right. \right. \\ \left. [ \boldsymbol {V}, \bar {\boldsymbol {V}} ] \boldsymbol {W} _ {2} ^ {v}, [ \boldsymbol {V}, \bar {\boldsymbol {V}} ] \boldsymbol {W} _ {3} ^ {v}) \right]. \tag {10}
+$$
+
+We clarify that two distinct modules with an identical structure are responsible for learning  $\bar{K}$  and  $\bar{V}$ , respectively. Throughout this process, the learnable features  $\bar{\bar{K}}$  and  $\bar{V}$  are seamlessly integrated with the adapter features  $K$  and  $V$  of the PTA, effectively bridging the unified coupling space to the upgraded space.
+
+Alignment with the Upgraded Model. The learned features in the upgraded space should be aligned with the attention layers of  $M_{up}$  to fully leverage the adapter's capabilities. Specifically, we first fetch the dimensions  $\bar{d}_i$  of the cross-attention layers within the original upgraded model. Then, we employ the linear layer to align the  $i$ -th row of the matrix  $\bar{\mathbf{K}}$  to  $\bar{d}_i$  dimensions through Alignment, which we denote as  $\bar{k}_i$ :
+
+$$
+[ \bar {\boldsymbol {k}} _ {1}, \dots , \bar {\boldsymbol {k}} _ {\bar {l}} ] = \operatorname {A l i g n} (\bar {\boldsymbol {K}}). \tag {11}
+$$
+
+Similarly, the identical operation is applied to the  $\bar{\mathbf{V}}$  matrix in order to derive the vector  $\bar{\pmb{v}}_i$ :
+
+$$
+[ \bar {\boldsymbol {v}} _ {1}, \dots , \bar {\boldsymbol {v}} _ {\bar {l}} ] = \operatorname {A l i g n} (\bar {\boldsymbol {V}}). \tag {12}
+$$
+
+For the  $i$ -th cross-attention layer, let  $\pmb{q}_i^{up}$ ,  $\pmb{k}_i^{up}$ , and  $\pmb{v}_i^{up}$  be the original features. The extracted features,  $\bar{\pmb{k}}_i$  and  $\bar{\pmb{v}}_i$ , are combined through linear weighting and summation with the prior values of the upgraded model using Attention Eq. (3):
+
+$$
+\begin{array}{l} \bar {\boldsymbol {Z}} = \operatorname {A t t e n t i o n} \left(\boldsymbol {q} _ {i} ^ {u p}, \boldsymbol {k} _ {i} ^ {u p}, \boldsymbol {v} _ {i} ^ {u p}\right) + \tag {13} \\ \lambda \text {A t t e n t i o n} \left(\boldsymbol {q} _ {i} ^ {u p}, \bar {\boldsymbol {k}} _ {i}, \bar {\boldsymbol {v}} _ {i}\right). \\ \end{array}
+$$
+
+The result of Eq. (13),  $\bar{Z}$ , serves as the output for the  $i$ -th cross-attention layer and will be forwarded to the next layer of the upgraded model. The parameter  $\lambda$  serves as a balancing factor, fixed at 1.0 during training and subsequently adjusted for downstream tasks during inference.
+
+# 3.4. Optimization Loss Function
+
+To optimize the A4A framework, we employ the loss function  $\mathcal{L}_{LDM}$  of the upgraded model  $M_{up}$  as defined in Equation Eq. (1):
+
+$$
+\mathcal {L} _ {L D M} = \mathbb {E} _ {z, \epsilon \sim \mathcal {N} (0, I), t} \| \epsilon - \epsilon_ {\theta} ^ {u p} \left(z _ {t}, t, c ^ {u p}\right) \| _ {2} ^ {2}, \tag {14}
+$$
+
+The condition  $c^{up}$  includes the original text prompt  $y_{t}$  and new control conditions  $y_{n}$ . The upgraded model  $\epsilon_{\theta}^{up}$  acquires new control conditions and capabilities by injecting learned adapter features.
+
+The base model and upgraded model remain frozen. The loss function is exclusively used to update the A4A module, which consists of the network with learnable features and the PTA for fine-tuning. To optimize model training, given the varying numbers of parameters in each trainable module, we adopt an asynchronous training strategy. Specifically, for training the projection in  $S_{co}$  and alignment in  $S_{up}$ , a learning rate of  $1 \times 10^{-5}$  is employed to avoid overfitting, while a learning rate of  $1 \times 10^{-4}$  is applied to the other components. If the pretrained adapter is fine-tuned, a smaller learning rate of  $1 \times 10^{-6}$  is used to effectively retain PTA's conditional encoding capabilities.
+
+# 4. Experiments
+
+# 4.1. Experimental Settings
+
+Datasets. In our study, we utilize the CelebAMask-HQ dataset [15], which consists of approximately 20,000 high-quality facial images, each with a resolution of  $1024 \times 1024$  pixels, and the OpenImages dataset [14], which offers a diverse collection of images featuring a wide range of clearly identifiable objects. We employ the BLIP-2 model [17] to generate captions for the aforementioned datasets, which serve as text prompts paired with the images. For validation, we randomly select 100 images from CelebAMask-HQ, ensuring they are distinct from those in the training set, and generate four images for each reference image.
+
+Implementation Details. We implement A4A using SD1.5 [26] as the base model, and SDXL [23] and Pixart-Alpha (XL) [4] as the upgraded models. Both SDXL and Pixart-Alpha are significantly larger text-to-image models compared to SD1.5, and we use them as upgraded models for the U-Net and transformer architectures, respectively. In this paper, we utilize the IP-Adapter [40] as our pretrained adapter. The IP-Adapter series has recently demonstrated remarkable capabilities, garnering significant interest for its ability to enhance personalization in generative models. Its performance across a variety of tasks highlights its increasing potential to advance text-to-image generation. Due to variations in GPU types across compared methods and the absence of comprehensive GPU hour reports, we use Sample Count (SC), which represents the number of samples processed up to a specific time point, as a metric
+
+![](images/66b93cd27e2503d438b30bfa123b5769814d45f9d50523f09cd82bea5f899aa3.jpg)  
+Figure 2. The visualization of personalized human generation using SDXL with U-Net architecture as the upgraded model. A4A(ours) compares with the previous work X-Adapter and pretrained adapter from the upgraded model (PTA-UM).
+
+![](images/9ce9673e3ffcd9fd32f55633093dce31a2d23a1288de851c5e4c5d47441de51a.jpg)  
+Figure 3. The visualization of personalized object generation using SDXL with U-Net architecture as the upgraded model. A4A(ours) compares with the previous work X-Adapter and pretrained adapter from the upgraded model (PTA-UM).
+
+for evaluating training costs and efficiency. For example, the officially published PTA has an SC of 64M (i.e., the PTA is trained with 8 V100 GPUs for 1M steps with a batch size of 8 per GPU). The terms in the following charts are defined as: (1) A4A (ours): transferring the PTA from the base model to the upgraded model using our method A4A; (2) X-Adapter: transferring the PTA using the published X-Adapter [25] checkpoint; (3) PTA-UM: the officially published pretrained adapter from the upgraded model.
+
+Evaluation Metrics. To verify the effectiveness and effi
+
+ciency of our method, we evaluate A4A on two tasks: personalized human generation (ID customization) and personalized object generation (IP customization). For ID customization, we utilize IDentity Alignment scores (IDA) to measure the similarity between generated and reference facial features, alongside the OMG method [12]. Specifically, we employ the Antelopev2 model from the InsightFace library [8] to detect faces and extract facial embeddings from both reference and generated images. For IP customization, we extract image embeddings using pretrained CLIP
+
+# A4A(ours)
+
+Photo of a man/woman standing in a garden, dressed in casual clothing, dressed in casual clothing
+
+![](images/fe64143bd4cf19a61c1bf3199a22b1d70b415ba7436a7f604f6aa56a82aa538b.jpg)
+
+![](images/7cbebc0524ffe155f0ad73ec4d8ecaf31faee6c9492bb38ad5ee3223746d5a13.jpg)
+
+![](images/47ac2fc31e6a7d274633709f46eda1e61a85864123096e5ec72d3fa992b45b5b.jpg)
+
+![](images/f3980b481ad7f811b9edbfb4db3d972ef35f68e0d8074f2b15b4ad6cbd0330fb.jpg)  
+Figure 4. The visualization of transferring the IP-Adapter from SD1.5 (U-Net architecture) to Pixart-Alpha (Transformer architecture). The middle line, framed in orange, serves as the reference for comparison. The left side shows the A4A effect, which closely resembles the reference, while the right side (IP-Adapter*) displays the results of training IP-Adapter from scratch.
+
+![](images/8f7780d3c305c94afee09681906fd201028bf1dd539e67ff149a9b2f836f12cd.jpg)
+
+![](images/a1041bd4031e5f914ab1d88e8219f1e2c2444a34b4fcaa721a492d8addd44746.jpg)
+
+![](images/83158e4f5833c57823086f319547980fdf46aba07f0b41f5b6e9a324039fc58c.jpg)
+
+![](images/337e5402090e1bbfd29065a07a30ca3b9b53cb40e8f89e1bbd30d525117e5a58.jpg)
+
+![](images/7c531b3162fde19d76daede2e22a3e8be96995b3a1790e2b383e8ef6e3c15251.jpg)
+
+![](images/16528312b9c32bd01ab2a8f9b83c5bed68a88e60f9c21df5e58aaa5feb0d3df2.jpg)
+
+![](images/4b72913cfc36aad22e8606f661f048f5b333a606e398c6ee29790df710b5a8b4.jpg)
+
+![](images/af99a3e34f50e28b99e049bc0a3f27ba947b4b200d5f87b2ef7e203bb92bf519.jpg)
+
+![](images/57ae4f7e95072d572b606bb37c9f5f6a14a0dc165cb0830d7edfeab86e59d2a4.jpg)  
+Text Prompt
+
+![](images/61d26fa82a7bb677a72b24b19ad76424bc57ba2a107e45ecbfd3bcfaafcb8239.jpg)
+
+![](images/848236a53755e1139544513f3d308a4305297bcda1f6f10336ca8cbcd9ca02f7.jpg)
+
+![](images/ae32af3ce002090ac247c4c2d85168234bc82d85ca77bd6053d2fbd1a25003e5.jpg)
+
+![](images/c7bc67cba504b80415a83eee1f1a51e7e2f5d6ef8950e1d978c7e39bfc1f22b1.jpg)
+
+![](images/5bc2b7e4ea6ee70730c32a70883a7d7d20f799edb14bd29fd180c609dd7bf10c.jpg)
+
+![](images/5fb976c3468f42757a85f83aa4eca62f05cc02e23375216a8f167825dda78ce2.jpg)
+
+![](images/a2283328ee278da6f9fba1185c9d3a8d7829de61d95a5a08045866e2e02d252e.jpg)
+
+# IP-Adapter\*
+
+Photo of a man/woman standing in a garden, dressed in casual clothing, dressed in casual clothing
+
+![](images/962e45ecfd2217bb41ba0a074ccdef3c37c8c0136df0fae9dcd51d9bad7d0de9.jpg)
+
+![](images/959c47cf92a3b815ce1eb45301729c6de4eedf17943a5249b17aaf16d2d7bb73.jpg)
+
+![](images/fdba5f17f5d669645cd571225b302c820053f927e6bf0ff0efe5b08c90a39b6d.jpg)
+
+![](images/6e44ce8e6807b350b95d84a69ae27961cdec95add122ba0a5be6afb69f5efa02.jpg)
+
+![](images/3e7d6088f62cdd2d630e57fd4eda834eac73b2b2fc292729dab221070bc55960.jpg)
+
+![](images/a25eb9338a194802f6bf62585c6c47b963d3c8212afc35a53caf27593f4eabd4.jpg)
+
+![](images/53512d3eae80263c154286529562d1c7bfc6e7d3016850b84a731822613a82cc.jpg)
+
+![](images/79f36e8373c041b56e98430c85e0e398b5791190220a2d660decdd554635447d.jpg)
+
+![](images/20bcbc720f725f45c4fdc3a1f29bd471a6bbcbcd51a9460863ffd252192a1dac.jpg)
+
+![](images/128dbbaf9f45590515898394dc2828d87dbc506efaa05e4fa0279c7ad9cc5c68.jpg)
+
+![](images/37f8a1f3a2e0e035f59c33aec3b06ab7a3c6a4afeb366f6d6b7038b88bb12ca3.jpg)
+
+![](images/079969bf3c7337de7a2f70e422babc77e6788101ecb5c08954fd16130ca45eea.jpg)
+
+![](images/55081e8dd368ae1851a919b8f7d61a0dbf81c0a74aa4f2d73f79c8620cdd262d.jpg)
+
+![](images/e51493f7821e830e5deca317a74b0dae8367f4398fe4c3ed78b7114f2b73bd39.jpg)
+
+![](images/21b4bfc819dbbaa88e276dcbdde80a291423726dc2c681a93e83bcdc22838a8a.jpg)
+
+![](images/4a1e99966750ed40efee9a98d7b465d20557986942b83b8fcb7631d2cf81ac04.jpg)
+
+model [24] and report the embedding similarity between generated and reference images, referred to as the CLIP-score. In the graph, we use the previously defined SC as the horizontal axis to represent the training process.
+
+# 4.2. Transferring to the U-Net model
+
+We use SDXL as the upgraded model and compare our results with the officially published PTA-UM [40] (represented by the green star in Fig. 5). To facilitate comparison, we extend a horizontal line from this point to represent the performance of PTA-UM, rather than the actual training curve. As illustrated in Fig. 5, transferring the PTA using A4A achieves an IDA comparable to that of the PTA-UM at approximately  $\mathrm{SC}0.5\mathrm{M}^2$ . Furthermore, as shown in Fig. 2, the lines "A4A (ours)" and "PTA-UM" demonstrate that A4A not only preserves the intellectual property of the characters but also maintains the editing capabilities of the upgraded model with minimal training cost.
+
+For personalized object generation (IP customization), as shown in Fig. 6, transferring the PTA using A4A achieves a CLIP-score comparable to that of PTA-UM at approximately 2.5M SC, compared to 64M SC for PTA-UM. As illustrated in Fig. 3, the lines labeled "A4A (ours)" and "PTA-UM" demonstrate that control ability, as guided by the text prompt, is also preserved. When the attention-based adapter is transferred to the upgraded U-Net model, A4A ef
+
+![](images/aa1bc97f37480ed25043a456cef3b14af810c985f912776542fd091739d160a3.jpg)  
+Figure 5. The graph shows the IDA of ID preservation when transferring to SDXL, compared to the pretrained adapter from SDXL (PTA-UM). The horizontal axis is in units of M.
+
+![](images/c93ac3380b00ea9ed059918b0e1a147a89f8ee44b8013b744a536d2b44511e41.jpg)  
+Figure 6. The graph shows the CLIP-score of personalized object generation when transferring to SDXL, compared to PTA-UM. The horizontal axis is in units of M.
+
+fectively retains and transfers the adapter's capabilities with minimal training cost. The data of the quantitative indica
+
+tors corresponding to the line chart are shown in Tab. 1.
+
+# 4.3. Transferring to Transformer model
+
+We use Pixart-Alpha [4] with the transformer architecture as the upgraded model. Given the absence of a corresponding published version of the IP-Adapter for Pixart-Alpha, we train it from scratch using the CelebAMask-HQ dataset as our baseline, represented by the orange line labeled "IP-Adapter*" in Fig. 7 and Fig. 4. As illustrated in Fig. 7, employing A4A to transfer pretrained adapters to transformer models offers a significant advantage over training adapters directly on the transformer models. It is worth noting that our work is the first to transfer the adapter from the U-Net model to the transformer model, achieving strong results. Fig. 4 presents a visualization comparing our method with training the IP-Adapter from scratch, both at 30k steps with a batch size of 8. The images generated by A4A show significant facial similarity to the reference image, while the image on the right does not yield comparable results.
+
+![](images/576d606fe6975be35450003a2984ee536f2e2db225ca61a8629aba5825bef934.jpg)  
+Figure 7. The IDA of transferring the pretrained IP-Adapter from SD1.5 to Pixart-Alpha using A4A (red line with dots), compared to training the IP-Adapter from scratch (orange line with stars). The horizontal axis is in units of K. Best viewed in color.
+
+# 4.4. Ablation Study
+
+In the previous section, we adopted the A4A paradigm, which includes training our modules, namely Coupling Space Projection and Upgraded Space Mapping, along with fine-tuning the PTA. To demonstrate that fine-tuning is not the core driving force of our method, we conducted the following experiment. As shown, the two curves are very close, with the fine-tuning paradigm showing only a slight improvement over the non-fine-tuning version.
+
+We present experiments on the hyperparameter settings of the learning rates for each component in Sec. 7. It is worth mentioning that, since Projection and Alignment have similar numbers of parameters, we group them together. The ablation study of the two core modules is presented in Sec. 8, which demonstrates that our design achieves a satisfactory transfer effect with an efficient structure.
+
+![](images/973239fcf626e413ae96724f8697f9c406221073a8f100f655bb295998e01bc3.jpg)  
+Figure 8. The yellow line labeled "A4A(ours w/fine-tuning)" represents training A4A without fine-tuning the PTA, while the red line represents the full A4A approach with fine-tuning the PTA.
+
+<table><tr><td>PTA: IP-Adapter</td><td>IDA↑</td><td>CLIP-score↑</td></tr><tr><td>X-Adapter</td><td>0.062</td><td>0.7894</td></tr><tr><td>PTA-UM</td><td>0.4531</td><td>0.9124</td></tr><tr><td>A4A(ours)</td><td>0.5127</td><td>0.9154</td></tr></table>
+
+Table 1. The evaluation metrics for IP customization (CLIP-score) and ID customization (IDA) are presented. Using SDXL as the upgraded model and IP-Adapter as the pretrained adapter, A4A (ours) is compared with the transfer method X-Adapter and the pretrained adapter from the upgraded model (PTA-UM).
+
+# 4.5. Comparison with X-Adapter
+
+The previous work X-Adapter [25] is designed specifically for transferring adapters from U-Net models. To demonstrate the effectiveness of A4A, we also compare it with X-Adapter. As shown in Tab. 1, our method achieves better results in generation using the transferred adapter for both IP and ID customization. The visualizations in Figure 2 and Fig. 3, particularly the row labeled "X-Adapter", further substantiate this when compared to the adjacent rows. It is also worth noting that our method requires only the adapter for training and inference, without the need for denoising using the base model as in X-Adapter, which makes it more efficient.
+
+# 5. Conclusion
+
+We propose A4A (Adapter for Adapter), a novel framework designed to address the challenges of transferring pretrained adapters across rapidly evolving model architectures. By employing an all-for-all mapping approach, A4A seamlessly transfers attention-based adapters from U-Net to transformer models without the need for extensive retraining. The framework's two key components, Coupling Space Projection and Upgraded Space Mapping, enable effective bridging of adapter features with upgraded model structures. Our experimental results demonstrate that A4A preserves both the generative power of upgraded models and the controllability of the original adapters. This work offers a scalable solution for cross-architecture adapter transfer.
+
+# 6. Acknowledgment
+
+This research is supported by Artificial Intelligence National Science and Technology Major Project 2023ZD0121200, and National Natural Science Foundation of China under Grant 62222212 and 623B2094.
+
+# References
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+# AA-CLIP: Enhancing Zero-Shot Anomaly Detection via Anomaly-Aware CLIP
+
+Wenxin Ma $^{1,2}$  Xu Zhang $^{1,2}$  Qingsong Yao $^{5}$  Fenghe Tang $^{1,2}$  Chenxu Wu $^{1,2}$
+
+Yingtai Li $^{1,2}$  Rui Yan $^{1,2}$  Zihang Jiang $^{1,2*}$  S.Kevin Zhou $^{1,2,3,4*}$
+
+<sup>1</sup> School of Biomedical Engineering, Division of Life Sciences and Medicine, USTC
+
+$^{2}$  MIRACLE Center, Suzhou Institute for Advance Research, USTC
+
+<sup>3</sup> Key Laboratory of Intelligent Information Processing of CAS, ICT, CAS
+
+$^{4}$  State Key Laboratory of Precision and Intelligent Chemistry, USTC
+
+5 Stanford University
+
+wxma@mail.ustc.edu.cn jzh0103@ustc.edu.cn s.kevin.zhou@gmail.com
+
+![](images/c262008dc6a5c352ce4c87a0c0b8d241c611605d740b4021175addac6a5ab112.jpg)  
+Features from Original CLIP  
+(Left)  
+Figure 1. (Left) CLIP's anomaly unawareness: Category-level image-text alignment in pre-training leads to CLIP's vague distinctions in anomaly/normal semantics and inaccurate patch-text alignment. (Middle) Our two-stage adaptation strategy: In Stage1, anomaly and normal text features are disentangled as anchors in text space; in Stage2, patch-level visual features are trained to align to these anchors, forming Anomaly-Aware CLIP. (Right) Generalizable anomaly awareness: Our method enables CLIP with generalizable anomaly awareness for both known and unseen classes.
+
+![](images/405427f90a30740df75eebe906d8559fa16b9540f06778b3baeee3d49ac5bb62.jpg)  
+Stage1: Disentangling Anomaly-Aware Text Anchors  
+(Middle)
+
+![](images/199d6c14ef078069f92c1d73c20758998ba76787d4d6aa8c8ad9f11f37685ab5.jpg)  
+Stage2: Aligning Patch Features According to Text Anchors
+
+![](images/f86c1c21560c68444a6a9dbb56d8d95195a458263ac431a206d76551bc0659ef.jpg)  
+Features from our Anomaly-Aware CLIP  
+(Right)
+
+# Abstract
+
+Anomaly detection (AD) identifies outliers for applications like defect and lesion detection. While CLIP shows promise for zero-shot AD tasks due to its strong generalization capabilities, its inherent Anomaly-Unawareness leads to limited discrimination between normal and abnormal features. To address this problem, we propose Anomaly-Aware CLIP (AA-CLIP), which enhances CLIP's anomaly discrimination ability in both text and visual spaces while preserving its generalization capability. AA-CLIP is achieved through a straightforward yet effective two-stage approach: it first creates anomaly-aware text anchors to differentiate normal and abnormal semantics clearly, then aligns patch-level visual features with these anchors for precise anomaly localization. This two-stage strategy, with the help of residual adapters, gradually adapts CLIP in a controlled man
+
+ner, achieving effective AD while maintaining CLIP's class knowledge. Extensive experiments validate AA-CLIP as a resource-efficient solution for zero-shot AD tasks, achieving state-of-the-art results in industrial and medical applications. The code is available at https://github.com/Mwxinnn/AA-CLIP.
+
+# 1. Introduction
+
+Anomaly detection (AD) involves modeling the distribution of a dataset to identify outliers, such as defects in industrial products [2] or lesions in medical images [13]. Despite that previous AD frameworks [10, 11, 15, 23, 31, 58] effectively detect anomalies when sufficient labeled data is available for specific classes, their high resource demands often limit their generalization ability to novel and rare classes. This limitation is particularly challenging in real-world scenarios where collecting comprehensive labeled datasets for AD is often infeasible, necessitating the exploration of low-shot
+
+learning and transfer learning approaches.
+
+Contrastive Language-Image Pretraining (CLIP) model has emerged as a promising solution, demonstrating remarkable generalization capabilities across various zero-shot tasks [24-26, 42]. Building upon CLIP's success, several recent studies have adapted CLIP for few/zero-shot AD tasks by utilizing anomaly-related descriptions to guide the detection of anomalous regions. Specifically, the vision encoder is trained to map anomaly images to visual features that align more closely with text features of abnormal descriptions than with those of normal descriptions [29, 30, 49, 60]. Further works [6, 7, 17, 41] have focused on enhancing CLIP's patch-level feature representations to achieve better alignment with text features, resulting in improved anomaly localization performance.
+
+These methods depend on text features that need to be anomaly-aware to effectively differentiate abnormalities. However, recent studies highlight CLIP's limitations in fine-grained semantic perception and reasoning [21, 22, 36, 38, 45, 46]. Upon exploring CLIP's texture features for AD, we observe that while CLIP's text encoder effectively captures object-level information, it struggles to reliably distinguish between normal and abnormal semantics. As shown in conceptual visualization Fig. 1(left) and sampled examples in Fig. 2, CLIP has the intrinsic Anomaly-Unawareness problem: the overlap of normal and abnormal texture features hampers the precision of text-guided anomaly detection. We argue that making CLIP anomaly-aware — by establishing clearer distinctions between normal and abnormal semantics in the text space — is essential for guiding the vision encoder to precisely detect and localize anomalies.
+
+This observation drives us to improve CLIP-based zero-shot AD through enhancing anomaly discrimination in text space, achieved with our method Anomaly-Aware CLIP (AA-CLIP) — a CLIP model with anomaly-aware information encoded. AA-CLIP is implemented through a novel two-stage adaptation approach. In the first stage, AA-CLIP adapts the text encoder with frozen visual encoder, creating "anchors" for anomaly-aware semantics within the text space for each trained class. As illustrated in Fig. 1(middle), each class's text features are disentangled to distinct anchors, with clear abnormality discrimination. Notably, this disentanglement also applies to novel, unseen classes, supporting effective zero-shot inference in AD tasks (refer to Fig. 1(right)). In the second stage, AA-CLIP aligns patch-level visual features with these specially adapted texture anchors, guiding CLIP's visual encoder to concentrate on anomaly-relevant regions. This two-stage approach ensures a focused and precise anomaly detection framework.
+
+Importantly, as CLIP is extensively trained on massive data, to preserve its pre-trained knowledge, we utilize simple-structured Residual Adapters in both stages. This design enables a controlled adaptation of CLIP while en
+
+hancing its capability to handle fine-grained AD tasks without sacrificing its generalization ability.
+
+Our extensive experiments in both industrial and medical domains demonstrate that our straightforward approach equips CLIP with improved zero-shot AD ability, even in data-limited scenarios. By training with a minimal sample — such as one normal sample and one anomaly sample (2-shot) per class — and testing across unseen datasets, our method achieves zero-shot performance comparable to other CLIP-based AD techniques. With only 64-shot of each class seen in the training set, our method reaches state-of-the-art (SOTA) results in cross-dataset zero-shot testing, validating our method's ability to maximize the CLIP's potential for AD with a minimal data requirement.
+
+Our contributions are summarized as follows:
+
+1. Anomaly-Aware CLIP with enhanced and generalizable anomaly-discriminative ability. We introduce AA-CLIP which is more sensitive to anomalies sequentially in text and visual spaces, encoding anomaly-aware information into the original CLIP.  
+2. Efficient adaptation using residual adapters. We implement simple residual adapters to boost zero-shot anomaly detection performance without compromising the model's generalization ability.  
+3. SOTA performance with high training efficiency. Our method achieves SOTA results across diverse datasets, showing robust anomaly detection capabilities even with limited training samples.
+
+# 2. Related Work
+
+Traditional Anomaly Detection in images involves modeling the normal data distribution to detect rare and diverse unexpected signals within visual data [44, 52, 53, 61]. Reconstruction-based [11, 16, 32, 33, 54, 56], augmentation-based [31, 44, 48, 55, 58] and discriminative [10, 15, 23, 31, 43, 61] methods are typically used to facilitate better modeling. Despite the huge progress of traditional anomaly detection methods, their effectiveness relies heavily on a well-modeled normal data distribution. Without sufficient normal data, their ability to accurately detect anomalies is significantly reduced.
+
+CLIP, trained on a vast amount of image-text data, leverages contrastive learning alongside powerful language models and visual feature encoders to capture robust concepts. This combination enables CLIP to achieve impressive zero-shot performance on image classification, as it can generalize well to new categories without requiring task-specific training [24-27, 42, 51]. More recently, numerous studies [9, 12, 35, 39] have explored ways to transfer the knowledge embedded in CLIP models to a variety of downstream tasks, yielding promising results in fields like image captioning, image-text retrieval, and image generation. These efforts demonstrate CLIP's versatility and potential to drive
+
+advancements across diverse applications.
+
+Despite the rapid advancements achieved by CLIP, numerous studies have highlighted persistent limitations in the features it extracts. While CLIP demonstrates strong generalization across various tasks, it often struggles to capture nuanced details and essential spatial relationships, which are crucial for tasks demanding precise boundary delineation and fine-grained feature extraction. This limitation results in suboptimal performance in downstream applications, especially that require high levels of detail, such as object detection, scene segmentation, or tasks in medical imaging [14, 29, 30, 37, 49, 50, 57, 60]. As a result, leveraging CLIP for fine-granular tasks frequently necessitates task-specific adaptations to bridge the gap between its generalized feature extraction and the precision required for specialized applications.
+
+CLIP-based Anomaly Detection There have been several efforts to leverage CLIP for AD tasks. One of the pioneering approaches, WinCLIP [19], proposes a method for extracting and aggregating visual features from multiple levels to align with text features, demonstrating the potential of CLIP in this context. Subsequent research investigates various adaptation methods to bridge the gap between natural domains and the AD domain, resulting in performance improvements. For instance, [7, 8, 18] focus on refining visual features by employing adapters to enhance patch-level visual representations. However, these approaches often rely on text embeddings from the original CLIP model as soft supervision and overlook a critical limitation of CLIP in AD: itsunclearness in distinguishing between anomalous and normal semantics, particularly within the text encoder, resulting in suboptimal performance. Other works have employed prompt-learning-based methods[5, 6, 41, 59], introducing learnable embeddings into the text encoder to better represent abnormality. However, the class information in CLIP can be damaged, potentially degrading generalization, especially in data-limited and zero-shot settings.
+
+Different from previous methods, we are the first to investigate CLIP's inherent limitation in capturing anomaly-aware information, specifically in differentiating between normal and anomalous semantics in text prompts. Rather than relying solely on the original anomaly-unaware text embeddings or unaltered feature spaces, our method is able to refine the embeddings to actively incorporate anomaly-discriminative representations.
+
+# 3. Method
+
+# 3.1. Overview
+
+# 3.1.1. Problem Formulation
+
+Zero-shot AD models are trained to identify anomalous samples whose categories may be unseen in the training dataset. Specifically, the model is expected to learn
+
+![](images/1f4b294e7d4def9bcc526a78197fc3385e97f3cb55a77e48738270adecb8c5f1.jpg)
+
+![](images/b75f5d93de627136e49c895ecdf83d74a7eab7e2e9f221c69e97c6c8bbd33721.jpg)
+
+"This is a [ ] carpet."  
+
+<table><tr><td>Semantics</td><td>Similarity</td><td>Probabilityτ=0.01</td></tr><tr><td>broken</td><td>0.18</td><td>0.22</td></tr><tr><td>normal</td><td>0.19</td><td>0.78</td></tr></table>
+
+"This is a [ ] zipper."  
+
+<table><tr><td>Semantics</td><td>Similarity</td><td>Probabilityτ=0.01</td></tr><tr><td>broken</td><td>0.20</td><td>0.38</td></tr><tr><td>normal</td><td>0.21</td><td>0.62</td></tr></table>
+
+![](images/467ee38e87dd5ff7fa4576a42be09710e9d3a22d802523419eec73f0820be9d3.jpg)  
+Figure 2. (Top) Examples illustrating CLIP's Anomaly Unawareness. Despite the obvious anomalies present in the images, image features have higher similarities to normal descriptions, rather than anomaly descriptions, mistakenly. This problem is enlarged with a low temperature  $\tau$ . (Bottom) Text Feature Similarity Heatmap among Normal and Anomaly Descriptions: Original CLIP vs. After Text Adaptation. Red indicates high similarity. In original CLIP, normal features exhibit strong similarity with anomaly features, whereas text adaptation successfully separates them, clarifying the semantic distinctions between normal and anomaly descriptions.
+
+both normal and abnormal patterns that are shared across different classes given a training set  $\mathcal{D}_{train}$  with normal or anomalous samples, in order to be capable of performing AD tasks on a series of different test datasets  $\{\mathcal{D}_{test}^{1},\mathcal{D}_{test}^{2},\dots,\mathcal{D}_{test}^{n}\}$ , where each  $\mathcal{D}_{test}^{i}$  is distinct from  $\mathcal{D}_{train}$ . Image-level AD can be formally defined as a binary classification problem, where the model aims to classify samples  $x\in \mathcal{D}$  as either normal ( $y = 0$ ) or anomalous ( $y = 1$ ). Anomaly segmentation extends this concept to pixel-level with mask  $S$ , aiming to identify anomalous regions by highlighting pixels associated with anomalies.
+
+# 3.1.2. Current Challenges
+
+Anomaly Unawareness in CLIP: The CLIP-based AD method classifies visual features as "anomalies" if they exhibit greater similarities to anomaly prompt embeddings than to normal prompt embeddings, thus requiring well-defined boundaries between these two kinds of prompts. However, in real applications, CLIP's text embeddings often lack the clear separability needed to reliably distinguish between normal and anomaly classes.
+
+We observe that, despite the visible defects in example images from the MVTec-AD [2], their features exhibit higher cosine similarity with "normal" prompts than with correct "anomaly" descriptions (see Fig. 2 (top)), indicating CLIP's inaccurate semantic understanding. Without adap
+
+![](images/85d153d5a9c1ba27ae30deddc2e6b7643a16c6f2889c919f03a81988d171c738.jpg)  
+Figure 3. t-SNE Visualization of Text Features from Original CLIP vs. AA-CLIP. Each point represents a text feature encoded from a prompt. Original CLIP's normal and anomaly text features are intertwined, while our method effectively disentangles them. This disentanglement is generalizable to novel classes, validating the anomaly-awareness of our model.
+
+tation, there persists a high similarity between the normal and abnormal text embeddings of a single class, as shown in Fig. 2 (bottom), suggesting a potential entanglement of normal and anomaly semantics within text space. We term this limitation Anomaly Unawareness and attribute it to the training process of CLIP: it is primarily trained on general, non-anomalous datasets and lacks specific guidance on defect detection. Consequently, it is challenging to rely on original CLIP embeddings to detect subtle or context-specific anomalies.
+
+This issue remains evident across different categories in our t-SNE analysis: as shown in Fig. 3 (top), only subtle separations are observed within an object cluster, where text embeddings for both normal and abnormal semantics are intermixed. This entangled pattern may potentially lead to anomaly-unaware text-image alignment, which reinforces the necessity to adapt CLIP's to enhance its ability of anomaly-awareness.
+
+**Embedding Adaptation Dilemma:** Discussion above renders the adaptation of CLIP essential for effective AD. However, since CLIP's embeddings are already optimized through extensive pretraining, it could be susceptible to overfitting to new dataset during adaptation. Overfitting convergence leads to minimized intra-class distinctions in the training data, often at the expense of the feature separability for effective generalization to unseen data.
+
+To address this, a carefully controlled refinement is crucial to preserve CLIP's generalization capabilities while enhancing its sensitivity to anomalies.
+
+# 3.1.3. Overview of Our Solution
+
+Motivated by Sec. 3.1.2, we propose Anomaly-Aware CLIP (AA-CLIP) with improved anomaly awareness. As shown in Fig. 4, AA-CLIP is trained through a two-stage training strategy that sequentially adapts the semantic-rich text space and detail-focused visual space, with original CLIP parameters remaining frozen. In the first stage (see Fig. 4 (Top)), we incorporate Residual Adapters into the shallow layers of the text encoder, and the visual features from the fixed image encoder serve as a stable reference for optimization. A Disentangle Loss is proposed to enforce effective discrimination by ensuring independence between normal and anomaly embeddings. In the second stage, we integrate Residual Adapters into the shallow layers of the visual encoder to align patch-level features with the fixed, specially adapted texture features from the fixed text encoder (see in Fig. 4 (Bottom)). Ultimately, our AA-CLIP succeeds in equipping CLIP with anomaly awareness across seen and unseen classes, as shown in Fig. 3 (bottom).
+
+# 3.2. AA-CLIP with Two-Stage Adaptation Strategy
+
+# 3.2.1. Residual Adapter
+
+To preserve CLIP's pre-trained knowledge while enabling targeted adaptation, we introduce lightweight Residual Adapters in the shallow layers (up to layer  $K$ ) of both text and vision encoders.
+
+The output feature  $x^{i} \in \mathbb{R}^{N \times d}$  of CLIP's  $i$ -th ( $i \leq K$ ) transformer layer is fed into the  $i$ -th adapter, outputting adapted feature  $x_{residual}^{i}$ , as shown in Eq. (1),
+
+$$
+x _ {\text {r e s i d u a l}} ^ {i} = \operatorname {N o r m} \left(\operatorname {A c t} \left(W ^ {i} x ^ {i}\right)\right), \tag {1}
+$$
+
+where  $W^{i} \in \mathbb{R}^{d \times d}$  is the trainable linear weight of  $i$ -th adapter,  $Act(\cdot)$  is an activation function, and  $Norm(\cdot)$  is a normalizing function. The original feature  $x^{i}$  and the enhanced feature  $x_{residual}^{i}$  are fused in a weighted manner, generating  $x_{enhanced}^{i}$ , the input to the next transformer layer, as shown in Eq. (2),
+
+$$
+x _ {\text {e n h a n c e d}} ^ {i} = \lambda x _ {\text {r e s i d u a l}} ^ {i} + (1 - \lambda) x ^ {i}, \tag {2}
+$$
+
+where  $\lambda$  is a hyper-parameter to control the residual ratio, adjusting the fusing degree of AD-specific knowledge for preserving the original CLIP's generalization ability and improved performance.
+
+# 3.2.2. Two-Stage Training Strategy
+
+Disentangling Anomaly-Aware Text Anchors: In the first stage, our objective is to learn anomaly-discriminative text anchors by adapting the text encoder while keeping the
+
+![](images/a4a610b1167236135a85d221e41e21c181b00e2ab31d2c098f0a54df24da772a.jpg)  
+Stage1: Disentangling Anomaly-Aware Text Anchors
+
+![](images/b1ece9f7bcb30903f6b874d348410a737150e0d213c2bd10ec011036cf8438ca.jpg)  
+Stage2: Aligning Patch Features According to Text Anchors  
+Figure 4. The Two-Stage Training Pipeline of Anomaly-Aware CLIP. In the first stage, the text encoder of AA-CLIP is trained to identify anomaly-related semantics, helped by a disentangle loss. In the second stage, patch features are aligned with these text anchors. Both stages are achieved by the integration of Residual Adapters into the shallow layers of CLIP's backbone. This controlled adaptation enables CLIP to effectively distinguish anomalies, which forms our Anomaly-Aware CLIP.
+
+image encoder fixed. We incorporate Residual Adapters into the first  $K_{T}$  layers of the CLIP text encoder, as illustrated in Fig. 4 (Top), and set the final projector in the text encoder to be learnable to facilitate improved alignment.
+
+Using prompts designed to encapsulate both normal and anomalous semantics (as detailed in Appendix), text encoder generates corresponding high-level embeddings. The average embeddings of the normal and anomaly prompts serve as our initial text anchors, denoted as  $T_{N}$  and  $T_{A} \in \mathbb{R}^{d}$ , respectively. These anchors are refined by being aligned with visual features extracted from an enhanced CLIP visual encoder, as [28, 59]. Alignment is conducted at both image and patch levels to incorporate both global and local semantics. By calculating the cosine similarity between these anchors and the image features  $V_{image} \in \mathbb{R}^{d}$  or patch features  $V_{patch} \in \mathbb{R}^{N \times d}$ , as shown in Eq. (3),
+
+$$
+p _ {c l s} = \operatorname {C o s S i m} \left(V _ {\text {i m a g e}}, \left[ T _ {N}, T _ {A} \right]\right), \tag {3}
+$$
+
+$$
+p _ {s e g} ^ {o} = \operatorname {C o s S i m} (V _ {p a t c h}, [ T _ {N}, T _ {A} ]),
+$$
+
+where  $[\cdot, \cdot]$  means concatenate operation, we obtain the classification prediction  $p_{cls} \in \mathbb{R}^2$  and the segmentation prediction  $p_{seg}^{o} \in \mathbb{R}^{N \times 2}$ . The segmentation prediction  $p_{seg}^{o}$  is then reshaped and upsampled to  $p_{seg} \in \mathbb{R}^{H \times W \times 2}$  to align
+
+with the height  $H$  and width  $W$  of segmentation mask  $S$ . Following previous works [6, 7, 18, 59], we compute the classification loss  $\mathcal{L}_{cls}$  and segmentation loss  $\mathcal{L}_{seg}$  to optimize parameters, as specified in Eq. (4). Specifically, the classification loss is a binary cross-entropy that compares classification predictions with ground-truth labels  $y$ , and the segmentation loss is a combination of dice loss and focal loss applied to segmentation predictions and the anomaly segmentation mask  $S$ .
+
+$$
+\mathcal {L} _ {c l s} = \operatorname {B C E} (p _ {c l s}, y),
+$$
+
+$$
+\mathcal {L} _ {\text {s e g}} = \operatorname {D i c e} \left(p _ {\text {s e g}}, S\right) + \operatorname {F o c a l} \left(p _ {\text {s e g}}, S\right), \tag {4}
+$$
+
+$$
+\mathcal {L} _ {\text {a l i g n}} = \mathcal {L} _ {\text {c l s}} + \mathcal {L} _ {\text {s e g}}.
+$$
+
+To enhance the separation between normal and anomaly text embeddings, we introduce a Disentangle Loss encouraging orthogonality between  $T_{N}$  and  $T_{A}$  to minimize correlation, as in Eq. (5):
+
+$$
+\mathcal {L} _ {\text {d i s}} = | <   T _ {N}, T _ {A} > | ^ {2}. \tag {5}
+$$
+
+The Disentangle Loss  $\mathcal{L}_{dis}$  is incorporated into the alignment loss  $\mathcal{L}_{\text {align }}$  as a regularization term, weighted by a factor  $\gamma$ , which forms the total loss, as in Eq. (6):
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {a l i g n}} + \gamma \mathcal {L} _ {\text {d i s}}. \tag {6}
+$$
+
+In this stage, the distinction between normal and anomaly semantics is embedded into CLIP's text encoder while its original object-recognition capability is preserved. Figure 3 indicates that this ability of anomaly-awareness is robust and generalizable to novel classes.
+
+Aligning Patch Features According to Text Anchors: Anomaly-aware semantic anchors can facilitate the adaptation of patch features, thereby improving the effectiveness and generalizability of anomaly localization. To achieve alignment between patch features and anchors from the previous stage, we introduce trainable Residual Adapters within the initial  $K_{I}$  layers of the CLIP visual encoder.
+
+Features with multi-granularities are utilized to enhance segmentation [7, 19, 59]. Specifically, as shown in Fig. 4 (bottom), the intermediate output feature  $F^i$  are extracted from four distinct granularities. These multi-granularity features are then projected to align with the channel of text anchors via a trainable projector  $Proj_i(\cdot)$ , yielding  $V_{patch}^i$  at four distinct levels of granularity. The aggregated output  $V_{patch}$  is computed by summing individual  $V_{patch}^i$  outputs, as in Eq. (7):
+
+$$
+\begin{array}{l} V _ {p a t c h} ^ {i} = \operatorname {P r o j} _ {i} \left(F ^ {i}\right), i \in \{1, 2, 3, 4 \} \\ V _ {p a t c h} = \sum_ {i = 1} ^ {4} V _ {p a t c h} ^ {i}. \tag {7} \\ \end{array}
+$$
+
+The cosine similarity scores between the aggregated  $V_{patch}$  and the text anchors are calculated to generate patch-level predictions as Eq. (3), resulting in the prediction maps.
+
+During training, alignment is guided by the loss function defined in Eq. (4), facilitating both global and local alignment. During inference, anomaly prediction maps and corresponding anomaly scores are derived by comparing the similarity scores of visual features against normal and anomaly text embeddings.
+
+# 4. Experiments
+
+# 4.1. Experiment Setups
+
+Datasets We evaluate our model on 11 widely used benchmarks, as previous AD works [6, 7, 18, 19, 59], with distinct foreground objects spanning a variety of modalities, including photography, endoscopy, CT, MRI, and OCT. For the industrial domain, we use MVtec AD [2], VisA [62], BTAD [34] and MPDD [20]. For medical domain, we use brain MRI, liver CT and retina OCT from BMAD [1], and four different colon polyp detection datasets with different views (CVC-ClinicDB [4], CVC-ColonDB [3], Kvasir-SEG [40] and CVC-300 [47]). Each dataset has both image-level labels and pixel-level masks for evaluation.
+
+We train our model on a real-world industrial AD dataset - VisA [62] - in which objects are different from other datasets. Results of VisA are obtained using MVtec-AD as
+
+the training dataset. To demonstrate adaptation efficiency, we conduct training under various data levels: 2-shot per class, 16-shot per class, 64-shot per class, and full-shot. The corresponding number of samples are randomly selected from each class, while maintaining a consistent 1:1 ratio between normal and anomaly samples.
+
+Metrics Following [6, 7, 10, 11, 18, 19, 43, 55], we use the Area Under the Receiver Operating Characteristic Curve (AUROC) as the metric. We compute AUROC at both the image and pixel levels to comprehensively assess the model's effectiveness in detecting and localizing anomalies. Implementation Details Following [6, 7, 41, 59], we use OpenCLIP with the ViT-L/14 architecture as the backbone, and input images are resized to  $518 \times 518$ . All parameters of CLIP remain frozen. We set  $\lambda$  to 0.1,  $K_{T}$  to 3,  $K_{I}$  to 6, and  $\gamma$  to 0.1. For multi-level feature extraction, we utilize outputs from the 6-th, 12-th, 18-th, and 24-th layers of the visual encoder to compose the overall output. For the first stage, we train the model for 5 epochs with a learning rate of  $1 \times 10^{-5}$ . For the second stage, we continue training for 20 epochs, adjusting the learning rate to  $5 \times 10^{-4}$ . Parameters are updated by Adam optimizers. All experiments are conducted on a single NVIDIA GeForce RTX 3090 GPU. More details are available in Appendix.
+
+# 4.2. Comparison with SOTA Methods
+
+We compare our method against CLIP and several recent SOTA models. Among them, WinCLIP [19], VAND [7] and MVFA-AD [18] use original CLIP text encoder, and AnomalyCLIP [59] and AdaCLIP [6] incorporate learnable prompts. To ensure a fair comparison, we re-train models that are originally trained on different datasets to match the dataset settings of other approaches (detailed in Appendix).
+
+Quantitative results are presented in Tab. 1 and Tab. 2. Although adapting only the patch feature with original text embeddings has made progress in AD, the superior performance of AA-CLIP highlights its effective disentanglement of anomaly-discriminative semantics, leading to further progress. Notably, even in data-limited situations, our method consistently demonstrates top performance. At the pixel level, with only 2 shots per class used for training, our method achieves improved average zero-shot performance compared to previous methods. With the full dataset, we set a new pixel-level SOTA with an AUROC of  $93.4\%$ . At the image level, our method is competitive with just 2 shots for training and establishes a new SOTA of  $83.1\%$  with 64 shots per class.
+
+Unlike previous methods, our approach does not rely heavily on data resources to achieve top-tier performance. Comparison under different levels of data available, as shown in Fig. 5, reveals that our approach consistently outperforms other methods in general. Even with limited data, our model reaches competitive results, while other methods
+
+<table><tr><td rowspan="3">Domain</td><td rowspan="2">Dataset</td><td>CLIP*</td><td>WinCLIP*</td><td>VAND*</td><td>MVFA-AD</td><td>AnomalyCLIP*</td><td>AdaCLIP</td><td colspan="4">Ours</td></tr><tr><td>OpenCLIP</td><td>CVPR 2023</td><td>CVPRw 2023</td><td>CVPR 2024</td><td>ICLR2024</td><td>ECCV2024</td><td colspan="4">-</td></tr><tr><td>Available training shots</td><td>-</td><td>-</td><td>full</td><td>full</td><td>full</td><td>full</td><td>2</td><td>16</td><td>64</td><td>full</td></tr><tr><td rowspan="4">Industrial</td><td>BTAD</td><td>30.6</td><td>32.8</td><td>91.1</td><td>90.1</td><td>93.3</td><td>90.8</td><td>92.8</td><td>94.4</td><td>96.5</td><td>97.0</td></tr><tr><td>MPDD</td><td>62.1</td><td>95.2</td><td>94.9</td><td>94.5</td><td>96.2</td><td>96.6</td><td>96.3</td><td>96.5</td><td>96.3</td><td>96.7</td></tr><tr><td>MVTec-AD</td><td>38.4</td><td>85.1</td><td>87.6</td><td>84.9</td><td>91.1</td><td>89.9</td><td>91.0</td><td>91.2</td><td>91.6</td><td>91.9</td></tr><tr><td>VisA</td><td>46.6</td><td>79.6</td><td>94.2</td><td>93.4</td><td>95.4</td><td>95.5</td><td>93.4</td><td>93.8</td><td>94.0</td><td>95.5</td></tr><tr><td rowspan="7">Medical</td><td>Brain MRI</td><td>68.3</td><td>86.0</td><td>94.5</td><td>95.6</td><td>96.2</td><td>93.9</td><td>96.3</td><td>96.4</td><td>96.5</td><td>95.5</td></tr><tr><td>Liver CT</td><td>90.5</td><td>96.2</td><td>95.6</td><td>96.8</td><td>93.9</td><td>94.5</td><td>97.3</td><td>97.7</td><td>97.7</td><td>97.8</td></tr><tr><td>Retina OCT</td><td>21.3</td><td>80.6</td><td>88.5</td><td>90.9</td><td>92.6</td><td>88.5</td><td>94.2</td><td>95.1</td><td>94.4</td><td>95.5</td></tr><tr><td>ColonDB</td><td>49.5</td><td>51.2</td><td>78.2</td><td>78.4</td><td>82.9</td><td>80.0</td><td>83.9</td><td>83.5</td><td>84.7</td><td>84.0</td></tr><tr><td>ClinicDB</td><td>47.5</td><td>70.3</td><td>85.1</td><td>83.9</td><td>85.0</td><td>85.9</td><td>89.2</td><td>87.6</td><td>87.8</td><td>89.9</td></tr><tr><td>Kvasir</td><td>44.6</td><td>69.7</td><td>80.3</td><td>81.9</td><td>81.9</td><td>86.4</td><td>82.1</td><td>84.6</td><td>85.2</td><td>87.2</td></tr><tr><td>CVC-300</td><td>49.9</td><td>-</td><td>92.8</td><td>82.6</td><td>95.4</td><td>92.9</td><td>96.0</td><td>97.4</td><td>96.0</td><td>96.4</td></tr><tr><td></td><td>Average</td><td>49.9</td><td>74.7</td><td>89.3</td><td>88.5</td><td>91.3</td><td>90.4</td><td>92.0</td><td>92.6</td><td>92.8</td><td>93.4</td></tr></table>
+
+Table 1. Pixel-level AUROC of zero-shot AD methods in Industrial and Medical domains. Method sources and the number of shots used for training are noted. Results of methods with * are copied from the papers or inferred from official weight. Best results are highlighted as first, second and third.  
+
+<table><tr><td rowspan="3">Domain</td><td rowspan="2">Dataset</td><td>CLIP&amp;VAND*</td><td>WinCLIP*</td><td>MVFA-AD</td><td>AnomalyCLIP*</td><td>AdaCLIP</td><td colspan="4">Ours</td></tr><tr><td>OpenCLIP</td><td>CVPR 2023</td><td>CVPR 2024</td><td>ICLR2024</td><td>ECCV2024</td><td colspan="4">-</td></tr><tr><td>Available training shots</td><td>-</td><td>-</td><td>full</td><td>full</td><td>full</td><td>2</td><td>16</td><td>64</td><td>full</td></tr><tr><td rowspan="4">Industrial</td><td>BTAD</td><td>73.6</td><td>68.2</td><td>94.3</td><td>85.3</td><td>90.9</td><td>88.0</td><td>90.9</td><td>94.7</td><td>94.8</td></tr><tr><td>MPDD</td><td>73.0</td><td>63.6</td><td>70.9</td><td>73.7</td><td>72.1</td><td>63.6</td><td>78.3</td><td>75.7</td><td>75.1</td></tr><tr><td>MVTec-AD</td><td>86.1</td><td>91.8</td><td>86.6</td><td>90.9</td><td>90.0</td><td>85.9</td><td>89.7</td><td>92.0</td><td>90.5</td></tr><tr><td>VisA</td><td>66.4</td><td>78.0</td><td>76.5</td><td>82.1</td><td>84.3</td><td>78.4</td><td>84.0</td><td>84.1</td><td>84.6</td></tr><tr><td rowspan="3">Medical</td><td>Brain MRI</td><td>58.8</td><td>66.5</td><td>70.9</td><td>83.3</td><td>80.2</td><td>84.3</td><td>80.4</td><td>83.4</td><td>80.2</td></tr><tr><td>Liver CT</td><td>54.7</td><td>64.2</td><td>63.0</td><td>61.6</td><td>64.2</td><td>69.4</td><td>68.1</td><td>69.2</td><td>69.7</td></tr><tr><td>Retina OCT</td><td>65.6</td><td>42.5</td><td>77.3</td><td>75.7</td><td>82.7</td><td>77.4</td><td>81.0</td><td>82.9</td><td>82.7</td></tr><tr><td colspan="2">Average</td><td>68.3</td><td>67.8</td><td>77.1</td><td>78.4</td><td>80.6</td><td>78.1</td><td>81.8</td><td>83.1</td><td>82.5</td></tr></table>
+
+display signs of underfitting. As data increases, our method maintains its lead, establishing a new SOTA at both pixel and image levels.
+
+# 4.3. Visualization
+
+To illustrate the alignment intuitively, we present visualization examples in Fig. 6 with original configuration for previous works. Although previous methods with can detect anomalous regions, our AA-CLIP demonstrates fewer false-negative predictions in both industrial and medical domains, accurately highlighting the correct anomaly regions.
+
+# 4.4. Ablations Analysis
+
+We conduct thorough ablation experiments of our refinement of both visual and text space, as shown in Tab. 3 and Fig. 7. The second row in Tab. 3, which mirrors the structure of VAND [7], serves as our baseline.
+
+Image Space: As shown in Tab. 3 line “2,” inserting the vallina linear adapter into transformer layers results in a significant decline in zero-shot performance, indicating the
+
+Table 2. Image-level AUROC of zero-shot AD methods in Industrial and Medical domains. Method sources and the number of shots used for training are noted. Results of methods with * are copied from the papers or inferred from official weight. Best results are highlighted as first, second and third.  
+
+<table><tr><td rowspan="2" colspan="2">Method</td><td colspan="2">Avg. AUROC</td></tr><tr><td>Pixel-Level</td><td>Image-Level</td></tr><tr><td colspan="2">CLIP</td><td>50.3</td><td>69.3</td></tr><tr><td rowspan="3">Image</td><td>1. + Linear Proj. (VAND [7])</td><td>88.9</td><td>69.3</td></tr><tr><td>2. + Adapter</td><td>48.9(-40.0)</td><td>53.4(-15.9)</td></tr><tr><td>3. + Residual Adapter</td><td>91.3(+2.4)</td><td>80.7(+11.4)</td></tr><tr><td rowspan="2">Text</td><td>4. + Residual Adapter</td><td>92.1(+3.2)</td><td>82.6(+13.3)</td></tr><tr><td>5. + Disentangle Loss</td><td>92.7(+3.8)</td><td>83.3(+14.0)</td></tr></table>
+
+Table 3. Ablation Study of Our Training Strategy with VisA-Trained 64-Shot Setup. Our contributions are bold. While VAND uses linear projectors to improve AD performance, incorporating Residual Adapters further refines patch feature adaptation. Moreover, integrating our Disentangle Loss yields the best overall results.
+
+damage of the original generalization ability of CLIP. Incorporating our Residual Adapters mitigates this issue (shown in line "3"). enhancing performance while preserving original information stored in CLIP.
+
+Text Space: The last two rows in Tab. 3 highlight the impact of our approach in equipping CLIP's encoder with
+
+![](images/7ed1b930e4e1be716f6dffd2599518a4b01f6650e935501bb949bd4c8306b1b1.jpg)  
+Figure 5. Average Results (Top) and Results on BTAD (Bottom) of Different methods Trained on 2-, 16-, 64-shot per Class and Full Data of VisA. Our method shows high fitting efficiency, achieving strong results across all data scales.
+
+![](images/4bd703a8e390087c44ea087922519b276bf75f577a1ad93c32da10a282ef7e44.jpg)
+
+![](images/54bc6d0e000fbbc5adb9f62b15ea2babb5449548126f172d62748e47bc6428f7.jpg)  
+Figure 6. Visualization of Anomaly Localization Results of Original CLIP [42], AnomalyCLIP [59], VAND [7] and our AA-CLIP. Compared to previous methods, AA-CLIP demonstrates more reliable prediction capabilities in localizing anomaly.
+
+anomaly-aware semantics. Line "4." validates that, with AA-CLIP, the model's ability to discriminate anomalies further improves, as the AA-CLIP's text encoder provides a more precise semantic foundation. Adding Disentangle Loss leads to an additional improvement (shown in Line "5"), especially at image-level, validating the necessity of independence between normal and anomaly anchors. These results underscore the crucial role of text space refinement in improved anomaly localization and classification.
+
+Two-Stage Training: To validate the necessity of two-stage training, we adapt both text and image encoders together within one stage (also adopted by AdaCLIP). As shown
+
+![](images/b940ce809bb20f102d5ab0c763d469f6ba1df9bd728863b2e2e5aa8edcb03ef5.jpg)  
+Figure 7. Visualization of Text Space from One-Stage Training and from AdaCLIP. During one-stage training, class information collapses easily, leading to damaged zero-shot performance.
+
+in Fig. 7, one-stage model can easily exaggerate anomaly semantics and forget class information embedded in CLIP, damaging the model's generalization ability. The two-stage training strategy allows controlled adaptation, preserving CLIP's class-relevant knowledge in one end while adapting the other, as shown in Fig. 3.
+
+# 5. Conclusion and Discussion
+
+To our knowledge, this is the first work to explicitly analyze the intrinsic Anomaly Unawareness problem in CLIP. To tackle this issue, we propose a simple yet effective two-stage training strategy to embed anomaly-aware information into CLIP, enabling clear disentanglement of anomaly representations across both seen and novel classes. By leveraging residual adapters, our method preserves CLIP's strong generalization ability, achieving outstanding zero-shot performance across multiple datasets.
+
+Our adapted AA-CLIP, developed through this two-stage adaptation strategy, reveals the potential of refining CLIP's feature space for improved performance in downstream applications. Beyond addressing anomaly unawareness, our work also provides a potential foundation for tackling other "unawareness" issues within CLIP. These may include limitations in context-awareness or specificity to domain-relevant nuances, suggesting further applications of our method in expanding CLIP's adaptability across diverse tasks. Additionally, we observe signs of overfitting with full-shot training, suggesting potential saturation during CLIP adaptation and warranting further investigation.
+
+# Acknowledgement
+
+This work is supported by Natural Science Foundation of China under Grant 62271465, Suzhou Basic Research Program under Grant SYG202338, Open Fund Project of Guangdong Academy of Medical Sciences, China (No. YKY-KF202206), and Jiangsu Province Science Foundation for Youths (NO. BK20240464).
+
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+# ABBSPO: Adaptive Bounding Box Scaling and Symmetric Prior based Orientation Prediction for Detecting Aerial Image Objects
+
+Woojin Lee $^{1*}$  Hyugjae Chang $^{1*}$  Jaeho Moon $^{1}$  Jaehyup Lee $^{2\dagger}$  Munchurl Kim $^{1\dagger}$ $^{1}$ KAIST  ${}^{2}$ KNU
+
+{woojin412, hmnc97, jaeho.moon, mkimee}@kaist.ac.kr jaehyuplee@knu.ac.kr
+
+https://kaist-viclab.github.io/ABBSPO_site/
+
+![](images/568859ed62ff0b20ad4e6ee353770fe3878e44cbdbe8d43e11f475ee89f78213.jpg)  
+① GT RBox ② GT C-HBox
+
+![](images/b27b775cfa0792a81a90726212506fafdc20232a590b12f4e10a34d0a8bb840b.jpg)
+
+![](images/4036c351f70e6be817546f6ab541a1e7b674cd0d755dd3972a0e99308263a526.jpg)  
+(a) Two types of GT HBox  
+(b) Visual comparison of HBox-supervised oriented detectors  
+Figure 1. Performance comparison of HBox-supervised orientated detectors. (a) Top: A coarse horizontal bounding box (C-HBox)  $(②)$  and its corresponding rotated bounding box (RBox)  $(①)$ . Bottom: A tight horizontal bounding box (T-HBox)( $(2)$ ) and its corresponding RBox  $(①)$ . (b) Our ABBSPO is capable of accurately detecting both orientations and scales for GT C-HBoxes and T-HBoxes. (c) Average Precision  $\left(\mathrm{AP}_{50}\right)$  for H2RBox [42], H2RBox-v2 [48], and our ABBSPO.  $3-\mathrm{AP}_{50}$  represents the mean  $\mathrm{AP}_{50}$  for three complex shaped objects: (i) DIOR: 'airplane', 'expressway service area', and 'overpass' and (ii) DOTA: 'plane', 'swimming pool', and 'helicopter'.
+
+![](images/abbe6ce2f4ccfae50e61911adbfc36c43a0599bc320175b91a448662945033d5.jpg)
+
+![](images/d935d857a5b65cffbee17d0414115fdc61d65805e5ef4c398351ff5540f95a21.jpg)
+
+![](images/8bd69b0bee5866f4cba10b95e82ac4c8cc5b57f2cd8ba8783c90a33616727935.jpg)
+
+![](images/e955c6c9f48296b82376f41da38d1df88096b41e872664228316cfcd675731db.jpg)
+
+![](images/949e5f4d898a521f3773f2cdc29482ebb42f4bc6bc2189ba275e0d71a3b33682.jpg)
+
+![](images/a5b098d46dbb0f780bcd7fc46372d3c5816887a0ef6a2fc8e0c422f150b54626.jpg)  
+H2RBox H2RBox-v2 ABBSPO) Performance overview 3-AP50 AP50
+
+# Abstract
+
+Weakly supervised Oriented Object Detection (WS-OOD) has gained attention as a cost-effective alternative to fully supervised methods, providing efficiency and high accuracy. Among weakly supervised approaches, horizontal bounding box (HBox) supervised OOD stands out for its ability to directly leverage existing HBox annotations while achieving the highest accuracy under weak supervision settings. This paper introduces adaptive bounding box scaling and symmetry-prior-based orientation prediction, called ABBSPO that is a framework for WS-OOD. Our ABB-
+
+SPO addresses the limitations of previous HBox-supervised OOD methods, which compare ground truth (GT) HBoxes directly with predicted RBoxes' minimum circumscribed rectangles, often leading to inaccuracies. To overcome this, we propose: (i) Adaptive Bounding Box Scaling (ABBS) that appropriately scales the GT HBoxes to optimize for the size of each predicted RBox, ensuring more accurate prediction for RBoxes' scales; and (ii) a Symmetric Prior Angle (SPA) loss that uses the inherent symmetry of aerial objects for self-supervised learning, addressing the issue in previous methods where learning fails if they consistently make incorrect predictions for all three augmented views (original, rotated, and flipped). Extensive experimental results demonstrate that our ABBsPO achieves state-of-the-art results, outperforming existing methods.
+
+# 1. Introduction
+
+Object detection often leverages supervised learning with ground truth horizontal bounding box labels (GT HBoxes) to locate the objects of interest. However, the usage of GT HBoxes limits the precise localization of the objects with their orientations and tight surrounding boundaries, especially for objects such as airplanes and ships of various orientations in aerial images. To handle object detection as an oriented object detection problem, more precise rotated bounding box labels (GT RBoxes) are required, which is very costly to generate [49]. So, to mitigate this challenge, previous methods [17, 23, 42, 47-49] have explored weakly supervised oriented object detection (OOD) that utilizes less expensive forms of annotations, such as image-level, point and HBox annotations. Among these, the use of HBoxes is the most popular due to their widespread availability in existing public datasets [4, 9, 12, 21, 30, 31] to predict the RBoxes for objects of interest. So, this approach can detour the costly process of generating GT RBoxes.
+
+The previous weakly supervised (WS) learning of OOD [22, 27, 42, 48] utilizes GT HBoxes in the forms of coarse HBoxes, called GT C-HBoxes, as supervision to compare with the HBoxes derived as the minimum circumscribed rectangles from the predicted RBoxes by their OOD models. As shown in the upper figure of Fig. 1-(a), the GT C-HBoxes are defined as coarse horizontal bounding boxes that loosely encompass the boundaries of objects (not tightly bounded). The GT HBoxes of the DOTA [29] dataset are in the forms of C-HBoxes which are derived as the minimum circumscribed horizontal bounding boxes of their GT RBoxes. However, when the previous OOD methods [42, 48] are supervised with the other GT HBoxes that are in the form of tight HBoxes, called GT T-HBoxes (e.g. DIOR dataset [13]), as shown in the bottom figure of Fig. 1-(a), we found that their performances are significantly degraded because GT T-HBoxes tend to have different scales, compared to those of GT C-HBoxes (see Fig. 1-(c)). As shown in Fig. 1-(b), this causes the previous methods to predict either RBoxes with accurate orientations but inaccurate scales smaller than the sizes of their corresponding objects, or the RBoxes with inaccurate (close to horizontal) orientations but somewhat accurate scales (almost the same as HBoxes).
+
+To overcome the above limitations of the previous WS-OOD methods, we propose an adaptive bounding box scaling and symmetry-prior-based orientation prediction, called as ABBSPO, as a WS-OOD framework that can be effectively trained with either GT C-HBoxes or GT T-Hboxes for aerial images. For this, (i) a novel Adaptive Bounding Box Scaling (ABBS) module is designed to have the flexibility of adjusting the GT HBoxes for each object into random sizes and then selecting the optimal scaled GT HBoxes that allow it to encompass the predicted RBoxes. Note that
+
+the previous methods are not possible to have such flexibility for the adjustment of GT HBoxes; (ii) An angle learning module is proposed in a self-supervised manner that utilizes the symmetric priors of the objects that open appear in top-down views of aerial images. As shown in Figs 1-(b) and (c), Our proposed method predicts accurate orientation and surrounding boxes of objects for both cases of using GT C-HBoxes and GT T-HBoxes, outperforming the previous methods in angle accuracy and localization in terms of average precision (AP). Our contributions are summarized as:
+
+- To the best of our knowledge, our work is the first to address the limitations of previous weakly supervised OOD learning methods with T-HBoxes as GT. To overcome this, we propose a novel weakly supervised OOD method that can be effectively trained with T-HBoxes or C-HBoxes that can be cheaply annotated as GT;  
+- The adaptive bounding box scaling (ABBS) module is proposed to flexibly adjust the HBox (GT) for each object toward an appropriately scaled HBox. This allows part of the predicted RBoxes to place outside the T-HBox (GT), yielding precise RBox prediction;  
+- A symmetric prior angle (SPA) loss is presented to enhance the orientation prediction accuracy by leveraging the symmetric priors of the objects in aerial images;  
+- Our method significantly outperforms the state-of-the-art OOD methods using weakly supervised learning with HBoxes (GT) for aerial datasets.
+
+# 2. Related Work
+
+# 2.1. RBox-supervised Oriented Object Detection
+
+Oriented Object Detection (OOD) has gained significant attention, leading to extensive research in RBox-supervised methods (using GT RBoxes) such as Rotated RetinaNet [20], Rotated FCOS [24],  $\mathrm{R}^3\mathrm{Det}$  [37], ROI Transformer [6], ReDet [8], and  $\mathrm{S}^2\mathrm{A}$ -Net [7]. Rotated FCOS [24] improves OOD performance by introducing center-ness, which assigns weights to samples based on their proposal locations, thereby emphasizing well-positioned proposals. OrientedRepPoints methods [3, 14, 43], in contrast, utilize flexible receptive fields to extract key object points. However, a common challenge in RBox-supervised OOD methods is the boundary discontinuity problem that arises from the definition and prediction of angle parameters  $(\theta)$  [33, 34]. To address this, several methods modified the ways of defining the RBox representations, such as Gaussian distributions [25, 26, 35, 36, 38-41], thereby avoiding straightforward regression of angle parameters. On the other hand, in weakly supervised learning, the boundary discontinuity issue does not arise thanks to the absence of direct RBox supervision, allowing for more stable angle predictions without the need for complex mitigation strategies.
+
+![](images/9058721b81e8835b11068c548c9030cde9f80c85472d688e79cb7a9fc205dd43.jpg)
+
+![](images/3b91cfd3d439130d68778ce5b060bd3e80c614824624b643e61de1a383877e2f.jpg)  
+Figure 2. Overall pipeline of our ABBsPO framework. Our ABBsPO leverages weakly supervised learning from HBox annotations to accurately predict RBoxes. The framework incorporates the Orientation Learning Branch (OLB) for precise angle estimation, using the Symmetric Prior Angle (SPA) loss, and the Scale Learning Branch (SLB) for optimal scale adjustment via the Adaptive Bounding Box Scaling (ABBS) module. The framework supports both C-HBox and T-HBox ground truths, ensuring robust and accurate predictions.
+
+![](images/55d9e3d1694b0495f9e982e4c5a131893a68faaf37d1a22e07983bd4262d8421.jpg)
+
+# 2.2. Weakly-supervised Orientd Object Detection
+
+Weakly supervised OOD methods learn to predict RBoxes without directly utilizing GT RBoxes. The approaches in this domain are primarily categorized based on the types of labels they employ: image-based [23], point-based [17, 47], and HBox-based [42, 48].
+
+Image-based supervision. WSODet [23], aims to generate pseudo-RBoxes without explicit localization supervision, thus encountering significant limitations when relying solely on image labels, especially for the scenes with numerous and diverse object types.
+
+Point-based supervision. By leveraging one representative point at the center location as a label for each object, point label-based methods offer the advantage of being cost-effective [1, 2, 11, 16, 19, 44]. PointOBB [17] estimates angles from geometric relationships across original, rotated, and flipped views, and determines scales by analyzing proposal distributions between original and scaled input images. PointOBB-v2 [18] improves single point supervision by refining pseudo-label generation, leading to enhanced efficiency and accuracy. Point2RBox [47] employed fundamental patterns as priors to guide the regression of RBoxes. Point-based methods are cost-effective and straightforward, but still struggle with limited supervision.
+
+HBox-based supervision. As annotating HBoxes is more
+
+straightforward than RBoxes, the HBox-supervised OOD has gained increasing attention in recent studies. H2RBox [42] utilized rotated views from the original view and provided self-supervision of object orientations without requiring the GT angles. H2RBox-v2 [48] expanded the use of geometric relationships between views by adding flipped views. These methods learn to predict RBoxes by converting minimum circumscribed HBoxes that encompass the predicted RBoxes to directly compare IoU with the GT HBoxes, thereby enabling HBox-supervised OOD. However, these methods only guarantee performance when trained with GT C-HBoxes that are derived from GT RBoxes. These methods struggle to learn precise OOD when being trained with GT T-HBoxes, because of the significant gap between the GT T-HBoxes and the HBoxes derived from predicted RBoxes. To address the issue, we propose an ABBS module to effectively handle both types of GTs (C-HBoxes and T-HBoxes).
+
+# 3. Method
+
+# 3.1. Overall Pipeline
+
+Weakly supervised OOD aims to predict RBoxes using less expensive annotations such as HBoxes. Existing methods such as H2RBox [42] and its improved version H2RBox-v2 [48] have laid the foundation for directly predicting RBoxes from HBoxes. Our proposed pipeline builds upon the H2RBox-v2 [48] framework to effectively enable weakly
+
+supervised OOD from either C-HBoxes or T-Boxes. Figure 2 depicts the conceptual framework of our weakly supervised OOD method. Given an input image  $\mathrm{I}_{\mathrm{ori}}$  and its rotated and flipped version  $\mathrm{I}_{\mathrm{rot}}$  and  $\mathrm{I}_{\mathrm{flp}}$ , our proposed pipeline obtains the RBox for each input view ( $\mathrm{I}_{\mathrm{ori}}$ ,  $\mathrm{I}_{\mathrm{rot}}$ ,  $\mathrm{I}_{\mathrm{flp}}$ ), including the center position  $(x,y)$ , size  $(w,h)$ , angle  $(\theta)$ , class scores  $(p)$ , and the center-ness  $(cn)$ . To classify each detected object, we follow FCOS [24] by supervising both the classification  $(p)$  and the center-ness  $(cn)$ . The angle  $(\theta)$  prediction is obtained by using the method proposed in PSC [46]. Our contribution mainly lies in the supervision for localization, consisting of two branches: a scale learning branch (SLB) and an orientation learning branch (OLB).
+
+In the SLB, the adaptive bounding box scaling (ABBS) module addresses the relationships between GT HBoxes and predicted RBoxes. This ABBS module provides proper minimum circumscribed rectangle for the accurately predicted RBoxes, by adaptively scaling the HBoxes based on a predefined scale range. The OLB guides accurate prediction of object orientation by utilizing three input views  $(\mathrm{I}_{\mathrm{ori}},\mathrm{I}_{\mathrm{rot}},\mathrm{I}_{\mathrm{flp}})$ , following H2RBox-v2 [48]. Additionally, the OLB utilizes these orientation predictions for our symmetric prior angle (SPA) loss, which leverages the inherent left-right symmetry of objects in aerial images. The SPA loss enforces to further adjust the orientations of the predicted RBoxes to be aligned with the orientations of the symmetric objects such as airplanes, ships, ground track fields etc.
+
+# 3.2. Adaptive Bounding Box Scaling Module
+
+In Fig. 2, 'Scale Learning Branch' illustrates the conceptual process of our adaptive bounding box scaling module (ABBS) module. In HBox-supervised OOD learning, the predicted RBoxes  $(RB^{\mathrm{pred}})$  must be compared with the GT HBoxes  $(HB^{\mathrm{gt}})$ . Since they cannot be directly compared,  $RB^{\mathrm{pred}}$  is first converted to  $HB^{\mathrm{pred}}$ , defined as the minimum circumscribed HBox of  $RB^{\mathrm{pred}}$  as:
+
+$$
+H B ^ {\text {p r e d}} = M C R (R B ^ {\text {p r e d}}), \tag {1}
+$$
+
+where  $MCR(\cdot)$  is an operator converting  $RB$  to the minimum circumscribed  $HB$ , allowing  $HB^{\mathrm{pred}}$  to be compared with  $HB^{\mathrm{gt}}$ .  $HB^{\mathrm{pred}}$  and  $RB^{\mathrm{pred}}$  are given by:
+
+$$
+R B ^ {\text {p r e d}} = \left[ x _ {r b} ^ {\text {p r e d}}, y _ {r b} ^ {\text {p r e d}}, w _ {r b} ^ {\text {p r e d}}, h _ {r b} ^ {\text {p r e d}}, \theta_ {r b} ^ {\text {p r e d}} \right], \tag {2}
+$$
+
+$$
+H B ^ {\text {p r e d}} = \left[ x _ {h b} ^ {\text {p r e d}}, y _ {h b} ^ {\text {p r e d}}, w _ {h b} ^ {\text {p r e d}}, h _ {h b} ^ {\text {p r e d}} \right],
+$$
+
+where  $(x_{rb}^{\mathrm{pred}},y_{rb}^{\mathrm{pred}})$  and  $(x_{hb}^{\mathrm{pred}},y_{hb}^{\mathrm{pred}})$  are the centers of  $RB^{\mathrm{pred}}$  and  $HB^{\mathrm{pred}}$ , respectively. The width  $w$  and height  $h$  of  $HB^{\mathrm{pred}}$  can be computed as:
+
+$$
+w _ {h b} ^ {\text {p r e d}} = w _ {r b} ^ {\text {p r e d}} \left| \cos \theta_ {r b} ^ {\text {p r e d}} \right| + h _ {r b} ^ {\text {p r e d}} \left| \sin \theta_ {r b} ^ {\text {p r e d}} \right|, \tag {3}
+$$
+
+$$
+h _ {h b} ^ {\text {p r e d}} = w _ {r b} ^ {\text {p r e d}} | \sin \theta_ {r b} ^ {\text {p r e d}} | + h _ {r b} ^ {\text {p r e d}} | \cos \theta_ {r b} ^ {\text {p r e d}} |.
+$$
+
+If  $RB^{\mathrm{opt}}$  is defined as the tightly surrounding object boundary RBox with the precise orientation, then we have
+
+![](images/0f0e3f67749295fd52092e18a0c6894c7b925e01576410d11a332bc47f5de4d9.jpg)  
+(a)
+
+![](images/325bb1fc626aaefc2c05d0140a6886eacafedfc82231735440732d56a2dee2c6.jpg)  
+(b)
+
+![](images/5c549cac7a8d8f46a869cf8c9dfc6cfb6146911f9a57937bfa47698c6a67e05b.jpg)  
+(c)
+
+![](images/11ae87346cdf7ff7e0c88c472005c62c18768baf3a886fa74174d5159e1b3c45.jpg)  
+(d)
+
+![](images/c71e66550e76ebe42e0f7ba49bef5c0a389b45ee411cfcf5cca25d30fde80b8f.jpg)  
+(e)
+
+![](images/d75f200c7a4f589524d78653290a80f31a6c6d2a6006a1a73ed76d29a5d60139.jpg)  
+(f)  
+Figure 3. Analysis of scale adjustment function  $(f(\cdot))$  based on the shape and angle of objects. (a) rectangular shape, (b) rounded rectangular shape, (c) complex shape, (d) horizontal orientation, (e) slightly tilted orientation, (f) diagonal orientation. The cyan solid box, green solid box and red dotted box represent GT T-HBox, RBox and adjusted GT HBox, respectively.
+
+$HB^{\mathrm{opt}} = MCR(RB^{\mathrm{opt}})$  for the 'Predicted RBox Projection Process' block in the SLB of Fig. 2. When the size of  $HB^{\mathrm{gt}}$  is larger or smaller than that of  $HB^{\mathrm{opt}}$ , the model needs to adaptively adjust and find the optimal scale within a predefined range of scale variations. We propose an ABBS module that estimates  $RB^{\mathrm{opt}}$  by adaptively adjusting the scale of  $HB^{\mathrm{gt}}$ . Notably, even if  $RB^{\mathrm{pred}}$  is accurately estimated, its  $HB^{\mathrm{pred}}$  may not overlap well with  $HB^{\mathrm{gt}}$ , leading to a low Intersection over Union (IoU) value. Enforcing  $HB^{\mathrm{pred}}$  to match  $HB^{\mathrm{gt}}$  can cause a misalignment with  $RB^{\mathrm{pred}}$  because  $HB^{\mathrm{gt}}$  may not be ideal in estimating  $RB^{\mathrm{opt}}$ . To address this, our ABBS module adaptively scales and adjusts  $HB^{\mathrm{gt}}$  in the context of  $RB^{\mathrm{pred}}$ , rather than forcing  $HB^{\mathrm{pred}}$  to match  $HB^{\mathrm{gt}}$ .
+
+For the detailed explanation of our ABBS module, we first define a set of scaled versions of  $HB^{\mathrm{gt}}$  for the 'Scaled GT HBoxes Generation Process' in the SLB of Fig. 2 as:
+
+$$
+\mathbf {H B} _ {\mathrm {s}} ^ {\mathrm {g t}} = \left\{H B _ {\mathrm {s}, 1} ^ {\mathrm {g t}}, H B _ {\mathrm {s}, 2} ^ {\mathrm {g t}}, \dots , H B _ {\mathrm {s}, \mathrm {K}} ^ {\mathrm {g t}} \right\}, \tag {4}
+$$
+
+where  $HB_{s,k}^{\mathrm{gt}}$  is the k-th scaled version of  $HB^{\mathrm{gt}}$  and  $\mathbf{K}$  is the total number of scaled variations of  $HB^{\mathrm{gt}}$ .  $\mathbf{HB}_{\mathbf{S}}^{\mathrm{gt}}$  is determined as the combinations of angle-adjusted width and height scale factors,  $\{s_{adj,i}^{w}\}_{i=1}^{N_s}$  and  $\{s_{adj,j}^{h}\}_{j=1}^{N_s}$ , that are transformed from basic width and height scale factors,  $\{s_i^{w}\}_{i=1}^{N_s}$  and  $\{s_j^{h}\}_{j=1}^{N_s}$  by considering angle prediction. Basic scale factors are uniformly spaced in a predefined scale range as:
+
+$$
+S _ {w} = \left\{s _ {1} ^ {w}, s _ {2} ^ {w}, \dots , s _ {N _ {s}} ^ {w} \right\}, S _ {h} = \left\{s _ {1} ^ {h}, s _ {2} ^ {h}, \dots , s _ {N _ {s}} ^ {h} \right\}, \tag {5}
+$$
+
+where  $S_w$  and  $S_h$  are the sets of basic width and height scale factors, respectively.  $s_i^w$  and  $s_i^h$  are calculated as:
+
+$$
+s _ {i} ^ {w} = s _ {1} ^ {w} + \left(s _ {N _ {s}} ^ {w} - s _ {1} ^ {w}\right) / \left(N _ {s} - 1\right) \cdot (i - 1),
+$$
+
+$$
+s _ {j} ^ {h} = s _ {1} ^ {h} + \left(s _ {N _ {s}} ^ {h} - s _ {1} ^ {h}\right) / \left(N _ {s} - 1\right) \cdot (j - 1), \tag {6}
+$$
+
+where  $s_{N_s}^w = s_{N_s}^h$  is the predefined largest basic scale factor for both width and height of  $HB^{\mathrm{gt}}$ , and  $N_{s}$  is the number of uniform quantization for the both range  $[s_1^w..s_{N_s}^w]$  and  $[s_1^h..s_{N_s}^h]$ . In order to generate  $HB_{s,i}^{\mathrm{gt}}$ , we transform the basic width and height scale factors,  $\{s_i^w\}_{i=1}^{N_s}$  and  $\{s_j^h\}_{j=1}^{N_s}$ , into angle-adjusted width and height scale factors,  $\{s_{adj,i}^w\}_{i=1}^{N_s}$  and  $\{s_{adj,j}^h\}_{j=1}^{N_s}$ , using the predicted angle  $\theta^{\mathrm{pred}}$  through the scale adjustment function  $f$ :
+
+$$
+s _ {a d j, i} ^ {w} = f \left(\theta_ {r b} ^ {\text {p r e d}}, s _ {i} ^ {w}\right), s _ {a d j, j} ^ {h} = f \left(\theta_ {r b} ^ {\text {p r e d}}, s _ {j} ^ {h}\right). \tag {7}
+$$
+
+To define  $f(\cdot)$ , it's essential to consider the object types and rotation angles. Fig. 3 shows the effect of scale adjustments on T-HBoxes for three object types: (i) For rectangular objects like tennis courts (Fig. 3-(a)), the adjusted T-HBox (red dotted box) aligns precisely with the GT T-HBox (cyan solid box) and tightly circumscribes the optimal RBox (green solid box); (ii) For rounded rectangular objects (Fig. 3-(b)), the optimal RBox slightly exceeds the GT T-HBox; (iii) Complex shapes like airplanes (Fig. 3-(c)) show a larger discrepancy, with parts of the optimal RBox lying outside the GT T-HBox. Furthermore, scale adjustments also depend on rotation angles: (i) Fig. 3-(d) for a vertically (or horizontally) aligned airplane, the GT T-HBox and optimal RBox are identical; (ii) For Fig. 3-(e) with a small rotation angle, they differ slightly; (iii) For Fig. 3-(f) with a larger angle, the difference is more pronounced. Therefore, to take the object's shape types and orientation degrees into account for the scale adjustment for the widths and heights of T-HBoxes,  $f(\cdot)$  in Eq. 7 is defined as:
+
+$$
+f (\theta , s) = \left\{ \begin{array}{l l} \frac {4}{\pi} (s - 1) \cdot \theta + 1, & \text {i f} 0 \leq \theta <   \frac {\pi}{4}, \\ \frac {4}{\pi} (1 - s) \cdot \theta + (2 s - 1), & \text {i f} \frac {\pi}{4} \leq \theta <   \frac {\pi}{2}, \end{array} \right. \tag {8}
+$$
+
+where the angle range is set to  $\theta \in [0,\pi /2)$  due to the periodicity of the angle. According to  $f(\cdot)$  and Eq. 7,  $HB_{s,k}^{\mathrm{gt}}$  in  $\mathbf{HB}_s^{\mathrm{gt}}$  can be expressed as:
+
+$$
+H B _ {s, k} ^ {\mathrm {g t}} = \left[ x ^ {\mathrm {g t}}, y ^ {\mathrm {g t}}, w ^ {\mathrm {g t}} \cdot s _ {a d j, i} ^ {w}, h ^ {\mathrm {g t}} \cdot s _ {a d j, j} ^ {h} \right], \tag {9}
+$$
+
+where  $(x^{\mathrm{gt}},y^{\mathrm{gt}})$  is the center point, and  $w^{\mathrm{gt}}$  and  $h^{\mathrm{gt}}$  are width and height of  $HB^{\mathrm{gt}}$ . As shown in the 'IoU Calculation' and 'Optimal Scale Learning' blocks in the SLB of Fig. 2,  $HB^{\mathrm{opt}}$  among  $\{HB_{s,k}^{\mathrm{gt}}\}_{k=1}^{K}$  can be determined which minimizes the IoU loss for all proposals by an ABBS loss as:
+
+$$
+\mathcal {L} _ {\mathrm {a s}} = \frac {1}{N _ {p}} \sum_ {l = 1} ^ {N _ {p}} \min  _ {s _ {i} ^ {w} \in S _ {w}, \atop s _ {j} ^ {h} \in S _ {h}} \mathcal {L} _ {\mathrm {I o U}} \left(H B _ {l} ^ {\text {p r e d}}, H B _ {s, k} ^ {\text {g t}, l} \left(s _ {i} ^ {w}, s _ {j} ^ {h}\right)\right), \tag {10}
+$$
+
+where  $N_{p}$  is the total number of proposals for input I.  $HB_{l}^{\mathrm{pred}}$  is  $HB^{\mathrm{pred}}$  for  $l$ -th proposal, and  $HB_{s,k}^{\mathrm{gt},l}(s_i^w,s_j^h)$  is  $k$ -th scaled  $HB^{\mathrm{gt}}$ , as  $HB_{s,k}^{\mathrm{gt}}$ , whose width and height are scaled for  $l$ -th proposal according to Eq. 7 to Eq. 9. Finally, by adding a regularization term using the IoU loss between  $HB^{\mathrm{pred}}$  and non-scaled  $HB^{\mathrm{gt}}$ , we formed the regression loss as:
+
+![](images/20f8eef00637ab7600c03ee878ea6683fc07db4f9171afee28e7c45469de0d08.jpg)  
+Airplane
+
+![](images/45fc781940dddcb8806fd987a3b42f61e4fd13f1476d76fda1771d4abaa461d1.jpg)  
+Ship
+
+![](images/a2d1e58850e2cd6b5de90fa8fe55dff6b4f19935e977bc1b59efc803fba9d08a.jpg)  
+Tennis court
+
+![](images/ee66c9f2b21acbe6db6b232718f3f1b68a60af53fcaff428182869ab07575ae3.jpg)  
+Vehicle  
+Figure 4. Examples of symmetric objects in aerial images. In SPA loss, the  $x,y$  coordinates and angle  $\theta$  are used to define the symmetry axis, splitting the object into two parts for comparison.
+
+$$
+\mathcal {L} _ {\mathrm {r e g}} = \mathcal {L} _ {\mathrm {a s}} + \alpha \cdot \left(1 / N _ {p}\right) \sum_ {l = 1} ^ {N _ {p}} \mathcal {L} _ {\mathrm {I o U}} \left(H B _ {l} ^ {\text {p r e d}}, H B ^ {\mathrm {g t}, l}\right), \tag {11}
+$$
+
+where  $\alpha$  is a hyperparameter which is set to 0.01 by default.
+
+# 3.3. Symmetric Prior Angle Loss
+
+In aerial images, objects such as airplanes, ships, tennis courts, and vehicles are often captured from top-down viewpoints, where most of these objects exhibit symmetries in their appearance, as shown in Fig. 4.
+
+In the previous pipelines [42, 48], both the regression loss associated with the bounding box's center point, width, and height, and the angle loss for accurate angle prediction were trained in a balanced manner. However, they tended to inaccurately predict the angles by maximizing the bounding box's IoUs at the same time. This issue stems from the fact that, since the angles could not be directly supervised due to the absence of angle annotations, the angles were indirectly supervised from augmented views with rotations and flips. This is problematic because, when the difference between two predicted angles for the same object in the original view and its rotated view are equal to the rotation angle applied for the original view, the angle loss is zero although the predicted angles are inaccurate.
+
+To mitigate such a predicted angle ambiguity, we propose a symmetric prior angle (SPA) loss. Based on the SPA loss, the model can be trained to predict precise angles by indirectly utilizing the object's symmetric characteristics. As shown in Fig. 4, the detected objects are symmetric against the symmetry axes (blue-dotted lines) passing the center points of their RBoxes. That is, the pixel contents in the two parts divided by the symmetry axis of the RBox are compared in similarity whose difference is used as supervision for our SPA loss. It is noted that our SPA loss utilizes only symmetric objects, incorporating the symmetry prior from GT class labels for proposals identified as symmetric, such as 'airplane,' 'ship,' 'vehicle,' and 'tennis court'
+
+To avoid applying the SPA loss when  $RB^{pred}$  are inaccurate for the respective objects, we first check the fidelity scores of proposal, and sample the Top-  $k$  proposals as supervision in the SPA loss as:
+
+$$
+\left\{R B _ {n} ^ {p r e d} \right\} _ {n = 1} ^ {N _ {\mathrm {s p a}}} = \operatorname {T o p - k} \left(\left\{R B _ {l} ^ {p r e d} \right\} _ {l = 1} ^ {N _ {p}} \mid \mathrm {s c} _ {\mathrm {c l s}} ^ {i} + \mathrm {s c} _ {\mathrm {l o c}} ^ {i}\right) \tag {12}
+$$
+
+where  $\mathrm{sc}_{\mathrm{cls}}^{(i)}$  and  $\mathrm{sc}_{\mathrm{loc}}^{(i)}$  are the classification and localization scores for the  $l$ -th  $RB^{pred}$ , and  $N_{p}$  is the total number of proposals. From Eq. 12, the selected  $N_{spa}$  proposals are considered in the SPA loss by which the predicted angles of  $RB^{pred}(\theta_{rb}^{pred})$  are enforced to align with the orientations of objects in the sense of maximizing the similarity, Structural Similarity Index (SSIM [28]), between the pixel contents in the two parts of each  $RB^{pred}$ . It should be noted that, even in cases where symmetric objects may not appear perfectly symmetric due to contextual factors like shadows or asymmetrical cargo arrangements, their symmetry is still maintained by the inherent structural symmetry between the two parts. Our SPA loss is defined as:
+
+$$
+\mathcal {L} _ {\mathrm {S P A}} = \left(1 / N _ {\mathrm {s p a}}\right) \sum_ {n = 1} ^ {N _ {\mathrm {s p a}}} \left(1 - \operatorname {S S I M} \left(I _ {p 1} ^ {(n)}, I _ {p 2} ^ {(n)}\right)\right) \tag {13}
+$$
+
+To remove the influence of object sizes in  $L_{\mathrm{SPA}}$  computation, the proposals  $(RB^{pred})$  are projected onto a fixed-size grid of  $50 \times 50$ . Then, the pixel content  $(I_{p1})$  in one part of the proposal's projection is compared with that  $(I_{p2})$  of the other part that is flipped before the comparison.
+
+# 3.4. Loss Functions
+
+In the orientation learning branch (OLB), two angle-based losses [48],  $\mathcal{L}_{\mathrm{rot}}$  and  $\mathcal{L}_{\mathrm{flp}}$ , are adopted to leverage the consistency between the original, rotated, and flipped views of each object proposal. For the rotated and flipped views,  $\mathcal{L}_{\mathrm{rot}}$  and  $\mathcal{L}_{\mathrm{flp}}$  are computed by comparing with the predicted angle  $\theta$  in the original view  $(\mathrm{I}_{\mathrm{ori}})$ :
+
+$$
+\mathcal {L} _ {\mathrm {r o t}} = l _ {s} \left(\theta_ {\mathrm {r o t}} - \theta , R\right), \mathcal {L} _ {\mathrm {f l p}} = l _ {s} \left(\theta_ {\mathrm {f l p}} + \theta , 0\right), \tag {14}
+$$
+
+where  $l_{s}$  denotes a smooth L1 loss-based snap loss [48], and  $R$  denotes the angle applied to  $\mathbf{I}_{ori}$ . The final angle loss is:
+
+$$
+\mathcal {L} _ {\text {a n g}} = \beta \left(\lambda_ {r} \mathcal {L} _ {\text {r o t}} + \lambda_ {f} \mathcal {L} _ {\text {f l p}}\right) + \gamma \mathcal {L} _ {\text {S P A}}, \tag {15}
+$$
+
+where  $\lambda_r = 1.0, \lambda_f = 0.05, \beta = 0.6$ , and  $\gamma = 0.05$  are empirically determined for all our experiments. In the shape learning branch (SLB), we use our IoU-based [45] regression loss  $\mathcal{L}_{\mathrm{reg}}$  in Eq. 11. The overall loss is defined as:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \lambda_ {\text {a n g}} \mathcal {L} _ {\text {a n g}} + \lambda_ {\text {r e g}} \mathcal {L} _ {\text {r e g}} + \lambda_ {\text {c n}} \mathcal {L} _ {\text {c n}} + \lambda_ {\text {c l s}} \mathcal {L} _ {\text {c l s}} \tag {16}
+$$
+
+where  $\mathcal{L}_{\mathrm{cn}}$  is the center-ness loss [24], and  $\mathcal{L}_{\mathrm{cls}}$  is the classification loss based on the focal loss [20]. The weighting factors,  $\lambda_{\mathrm{ang}}, \lambda_{\mathrm{reg}}, \lambda_{\mathrm{cn}}$ , and  $\lambda_{\mathrm{cls}}$  are all set to 1.
+
+# 4. Experiments
+
+# 4.1. Datasets
+
+We trained and tested all the methods across four different datasets: DIOR [5, 13], DOTA-v1.0 [29], SIMD [9] and NWPU VHR-10 [4], which are summarized in Table 1. The details for the datasets and results for SIMD and NWPU are described in Suppl.
+
+<table><tr><td>Datasets</td><td># of Images</td><td>Image Widths</td><td># of Objects</td><td># of Classes</td><td>Annotation Types</td></tr><tr><td>DIOR [13]</td><td>22,463</td><td>800</td><td>190,288</td><td>20</td><td>T-HBox</td></tr><tr><td>DIOR-R [5]</td><td>22,463</td><td>800</td><td>190,288</td><td>20</td><td>RBox</td></tr><tr><td>DOTA-v1.0 [29]</td><td>2,806</td><td>800 ~ 4K</td><td>188,282</td><td>15</td><td>C-HBox, RBox</td></tr><tr><td>SIMD [9]</td><td>5,000</td><td>1024</td><td>45,096</td><td>15</td><td>T-HBox</td></tr><tr><td>NWPU VHR-10 [4]</td><td>800</td><td>~1000</td><td>3,775</td><td>10</td><td>T-HBox</td></tr></table>
+
+Table 1. Characteristics of datasets used for experiments
+
+# 4.2. Implementation Details
+
+Our proposed ABBSPO pipeline adopts the FCOS [24] detector as the baseline architecture, utilizing a ResNet-50 [10] backbone and an FPN [15] neck, based on the H2RBox-v2 [48] framework. To ensure fairness, all models are configured with the ResNet-50 [10] backbone and trained for 12 epochs on NVIDIA RTX3090 GPUs.
+
+# 4.3. Experimental Results
+
+# 4.3.1 Quantitative Comparison
+
+It should be noted that objects such as round-shaped pools have orientation ambiguities regardless of their annotations (RBoxes) [42]. In order to avoid confusion in orientation learning, annotations are modified as having horizontal orientations if the objects belong to the following categories: (i) DIOR-R: 'baseball field', 'chimney', 'golf field', 'stadium', 'storage tank', 'windmill'; and (ii) DOTA-v1.0: 'baseball diamond', 'stadium', 'roundabout'. Accordingly, their orientation learning is enforced to predict the horizontal orientations, similar to previous works [42, 48].
+
+Results on DIOR-R. Table 2 shows the OOD results. In addition to  $\mathrm{AP}_{50}$  metric, we use  $3\text{-AP}_{50}$  that focuses on the detection performance of the three complex-shaped object categories: 'airplane' (APL), 'expressway service area' (ESA), and 'overpass' (OP). As shown, our ABBSPO outperforms all weakly supervised OOD methods. Especially, in terms of  $3\text{-AP}_{50}$ , our ABBSPO is superior to the HBox-supervised SOTA methods, H2RBox and H2RBox-v2, with large margins of average  $12.9\%$  -point and average  $9.1\%$  -point improvements. In overall  $\mathrm{AP}_{50}$  performance, our ABBSPO surpasses H2RBox by  $5.13\%$  -point and the H2RBox-v2 by  $3.03\%$  -point. It is noted that our ABBSPO not only surpasses our base detector (H2RBox-v2 [48]) but also performs comparably to other RBox-supervised OOD methods, such as FCOS [24] and Oriented R-CNN [32]. It is worth noting that, compared to the RBox-supervised OOD methods, our ABBSPO shows even superior performance with large margins from  $6.5\%$  -point to  $11.7\%$  -point, especially on the 'airplane' that has the most complex shape. Notably, the ABBS module is less effective for rectangular objects, such as 'tennis court' (TC) and 'vehicle' (VE), as scaling is often unnecessary. However, it proves highly beneficial for complex-shaped objects, such as the ESA. The SPA loss is applied only to symmetric categories and helps
+
+<table><tr><td colspan="2">Methods</td><td>\( \underline{\mathbf{APL}} \)</td><td>\( \mathbf{APO} \)</td><td>\( \mathbf{BF} \)</td><td>\( \mathbf{{BC}} \)</td><td>\( \mathbf{{BR}} \)</td><td>\( \mathbf{{CH}} \)</td><td>\( \underline{\mathbf{ESA}} \)</td><td>\( \mathbf{{ETS}} \)</td><td>\( \mathbf{{DAM}} \)</td><td>\( \mathbf{{GF}} \)</td><td>\( \mathbf{{GTF}} \)</td><td>\( \mathbf{{HA}} \)</td><td>\( \mathbf{{OP}} \)</td><td>\( \mathbf{{SH}} \)</td><td>\( \mathbf{{STA}} \)</td><td>\( \mathbf{{STO}} \)</td><td>\( \mathbf{{TC}} \)</td><td>\( \mathbf{{TS}} \)</td><td>\( \mathbf{{WE}} \)</td><td>\( \mathbf{{WM}} \)</td><td>\( 3-AP_{50} \)</td><td>\( AP_{50} \)</td></tr><tr><td rowspan="6">\( S_R \)</td><td>RetinaNet [20]</td><td>59.8</td><td>19.3</td><td>69.7</td><td>81.3</td><td>17.2</td><td>72.7</td><td>68.7</td><td>49.4</td><td>18.4</td><td>69.5</td><td>71.3</td><td>33.3</td><td>34.1</td><td>75.8</td><td>67.1</td><td>59.6</td><td>81.0</td><td>44.1</td><td>38.0</td><td>62.5</td><td>54.20</td><td>54.64</td></tr><tr><td>FCOS [24]</td><td>62.1</td><td>37.9</td><td>74.6</td><td>81.2</td><td>32.9</td><td>72.1</td><td>75.3</td><td>61.8</td><td>27.4</td><td>69.1</td><td>78.7</td><td>34.4</td><td>50.6</td><td>80.1</td><td>68.6</td><td>68.1</td><td>81.3</td><td>49.1</td><td>43.4</td><td>64.5</td><td>62.67</td><td>60.66</td></tr><tr><td>Oriented R-CNN [32]</td><td>63.0</td><td>36.7</td><td>71.9</td><td>81.6</td><td>41.1</td><td>72.6</td><td>77.8</td><td>65.5</td><td>24.8</td><td>72.9</td><td>82.1</td><td>40.9</td><td>56.5</td><td>81.2</td><td>73.4</td><td>62.4</td><td>81.5</td><td>53.3</td><td>65.6</td><td>65.77</td><td>62.41</td><td></td></tr><tr><td>GWD [38] (RetinaNet)</td><td>61.5</td><td>23.6</td><td>73.6</td><td>81.1</td><td>17.4</td><td>72.7</td><td>68.3</td><td>47.2</td><td>20.7</td><td>71.2</td><td>73.2</td><td>33.9</td><td>34.3</td><td>77.6</td><td>64.7</td><td>57.5</td><td>80.9</td><td>42.1</td><td>39.7</td><td>60.2</td><td>54.70</td><td>55.07</td></tr><tr><td>KLD [39] (RetinaNet)</td><td>57.8</td><td>22.6</td><td>71.5</td><td>81.2</td><td>16.9</td><td>72.7</td><td>68.9</td><td>52.1</td><td>20.6</td><td>73.5</td><td>71.0</td><td>33.7</td><td>33.2</td><td>77.1</td><td>68.9</td><td>59.9</td><td>80.9</td><td>43.9</td><td>39.1</td><td>60.9</td><td>53.30</td><td>55.32</td></tr><tr><td>KFIoU [41] (RetinaNet)</td><td>60.6</td><td>36.6</td><td>73.6</td><td>80.9</td><td>27.0</td><td>72.6</td><td>73.4</td><td>56.5</td><td>25.4</td><td>73.9</td><td>72.0</td><td>32.9</td><td>45.8</td><td>75.8</td><td>65.2</td><td>57.6</td><td>80.0</td><td>48.0</td><td>40.1</td><td>58.8</td><td>59.93</td><td>57.84</td></tr><tr><td>\( \underline{\mathbf{S_I}} \)</td><td>\( WSODet^† \)[23]</td><td>20.7</td><td>29.0</td><td>63.2</td><td>67.3</td><td>0.2</td><td>65.5</td><td>0.4</td><td>0.1</td><td>0.3</td><td>49.0</td><td>28.9</td><td>0.3</td><td>1.5</td><td>1.2</td><td>53.4</td><td>16.4</td><td>40.0</td><td>0.1</td><td>6.1</td><td>0.1</td><td>7.53</td><td>22.20</td></tr><tr><td rowspan="2">\( S_P \)</td><td>\( PointOBB^† \)[17]</td><td>58.2</td><td>15.3</td><td>70.5</td><td>78.6</td><td>0.1</td><td>72.2</td><td>69.6</td><td>1.8</td><td>3.7</td><td>0.3</td><td>77.3</td><td>16.7</td><td>40.4</td><td>79.2</td><td>39.6</td><td>32.4</td><td>29.6</td><td>16.8</td><td>33.6</td><td>27.7</td><td>56.07</td><td>38.08</td></tr><tr><td>Point2RBox-SK [47]</td><td>41.9</td><td>9.1</td><td>62.9</td><td>52.8</td><td>10.8</td><td>72.2</td><td>3.0</td><td>43.9</td><td>5.5</td><td>9.7</td><td>25.1</td><td>9.1</td><td>21.0</td><td>24.0</td><td>20.4</td><td>25.1</td><td>71.7</td><td>4.5</td><td>16.1</td><td>16.3</td><td>21.97</td><td>27.26</td></tr><tr><td rowspan="3">\( S_H \)</td><td>H2RBox [42]</td><td>57.1</td><td>14.4</td><td>72.2</td><td>82.6</td><td>17.5</td><td>71.2</td><td>56.5</td><td>55.2</td><td>14</td><td>67.7</td><td>77.9</td><td>31</td><td>40.7</td><td>76.3</td><td>66.2</td><td>63.4</td><td>81.5</td><td>50.4</td><td>38</td><td>57.6</td><td>51.43</td><td>54.57</td></tr><tr><td>H2RBox-v2 [48]</td><td>55.5</td><td>17.8</td><td>76.9</td><td>80.5</td><td>27.7</td><td>72.2</td><td>63.0</td><td>58.6</td><td>24.4</td><td>73.9</td><td>80.3</td><td>33.9</td><td>47.2</td><td>77.4</td><td>58.7</td><td>60.9</td><td>81.4</td><td>48.1</td><td>41.1</td><td>53.9</td><td>55.23</td><td>56.67</td></tr><tr><td>ABBSPO (Ours)</td><td>69.5</td><td>15.7</td><td>76.2</td><td>87.5</td><td>29.9</td><td>72.3</td><td>75.3</td><td>61.2</td><td>28.1</td><td>74.1</td><td>81.7</td><td>34.7</td><td>48.2</td><td>79.3</td><td>67.4</td><td>61.4</td><td>81.5</td><td>54.7</td><td>41.5</td><td>53.8</td><td>64.33</td><td>59.70</td></tr></table>
+
+Table 2. Quantitative results of each category on the DIOR-R [5] test dataset for RBox-supervised  $(S_R)$ , Image-supervised  $(S_I)$ , Point-supervised  $(S_P)$  and HBox-supervised  $(S_H)$  methods. The  $3-\mathrm{AP}_{50}$  represents the mean  $\mathrm{AP}_{50}$  scores for three complex-shaped object categories: 'airplane' (APL), 'expressway service area' (ESA), and 'overpass' (OP). The notation  $\dagger$  indicates its results in the paper [17].  
+
+<table><tr><td colspan="2">Methods</td><td>PL</td><td>BD</td><td>BR</td><td>GTF</td><td>SV</td><td>LV</td><td>SH</td><td>TC</td><td>BC</td><td>ST</td><td>SBF</td><td>RA</td><td>HA</td><td>SP</td><td>HC</td><td>3-AP50</td><td>AP50</td></tr><tr><td rowspan="7">SR</td><td>RetinaNet [20]</td><td>87.5</td><td>75.1</td><td>39.9</td><td>59.6</td><td>66.3</td><td>66.3</td><td>78.2</td><td>90.5</td><td>55.0</td><td>62.7</td><td>47.1</td><td>63.6</td><td>59.4</td><td>55.1</td><td>43.0</td><td>61.87</td><td>63.3</td></tr><tr><td>FCOS [24]</td><td>88.8</td><td>74.0</td><td>46.8</td><td>59.1</td><td>70.1</td><td>81.4</td><td>87.7</td><td>90.7</td><td>67.7</td><td>68.3</td><td>60.2</td><td>66.1</td><td>64.9</td><td>58.7</td><td>44.0</td><td>63.83</td><td>68.6</td></tr><tr><td>Oriented R-CNN [32]</td><td>89.3</td><td>76.1</td><td>53.8</td><td>78.7</td><td>68.6</td><td>84.9</td><td>89.3</td><td>90.8</td><td>74.3</td><td>62.8</td><td>66.3</td><td>66.5</td><td>74.7</td><td>58.6</td><td>46.8</td><td>64.90</td><td>72.1</td></tr><tr><td>Oriented RepPoints[14]</td><td>89.7</td><td>80.1</td><td>50.5</td><td>74.4</td><td>75.0</td><td>82.0</td><td>88.7</td><td>90.4</td><td>64.0</td><td>70.0</td><td>45.7</td><td>60.6</td><td>73.6</td><td>60.4</td><td>42.8</td><td>64.30</td><td>69.86</td></tr><tr><td>GWD [38] (RetinaNet)</td><td>88.2</td><td>74.9</td><td>41.3</td><td>60.5</td><td>66.7</td><td>68.1</td><td>85.8</td><td>90.5</td><td>50.4</td><td>66.8</td><td>45.8</td><td>65.1</td><td>60.7</td><td>52.9</td><td>38.9</td><td>60.0</td><td>63.77</td></tr><tr><td>KLD [39] (RetinaNet)</td><td>88.4</td><td>75.8</td><td>41.4</td><td>60.0</td><td>66.1</td><td>68.8</td><td>84.7</td><td>90.6</td><td>56.8</td><td>60.4</td><td>50.4</td><td>70.1</td><td>60.0</td><td>50.5</td><td>45.7</td><td>61.53</td><td>64.65</td></tr><tr><td>KFIuU [41] (RetinaNet)</td><td>84.4</td><td>74.3</td><td>40.7</td><td>55.2</td><td>57.9</td><td>56.9</td><td>76.4</td><td>71.2</td><td>46.1</td><td>64.8</td><td>54.3</td><td>65.0</td><td>58.3</td><td>48.7</td><td>42.9</td><td>58.67</td><td>59.81</td></tr><tr><td rowspan="2">SP</td><td>PointOBB [17]+FCOS</td><td>32.4</td><td>67.3</td><td>0.8</td><td>53.6</td><td>2.3</td><td>9.7</td><td>18.8</td><td>0.3</td><td>9.9</td><td>12.8</td><td>0.5</td><td>54.0</td><td>11.0</td><td>34.1</td><td>11.4</td><td>25.97</td><td>21.26</td></tr><tr><td>Point2RBox-SK [47]</td><td>50.1</td><td>63.7</td><td>1.6</td><td>44.7</td><td>23.9</td><td>34.7</td><td>32.7</td><td>78.8</td><td>41.2</td><td>32.2</td><td>2.1</td><td>34.3</td><td>20.8</td><td>42.5</td><td>7.2</td><td>33.27</td><td>34.03</td></tr><tr><td rowspan="3">SH</td><td>H2RBox [42]</td><td>89.5</td><td>73.1</td><td>37.3</td><td>55.1</td><td>70.7</td><td>76.4</td><td>85.4</td><td>90.3</td><td>66.5</td><td>67.3</td><td>59.6</td><td>64.9</td><td>60.6</td><td>57.9</td><td>36.5</td><td>61.30</td><td>66.07</td></tr><tr><td>H2RBox-v2 [48]</td><td>89.4</td><td>74.8</td><td>45.4</td><td>56.0</td><td>70.3</td><td>76.6</td><td>87.9</td><td>90.5</td><td>69.3</td><td>67.5</td><td>56.7</td><td>64.7</td><td>65.3</td><td>55.5</td><td>45.5</td><td>63.47</td><td>67.69</td></tr><tr><td>ABBSPO (Ours)</td><td>89.2</td><td>75.6</td><td>47.4</td><td>52.8</td><td>70.3</td><td>77.6</td><td>88.2</td><td>90.5</td><td>67.9</td><td>66.8</td><td>68.2</td><td>66.2</td><td>71.6</td><td>55.6</td><td>51.0</td><td>65.27</td><td>69.26</td></tr></table>
+
+Table 3. Quantitative results of each category on the DOTA-v1.0 [29] validation dataset for  $S_R$ ,  $S_I$ ,  $S_P$  and  $S_H$  methods. The  $\underline{3 - AP}_{50}$  represents the mean  $\mathrm{AP}_{50}$  scores for three complex-shaped object categories: plane (PL), swimming pool (SP), and helicopter (HC). All the methods are re-trained using only train dataset for fair comparison.
+
+improve their performance, except for the categories with orientation ambiguities, such as 'storage tank' (STO). Since the predicted angles learned through the SPA loss are also utilized in the ABBS module for scale adjustment, both the SPA loss and the ABBS module jointly contribute to performance improvement in symmetric categories. This joint effect is particularly evident in complex-shaped symmetric categories, such as APL and ESA, where performance gains are more significant. Nevertheless, the performance gains for the two symmetric and rectangular categories, TC and VE, are marginal. This is mainly because the ABBS module has limited impact on rectangular shapes, and the small object sizes lead to an insufficient number of pixels for reliably determining the symmetry axis via the SPA loss.
+
+Results on DOTA-v1.0. Table 3 shows the detection performance results on the DOTA-v1.0 [29]. Due to the nonresponsiveness of the DOTA evaluation server, we report our experimental results on the validation dataset (458 images) instead of the test dataset (937 images). It should be noted that the validation dataset was not used for training all the methods for fair comparison. We use  $3\mathrm{-AP}_{50}$  that measures the detection performance for the three complex-shaped object categories: 'plane', 'swimming pool' and 'helicopter'. Our ABBsPO achieves SOTA performance, outperforming H2RBox by  $3.19\%$  -point and H2RBox-v2 by  $1.57\%$  -point improvements. Moreover, our ABBsPO
+
+even surpasses the FCOS Baseline by  $0.66\%$  -point lift.
+
+# 4.3.2 Qualitative Comparison
+
+Results on DIOR. As shown in the figures of the first row in Fig. 5, our ABBSPO is the only method that accurately captures both the orientation and scale of the airplane. Since DIOR annotations provide GT in T-HBox format, direct usage of T-HBoxes as GT for training to predict RBox leads to degradations in orientation and scale prediction accuracy for the existing HBox-supervised OOD methods as shown in the figures of columns 2 and 3 in Fig. 5. In contrast, our ABBSPO avoids such degradation by utilizing the ABBS module that optimally scales the GT HBox sizes for precise RBox prediction during training. It is also worthwhile to mention that the predicted orientations by our ABBSPO are more precisely obtained via our SPA loss. Furthermore, it should be noted that compared to the RBox-supervised baseline method (Rotated FCOS [24]), our approach demonstrates superior visual results, even under weakly supervised learning.
+
+Results on DOTA-v1.0. As shown in the figures of the second row in Fig. 5, ABBSPO very accurately predicts both the orientation and scale of the swimming pool, achieving similar accuracy for tennis court. Interestingly, only ABBSPO successfully detects the two tennis courts that are partially occluded by trees (red solid circle) while the other
+
+<table><tr><td colspan="2">Module</td><td colspan="2">DIOR-R</td><td>DOTA-v1.0</td></tr><tr><td>ABBS</td><td>SPA</td><td>3-AP50</td><td>AP50</td><td>AP50</td></tr><tr><td></td><td></td><td>55.23</td><td>56.67</td><td>67.69</td></tr><tr><td>✓</td><td></td><td>62.13</td><td>58.35</td><td>68.59</td></tr><tr><td></td><td>✓</td><td>58.77</td><td>58.99</td><td>69.16</td></tr><tr><td>✓</td><td>✓</td><td>64.33</td><td>59.70</td><td>69.26</td></tr></table>
+
+Table 4. Ablation results on ABBS module and SPA loss  $(\mathcal{L}_{\mathrm{SPA}})$  
+
+<table><tr><td colspan="2">Sampling</td><td colspan="2">DIOR-R</td></tr><tr><td>L SPA</td><td>Others</td><td>3-AP50</td><td>AP50</td></tr><tr><td></td><td></td><td>61.67</td><td>58.93</td></tr><tr><td>✓</td><td></td><td>64.33</td><td>59.70</td></tr><tr><td></td><td>✓</td><td>43.63</td><td>50.51</td></tr><tr><td>✓</td><td>✓</td><td>45.1</td><td>50.91</td></tr></table>
+
+Table 5. Ablation results on proposal sampling in  ${\mathcal{L}}_{\mathrm{{SPA}}}$  and other components.  
+
+<table><tr><td colspan="3">Scale Range</td><td colspan="2">DIOR-R</td><td>DOTA-v1.0</td></tr><tr><td>Min</td><td>Max</td><td>Interval</td><td>3-AP50</td><td>AP50</td><td>AP50</td></tr><tr><td>0.9</td><td>1.1</td><td>0.05</td><td>57.97</td><td>58.15</td><td>69.26</td></tr><tr><td>0.5</td><td>1.5</td><td>0.1</td><td>61.67</td><td>59.62</td><td>68.8</td></tr><tr><td>1.0</td><td>1.5</td><td>0.1</td><td>64.33</td><td>59.70</td><td>68.9</td></tr><tr><td>1.0</td><td>2.0</td><td>0.1</td><td>56.07</td><td>55.46</td><td>66.55</td></tr></table>
+
+Table 6. Ablation results on scale range in ABBS module.
+
+![](images/f838ad4df2e507e0e2ecfce0c5614d593565459003deab0ecdc911cd4cdab3c7.jpg)  
+Figure 5. Qualitative results on DIOR [5, 13] and DOTA-v1.0 [29]. Zoom-in for better visualization. Rotated FCOS was trained only with GT RBoxes, while H2RBox, H2RBox-v2 and our ABBsPO were trained with GT T-HBoxes (1st row) and GT C-HBoxes (2nd row).
+
+methods failed. These results visually support the effectiveness of our ABBS module and SPA loss in learning the scales and orientations of objects accurately.
+
+# 4.4. Ablation Studies
+
+Ablation study on SPA loss and ABBS module. As shown in Table 4, both components contribute to performance improvements. The ABBS module effectively scales the GT HBoxes, leading to an increase in  $\mathrm{AP}_{50}$  performance on the DIOR dataset. Notably, it has a greater effect on complex-shaped object categories, resulting in a significant improvement in  $3\text{-AP}_{50}$ . Similarly, the SPA loss enhances angle prediction accuracy, also bringing an improvement in  $\mathrm{AP}_{50}$ .
+
+Ablation study on proposal sampling. As shown in Table 5, applying Top-  $k$  proposal sampling exclusively to the SPA loss  $(\mathcal{L}_{\mathrm{SPA}})$  yields the highest  $\mathrm{AP}_{50}$  performance, as the symmetric proposals of high-quality benefits  $\mathcal{L}_{\mathrm{SPA}}$ . But, additional proposal sampling to the others  $(\mathcal{L}_{\mathrm{rot}},\mathcal{L}_{\mathrm{flp}},\mathcal{L}_{\mathrm{reg}},\mathcal{L}_{\mathrm{cn}},\mathcal{L}_{\mathrm{cls}})$  significantly lowers the performance.
+
+Ablation study on scale range in the ABBS module. As shown in Table 6, the optimal scale range is influenced by the type of GT HBoxes. For DIOR's T-HBoxes, a scale range of 1 to 1.5 works well because it ensures that the
+
+predicted RBoxes fully cover the objects boundary. On the other hand, for DOTA's C-HBoxes, which are already close to the optimal HBoxes, the optimal scale range is closer to 1. By adjusting the scale range based on the type of HBoxes, the ABBS module achieves high accuracy in predicting RBoxes for both datasets.
+
+# 5. Conclusion
+
+Our ABBSPO, a weakly supervised OOD framework, effectively learns RBox prediction regardless of the type of HBox annotations (T-HBox and C-HBox). With our proposed Adaptive Bounding Box Scaling (ABBS) and Symmetric Prior Angle (SPA) loss, we achieved enhanced orientation and scale accuracy for OOD, which is comparable to or even better than RBox-supervised methods. Extensive experimental results underscore the superiority of our approach, surpassing state-of-the-art HBox-supervised methods. Our method effectively bridges the gap between weakly supervised OOD and fully supervised OOD, making it a promising solution for applications requiring efficient and accurate object detection via training with relatively cheap annotations of HBoxes compared to RBoxes.
+
+# Acknowledgement
+
+This research was supported by Korea Institute of Marine Science & Technology Promotion (KIMST) funded by the Korea Coast Guard (RS-2023-00238652, Integrated Satellite-based Applications Development for Korea Coast Guard,  $100\%$ ).
+
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+# ABC-Former: Auxiliary Bimodal Cross-domain Transformer with Interactive Channel Attention for White Balance
+
+Yu-Cheng Chiu* Guan-Rong Chen* Zihao Chen Yan-Tsung Peng† National Chengchi University
+
+No. 64, Section 2, Zhinan Rd, Wenshan District, Taipei City, 116
+
+111753202@nccu.edu.tw 111753139@nccu.edu.tw 113761501@nccu.edu.tw ytpeng@cs.nccu.edu.tw
+
+# Abstract
+
+The primary goal of white balance (WB) for sRGB images is to correct inaccurate color temperatures, ensuring that images display natural, neutral colors. While existing WB methods yield reasonable results, their effectiveness is limited. They either focus solely on global color adjustments applied before the camera-specific image signal processing pipeline or rely on end-to-end models that generate WB outputs without accounting for global color trends, leading to suboptimal correction. To address these limitations, we propose an Auxiliary Bimodal Cross-domain Transformer (ABC-Former) that enhances WB correction by leveraging complementary knowledge from global color information from CIELab and RGB histograms alongside sRGB inputs. By introducing an Interactive Channel Attention (ICA) module to facilitate cross-modality global knowledge transfer, ABC-Former achieves more precise WB correction. Experimental results on benchmark WB datasets show that ABC-Former performs favorably against state-of-the-art WB methods. The source code is available at https://github.com/ytpeng-aimlab/ABC-Former.
+
+# 1. Introduction
+
+White balance (WB) correction ensures consistent and accurate color production across varying lighting conditions. However, camera Image Signal Processing (ISP) can introduce color casts in sRGB images due to inaccurate or customized WB settings applied to raw-RGB inputs. These distortions can degrade the accuracy of tasks like image classification and segmentation, where precise color is crucial [10, 12, 23]. Consequently, WB correction has gained significant research interest.
+
+Significant effort has been made to improve WB within the camera's ISP pipeline. Raw-WB methods estimate the
+
+![](images/dc3a462b8e9f99c49514e17bdd64749d9d84856929305498c0a53ba146854fdf.jpg)
+
+![](images/d84a832deedf8ac4ac147fb047a3056f07187691fd7a0655c9afd11b305027a2.jpg)
+
+![](images/3ce855a07bd457cdced9502f45450bc79508178e0c0b9ea05bbe7a156d755c83.jpg)  
+Figure 1. (a) Traditional raw-WB methods predict the scene's illuminant, perform Illumination Correction (IC), and generate the sRGB output via camera-specific ISP. (b) DNN-based sRGB-WB methods apply end-to-end models directly to sRGB images for WB correction. (c) ABC-Former improves WB accuracy by converting the input into multiple modalities, enhancing illumination correction through auxiliary and primary models.
+
+scene's illuminant to correct color shifts in raw images before further processing. However, due to the non-linear transformations applied by the ISP during rendering, these corrections may not fully compensate for color shifts in the final sRGB output [1].
+
+Several sRGB-WB methods address color shifts caused by imprecise WB in the camera's ISP, categorized into exemplar-based and DNN-based approaches. Exemplar-based methods like KNN [3] classify images from the Rendered WB dataset and apply the best-matching nonlinear
+
+mappings for correction. DNN-based methods such as DEEP-WB [2] use CNNs for single-illuminant color correction, while WBFlow [18] extracts pseudo-raw features via a reversible flow model for sRGB correction. SWBNet [19] employs a transformer in the DCT domain to refine color-sensitive features. While effective, these methods fail to fully integrate global color trends and scene information for more comprehensive WB correction.
+
+Our work utilizes alternative modalities, such as color histograms, to learn global color temperature for effective WB correction. Unlike images, which encode spatial and color information, histograms capture color distribution across channels without spatial details. While per-channel histograms do not fully preserve color relationships between pixels, we can explore both sRGB and CIELab color histograms to go beyond sRGB-input images, extracting global color information. Inspired by [26], we propose ABC-Former, an Auxiliary Bimodal Cross-domain Transformer architecture that integrates global color information from both sRGB and CIELab histograms. It consists of two auxiliary models for histogram-based learning and a target model for sRGB image WB correction, where the sRGB histogram supervises raw color intensity, and CIELab ensures perceptually uniform color distribution. To enhance WB correction in the target sRGB model, we introduce the Interactive Channel Attention (ICA) module, which transfers modality-complementary knowledge using re-parameterization, allowing the target model to adaptively reweight image features for improved accuracy. Our key contributions are listed as follows:
+
+- We propose ABC-Former, which leverages histogram-based global color features via auxiliary models to refine WB correction in the target sRGB model.  
+- We introduce the ICA module to facilitate effective cross-modality knowledge transfer, optimizing sRGB feature reweighting for better WB results.  
+- Extensive experiments on benchmark WB datasets demonstrate that ABC-Former outperforms state-of-the-art (SOTA) sRGB-WB methods.
+
+# 2. Related Works
+
+Raw-WB Approaches. The WB module in a camera's ISP corrects raw images for accurate color temperature, compensating for lighting variations. Traditional WB methods estimate the global light source color and apply uniform gain coefficients for illumination correction. However, they assume a consistent color temperature across the scene, making them ineffective under mixed lighting. Additionally, these methods irreversibly alter raw images, limiting precise sRGB adjustments in post-processing [4, 7-9, 15, 20, 21, 24].
+
+sRGB-WB Approaches. To address the shortcomings of traditional WB methods, recent research has explored
+
+sRGB-WB approaches, which refine color correction beyond the ISP stage. These methods can be classified into exemplar-based methods [3, 5] and DNN-based methods [18, 19]. Exemplar-based methods apply trained nonlinear mappings for color correction. For example, Affi et al. [3] use histogram features to find images with similar color distributions and derive a correction matrix to adjust colors accordingly. Mixed-WB [5] generates multiple WB versions of an image, averaging their weighting maps to achieve optimal correction. However, these methods rely heavily on predefined training data, making them less adaptable to diverse lighting conditions.
+
+DNN-based methods, such as WBFlow [18], use neural flow for reversible color correction, mapping color-cast sRGB images to a pseudo-raw feature space for linear WB. WBFlow also incorporates a camera transformation module for few-shot adaptation, improving generalization ability. SWBNet [19] suppresses temperature-sensitive low-frequency information and employs a contrast loss to align scene features across varying temperatures, enhancing WB stability. It also uses adaptive weights to correct multiple color shifts under mixed lighting. Although these methods are effective, they remain constrained by the sRGB image modality.
+
+Multimodal Training Approaches. Unimodal training uses data from a single modality, limiting its ability to generalize across different modalities. In contrast, multimodal training enables models to learn from multiple modalities, which can be strongly correlated (paired data) or weakly correlated (irrelevant data). CLIP [22] exemplifies strongly correlated multimodal data, using contrastive learning to align image and text features, requiring paired data. In contrast, M2PT [26] integrates irrelevant data from different modalities by leveraging re-parameterization to transfer knowledge from pre-trained auxiliary models. While this enhances cross-modal learning, it increases data collection costs and pre-training demands.
+
+Inspired by M2PT, we adopt multimodal training to capture global color information from sRGB images to enhance WB correction. Unlike M2PT, which uses irrelevant data, we train sRGB images to learn corrected histogram-based color features from their color and CIELab histograms. Figure 1 compares conventional DNN-based raw-WB and sRGB-WB methods with the proposed ABC-Former.
+
+# 3. Proposed Method
+
+The proposed ABC-Former consists of three transformer models: two auxiliary transformers that learn to correct color and CIELab histograms, and a primary transformer that processes the input sRGB image for the final WB correction. Unlike M2PT [26], which tokenizes irrelevant multimodal data for unified processing, our approach leverages sRGB images with their strongly related color information.
+
+To efficiently transfer complementary color knowledge, we introduce the Interactive Channel Attention (ICA) module, which utilizes condensed histogram-based features to enhance color temperature correction, improving accuracy and visual quality. The overall architecture is shown in Figure 2.
+
+# 3.1. Auxiliary Model — PDFformer
+
+Most prior sRGB-WB works [2, 3, 5, 18] focus on local pixel information within the sRGB domain, often overlooking global color temperature and perceptual color relationships, which are crucial for effective WB correction. Therefore, integrating global color information from alternative modalities can enhance accuracy by providing a broader context for color adjustments. Given an input sRGB image  $\mathbf{I} \in \mathbb{R}^{H \times W \times 3}$ , where  $H$  and  $W$  denote the image's height and width, and the three channels represent the RGB color components, we first convert it to the CIELab color space, represented as  $\mathbf{I}_{\mathrm{Lab}} \in \mathbb{R}^{H \times W \times 3}$ , where the three channels correspond to the  $L^*$ ,  $a^*$ , and  $b^*$  components. To efficiently capture global color temperature while maintaining low model complexity, we convert  $\mathbf{I}$  into its probability density function (PDF) representation,  $\mathbf{H}_{\mathrm{sRGB}} \in \mathbb{R}^{L \times 3}$ , where  $L = 256$  represents the number of histogram bins per channel. Similarly, we transform  $\mathbf{I}_{\mathrm{Lab}}$  into its PDF form, referred to as  $\mathbf{H}_{\mathrm{Lab}} \in \mathbb{R}^{L \times 3}$ , with  $L = 256$ , providing a histogram-based representation for each color space.
+
+The ABC-Former framework incorporates two auxiliary models to enhance the target model's performance. These models process global color PDF data,  $\mathbf{H}^{\mathrm{sRGB}}$  and  $\mathbf{H}^{\mathrm{Lab}}$ , which serve as distinct inputs. Each auxiliary model, called PDFformer, employs a 1D transformer architecture with a shared structure but separate training. Initially, the input histograms,  $\mathbf{H}^{\mathrm{sRGB}}$  or  $\mathbf{H}^{\mathrm{Lab}}$ , pass through a one-dimensional convolutional layer to produce histogram features  $\mathbf{H}_0^{\mathbf{A}} \in \mathbb{R}^{L \times C}$ , where  $\mathbf{A} \in [\mathbf{sRGB}, \mathbf{Lab}]$ , and  $C$  is the feature dimension. These features are subsequently processed through a U-shape transformer structure with PDFformer blocks that facilitate upsampling and downsampling in the encoding and decoding paths. Each block consists of two sequences of Layer Normalization (LN), Channel Attention (CA) [14], and a feed-forward Multilayer Perceptron (MLP) [11], arranged in the following order:
+
+$$
+\hat {\mathbf {H}} _ {\mathbf {i}} ^ {\mathbf {A}} = \operatorname {C A} \left(\operatorname {L N} \left(\mathbf {H} _ {\mathbf {i} - 1} ^ {\mathbf {A}}\right)\right) + \mathbf {H} _ {\mathbf {i} - 1} ^ {\mathbf {A}}; \tag {1}
+$$
+
+$$
+\mathbf {H} _ {\mathbf {i}} ^ {\mathbf {A}} = \operatorname {G E L U} (\operatorname {M L P} (\operatorname {L N} (\hat {\mathbf {H}} _ {\mathbf {i}} ^ {\mathbf {A}}))) + \hat {\mathbf {H}} _ {\mathbf {i}} ^ {\mathbf {A}},
+$$
+
+where  $\mathrm{GELU}(\cdot)$  denotes the GELU activation function, and  $\mathbf{i}$  is the block index, starting from 1. PDFformer has  $K$  PDFformer blocks in the encoding path, followed by a bottleneck stage, which is also a PDFformer block. These blocks are interconnected via downsampling, implemented through a  $4\times 1$  convolution with a stride of 2 and channel doubling. This process yields an output of  $\mathbf{H}_{\mathbf{K} + 1}^{\mathbf{A}}\in$
+
+$\mathbb{R}^{\frac{L}{2K}\times 2^K C}$ . Following the bottleneck, the decoding path contains  $K$  PDFformer blocks, with upsampling and channel reduction applied between blocks. The first two blocks halve the number of channels, while the remaining blocks quarter them, as in [25]. Upsampling is achieved using a  $2\times 1$  transposed convolution with a stride of 2. Additionally, each block in the decoding path takes the output from the previous block and concatenates it with the corresponding output from the encoding path of the same spatial size. The final output,  $\mathbf{H}^{\mathbf{A}}\in \mathbb{R}^{L\times 2C}$ , passes through a convolutional layer with a residual connection to the input histograms and a softmax function to produce the corrected color or CIELab histograms  $\mathbf{H}_{\mathbf{c}}^{\mathbf{A}}\in \mathbb{R}^{L\times 3}$  as:
+
+$$
+\mathbf {H} _ {\mathrm {c}} ^ {\mathbf {A}} = \operatorname {S O F T M A X} \left(\operatorname {C o n v} _ {3 \times 1} \left(\mathbf {H} _ {2 \mathrm {K} + 1} ^ {\mathbf {A}}\right) + \mathbf {H} _ {0} ^ {\mathbf {A}}\right). \tag {2}
+$$
+
+# 3.2. Target model — sRGBformer
+
+To achieve a color-calibrated correction, we employ sRGBformer, a vision transformer designed to address color deviations. It systematically processes input features  $\mathbf{X}_0$  to generate the final WB-corrected image. Similar to PDFformer, sRGBformer employs a U-shaped transformer architecture with upsampling and downsampling. However, it uniquely integrates cross-modality knowledge from auxiliary models, using their corrected global color information as guidance. To enable this, we introduce our proposed Interactive
+
+Channel Attention (ICA) in each sRGBformer block, incorporating auxiliary model knowledge through dedicated pathways. Each sRGBformer block consists of two sets of LN, ICA, and an MLP, structured as follows:
+
+$$
+\hat {\mathbf {X}} _ {\mathbf {i}} = \operatorname {I C A} (\ln (\mathbf {X} _ {\mathbf {i} - \mathbf {1}})) + \mathbf {X} _ {\mathbf {i} - \mathbf {1}}; \tag {3}
+$$
+
+$$
+\mathbf {X} _ {\mathbf {i}} = \operatorname {G E L U} (\operatorname {M L P} (\ln (\hat {\mathbf {X}} _ {\mathbf {i}}))) + \hat {\mathbf {X}} _ {\mathbf {i}},
+$$
+
+where  $\mathbf{X_i}$  is the image features produced by the sRGBformer block at  $i$ -th level. The encoder and decoder each consist of  $K$  sRGBformer blocks, connected via a bottleneck stage with one sRGBformer block. In the encoder, downsampling is achieved using a  $4\times 4$  convolution with a stride of 2 and channel doubling, while the decoder applies upsampling via a  $2\times 2$  transposed convolution with a stride of 2 and channel halving. As in PDFformer, each decoder block receives the output from the previous block, concatenated with the corresponding output from the encoder of the same spatial size. The final decoder output  $\mathbf{X_{2K + 1}}\in \mathbb{R}^{H\times W\times 2C}$  passes through a  $3\times 3$  convolutional layer with a residual connection to the input, producing the final WB-corrected image,  $\mathbf{X_c}\in \mathbb{R}^{H\times W\times 3}$ .
+
+Interactive Channel Attention. The goal of ICA is to facilitate knowledge transfer from auxiliary models to sRGBformer, enhancing WB correction. In sRGBformer, each encoder and decoder block is equipped with an ICA module to correspond to the respective blocks in the encoders and decoders of the auxiliary models. First,  $\mathbf{X}_{\mathrm{i}}$  is condensed
+
+![](images/cbb3ff0b83c41d00a1bf7c82b0173d3179f0e6e159f7b222f16f183168a5fcbd.jpg)  
+Figure 2. The ABC-Former framework consists of two key components:: Auxiliary models (PDFformers) and a Target model (sRG-Bformer). The auxiliary models process sRGB and CIELab histograms to learn color features from different modalities, while the ICA module in the target model integrates this information to generate the final WB correction.
+
+into a vector with one value per channel by global average pooling (Avg.), followed by a convolution and sigmoid activation, generating a channel-wise weighting vector  $\mathbf{W}_{\mathrm{i}}^{\mathrm{T}} \in \mathbb{R}^{1 \times 1 \times C}$  at the  $i$ -th level of the sRGBformer block. Similarly, weighting vectors  $\mathbf{W}_{\mathrm{i}}^{\mathrm{sRGB}}$ ,  $\mathbf{W}_{\mathrm{i}}^{\mathrm{Lab}} \in \mathbb{R}^{1 \times 1 \times C}$  are extracted by feeding  $\mathbf{H}_{\mathrm{i}}^{\mathrm{sRGB}}$  and  $\mathbf{H}_{\mathrm{i}}^{\mathrm{Lab}}$  into the CA module within their corresponding PDFformer's blocks, which include the average pooling  $\mathrm{Avg}(\cdot)$ , convolution, the unsqueeze operation, and the excitation operation (sigmoid activation) at the  $i$ -th level. Next, to integrate cross-modal knowledge, we apply cross-modal re-parameterization [26], introducing learnable parameters  $\lambda_{\mathrm{i}}^{\mathrm{sRGB}}$  and  $\lambda_{\mathrm{i}}^{\mathrm{Lab}}$  to adjust  $\mathbf{W}_{\mathrm{i}}^{\mathrm{sRGB}}$  and  $\mathbf{W}_{\mathrm{i}}^{\mathrm{Lab}}$ , respectively. These are then combined with  $\mathbf{W}_{\mathrm{i}}^{\mathrm{T}}$  along the channel dimension to obtain  $\mathbf{W}_{\mathrm{total}}$  as:
+
+$$
+\mathbf {W} _ {\mathbf {i}} ^ {\mathbf {T}} = \text {S i g m o i d} (\mathbf {C o n v} (\operatorname {A v g} (\mathbf {X} _ {\mathbf {i}}))) \tag {4}
+$$
+
+$$
+\mathbf {W} _ {\mathrm {i}} ^ {\text {t o t a l}} = \mathbf {W} _ {\mathrm {i}} ^ {\mathrm {T}} + \lambda_ {\mathrm {i}} ^ {\text {L a b}} \mathbf {W} _ {\mathrm {i}} ^ {\text {L a b}} + \lambda_ {\mathrm {i}} ^ {\text {s R G B}} \mathbf {W} _ {\mathrm {i}} ^ {\text {s R G B}}.
+$$
+
+At last,  $\mathbf{X_i}$  is channel-wise re-weighted by  $\mathbf{W_i^{total}}$  to gen-
+
+erate the refined sRGB features  $\tilde{\mathbf{X}}_{\mathrm{i}}$  as:
+
+$$
+\tilde {\mathbf {X}} _ {\mathbf {i}} = \mathbb {F} _ {\text {s c a l e}} \left(\mathbf {W} _ {\mathbf {i}} ^ {\text {t o t a l}}, \mathbf {X} _ {\mathbf {i}}\right), \tag {5}
+$$
+
+where  $\mathbb{F}_{scale}(\cdot, \cdot)$  represents the channel-wise multiplication function, applying scalar weights to the corresponding feature maps. Through ICA, we leverage calibrated global color information from modality-specific histogram-based features, enabling effective knowledge transfer for improved WB correction.
+
+# 3.3. Loss Function
+
+The proposed framework optimizes two auxiliary models and one target model. Specifically, two auxiliary PDF-formers process histogram inputs in a PDF format from either the sRGB or CIELab domains, while the target model, sRGBformer, is responsible for the final WB sRGB output. The cooperative interaction between the auxiliary and target models is crucial for achieving accurate WB in the output sRGB image. To train the auxiliary models, we use L2 loss
+
+to measure the difference between the PDFs of the predicted and ground-truth color channel histograms, formulated as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {p d f}} ^ {s R G B} = \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {R}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {R}} \right\| _ {2} + \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {G}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {G}} \right\| _ {2} + \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {B}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {B}} \right\| _ {2}; \\ \mathcal {L} _ {\mathrm {p d f}} ^ {L a b} = \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {L}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {L}} \right\| _ {2} + \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {a}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {a}} \right\| _ {2} + \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {b}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {b}} \right\| _ {2}, \tag {6} \\ \end{array}
+$$
+
+where  $\mathbf{H}_{\mathrm{c}}^{\mathrm{sRGB}} = [\mathbf{H}_{\mathrm{c}}^{\mathrm{R}};\mathbf{H}_{\mathrm{c}}^{\mathrm{G}};\mathbf{H}_{\mathrm{c}}^{\mathrm{B}}]$  and  $\mathbf{H}_{\mathrm{c}}^{\mathrm{Lab}} = [\mathbf{H}_{\mathrm{c}}^{\mathrm{L}};\mathbf{H}_{\mathrm{c}}^{\mathrm{a}};\mathbf{H}_{\mathrm{c}}^{\mathrm{b}}]$  denote the corrected RGB and CIELab histograms, respectively, as estimated by PDFformers.  $\mathbf{H}_{\mathrm{gt}}^{\mathrm{sRGB}}$  and  $\mathbf{H}_{\mathrm{gt}}^{\mathrm{Lab}}$  represent the ground-truth histograms. We adopt L2 loss as it penalizes large deviations more heavily, encouraging the model to align histogram bins across the distribution evenly.
+
+For sRGBformer, we use the L1 loss for training, as follows:
+
+$$
+\mathcal {L} _ {\mathrm {r e c}} = \left\| \mathbf {X} _ {\mathbf {c}} - \mathbf {X} _ {\mathbf {g t}} \right\| _ {1}, \tag {7}
+$$
+
+where  $\mathbf{X}_{\mathbf{c}}$  is the estimated WB image produced by sRGBformer, and  $\mathbf{X}_{\mathbf{gt}}$  is the ground truth. The total loss is defined as  $\mathcal{L}_{\mathrm{total}} = \mathcal{L}_{\mathrm{pdf}}^{sRGB} + \mathcal{L}_{\mathrm{pdf}}^{Lab} + \mathcal{L}_{\mathrm{rec}}$ .
+
+# 4. Experimental Results
+
+Datasets. The commonly used public dataset, the Rendered WB dataset Set1 [3], is divided into three non-overlapping folds. For training, we randomly selected 12,000 rendered sRGB images with different WB settings from two of the folds. For testing, we use the third fold of Set1, also known as Set1-Test (21,046 images), as well as other datasets that have no overlap in scenes or cameras with the training data: Set2 of the Rendered WB dataset (2,881 images) [3] and the Rendered Cube+ dataset (10,242 images) [3, 6]. These datasets serve as benchmarks to evaluate the WB correction performance of our ABC-Former.
+
+Evaluation Metrics. We evaluated our results using three widely used metrics: Mean Squared Error (MSE), Mean Angular Error (MAE), and  $\Delta E$  2000 [13], which quantify the differences between the predicted WB images and the ground truth. For each metric, we reported the mean, first quantile (Q1), median (Q2), and upper quantile (Q3) of the error. Lower values in these metrics indicate better WB correction performance, consistent with those used in recent works [2, 3, 5, 18, 19].
+
+Implementation Details. We implemented ABC-Former using PyTorch. During training, we optimize both the auxiliary and target models simultaneously over 350 epochs using the Adam optimizer [17] with  $\beta_{1} = 0.5$  and  $\beta_{2} = 0.999$  for each model. The learning rate is set to  $2 \times 10^{-4}$ , and the embedding feature dimension to 16. For training, we randomly cropped four  $128 \times 128$  patches from each training image as input. Additionally, we apply geometric transformations, including rotation and flipping, to augment the data.
+
+Quantitative Experimental Results. The quantitative results in Table 1 show that ABC-Former performs favorably against five SOTA methods [2, 3, 5, 18, 19] across three
+
+public benchmark datasets [3, 6]. The compared methods were evaluated using either their publicly available pretrained models or results directly cited from their respective publications. However, SWBNet [19] was retrained to be tested on the Set1-Test and Set2 datasets, as its code and original results for these datasets were not provided (marked with * in Table 1). SWBNet's scores on the Cube+ Dataset were taken from the original paper. On the Rendered WB Dataset Set1-Test and Set2, ABC-Former achieved the best performance on MSE, MAE, and  $\Delta E$  2000, indicating that it effectively removes color casts from images and achieves superior WB correction. On the Rendered Cube+ dataset, ABC-Former also delivered superior results, with the lowest mean scores in MSE, MAE, and  $\Delta E$  2000. Additionally, it maintains a competitive model size, only larger than Deep-WB [2] and Mixed-WB [5]. These results demonstrate ABC-Former's efficiency in achieving efficient WB correction across various datasets without significantly increasing model complexity, showcasing its robustness and generalization capabilities.
+
+Qualitative Experimental Results. We present the qualitative comparison results on the Rendered WB and Rendered Cube+ datasets in Figure 3 and Figure 4. Analyzing the color correction performance of different methods, we see that while KNN [3], Deep-WB [2], Mixed-WB [5], and WBFlow [18] generally reduce color casts, they often exhibit color inconsistencies across different regions of the image. For example, in Figure 3, these methods tend to correct the colors of objects while neglecting the sky's color accuracy, resulting in an undesirable yellow tint. Similarly, in Figure 4, strong color casts lead to suboptimal WB correction, often leaving the image with an overall blue or yellow tone. In contrast, our method, guided by corrected global color information from multiple modalities, achieves a more balanced and consistent color correction across the entire image, producing natural and harmonious results.
+
+In addition, Figure 5 demonstrates a comparative analysis of global color distribution accuracy in the average WB results across different methods. The Bhattacharyya coefficient, as introduced in [16], is employed to measure the similarity between the red, green, and blue histograms of the processed images and those of the ground-truth WB images across three benchmark datasets. This coefficient ranges from 0 to 1, with higher values indicating a closer match to the ground truth color distributions. The results show that ABC-Former achieves a higher similarity compared to other methods. Additionally, the visualization at the bottom of the figure illustrates an example of the color distributions in WB results obtained by the compared methods, highlighting that ABC-Former produces color distributions more consistent with the ground truth.
+
+Ablation Studies. In the ablation studies, we investigated the impact of various combinations of modalities used for
+
+Table 1. The quantitative results of ABC-Former and competing WB methods are evaluated on three public benchmark datasets, including Rendered WB Dataset (Set1-Test and Set2) [3], and Rendered Cube+ Dataset [3, 6]. The best results are highlighted in red, while the second-best results are highlighted in blue.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">MSE ↓</td><td colspan="4">MAE ↓</td><td colspan="4">ΔE 2000 ↓</td><td>Size</td></tr><tr><td>Mean</td><td>Q1</td><td>Q2</td><td>Q3</td><td>Mean</td><td>Q1</td><td>Q2</td><td>Q3</td><td>Mean</td><td>Q1</td><td>Q2</td><td>Q3</td><td>MB</td></tr><tr><td colspan="14">Rendered WB Dataset: Set1-Test (21,046 images) [3]</td></tr><tr><td>KNN [3]</td><td>77.49</td><td>13.74</td><td>39.62</td><td>94.01</td><td>3.06°</td><td>1.74°</td><td>2.54°</td><td>3.76°</td><td>3.58</td><td>2.07</td><td>3.09</td><td>4.55</td><td>21.8</td></tr><tr><td>Deep-WB [2]</td><td>82.55</td><td>13.19</td><td>42.77</td><td>102.09</td><td>3.12°</td><td>1.88°</td><td>2.70°</td><td>3.84°</td><td>3.77</td><td>2.16</td><td>3.30</td><td>4.86</td><td>16.7</td></tr><tr><td>Mixed-WB [5]</td><td>142.25</td><td>26.81</td><td>67.17</td><td>164.66</td><td>4.07°</td><td>2.64°</td><td>3.68°</td><td>5.16°</td><td>4.55</td><td>3.00</td><td>4.15</td><td>5.63</td><td>5.1</td></tr><tr><td>WBFlow [18]</td><td>78.89</td><td>12.99</td><td>35.09</td><td>79.35</td><td>2.67°</td><td>1.73°</td><td>2.39°</td><td>3.24°</td><td>3.13</td><td>1.92</td><td>2.79</td><td>3.94</td><td>30.2</td></tr><tr><td>SWBNet* [19]</td><td>111.62</td><td>20.61</td><td>60.68</td><td>137.91</td><td>4.11°</td><td>2.56°</td><td>3.75°</td><td>5.22°</td><td>4.54</td><td>2.73</td><td>4.16</td><td>5.86</td><td>258.8</td></tr><tr><td>ABC-Former</td><td>20.47</td><td>4.65</td><td>10.02</td><td>21.05</td><td>1.99°</td><td>1.25°</td><td>1.73°</td><td>2.33°</td><td>2.18</td><td>1.38</td><td>1.86</td><td>2.59</td><td>20.2</td></tr><tr><td colspan="14">Rendered WB Dataset: Set2 (2,881 images) [3]</td></tr><tr><td>KNN [3]</td><td>171.09</td><td>37.04</td><td>87.04</td><td>190.88</td><td>4.48°</td><td>2.26°</td><td>3.64°</td><td>5.95°</td><td>5.60</td><td>3.43</td><td>4.90</td><td>7.06</td><td>21.8</td></tr><tr><td>Deep-WB [2]</td><td>124.07</td><td>30.13</td><td>76.32</td><td>154.44</td><td>3.75°</td><td>2.02°</td><td>3.08°</td><td>4.72°</td><td>4.90</td><td>3.13</td><td>4.35</td><td>6.08</td><td>16.7</td></tr><tr><td>Mixed-WB [5]</td><td>188.76</td><td>48.64</td><td>112.32</td><td>219.91</td><td>4.92°</td><td>2.69°</td><td>4.10°</td><td>6.37°</td><td>6.05</td><td>3.45</td><td>4.92</td><td>7.20</td><td>5.1</td></tr><tr><td>WBFlow [18]</td><td>117.60</td><td>31.25</td><td>61.68</td><td>143.90</td><td>3.51°</td><td>1.93°</td><td>2.92°</td><td>4.47°</td><td>4.64</td><td>3.16</td><td>4.07</td><td>5.56</td><td>30.2</td></tr><tr><td>SWBNet* [19]</td><td>219.02</td><td>55.45</td><td>113.98</td><td>236.25</td><td>5.46°</td><td>3.45°</td><td>4.78°</td><td>6.63°</td><td>6.51</td><td>4.39</td><td>5.84</td><td>8.08</td><td>258.8</td></tr><tr><td>ABC-Former</td><td>104.31</td><td>25.55</td><td>58.61</td><td>132.90</td><td>3.39°</td><td>1.87°</td><td>2.73°</td><td>4.30°</td><td>4.56</td><td>2.97</td><td>4.13</td><td>5.63</td><td>20.2</td></tr><tr><td colspan="14">Rendered Cube+ Dataset (10,242 images) [3, 6]</td></tr><tr><td>KNN [3]</td><td>194.98</td><td>27.43</td><td>57.08</td><td>118.21</td><td>4.12°</td><td>1.96°</td><td>3.17°</td><td>5.04°</td><td>5.68</td><td>3.22</td><td>4.61</td><td>6.70</td><td>21.8</td></tr><tr><td>Deep-WB [2]</td><td>80.46</td><td>15.43</td><td>33.88</td><td>74.42</td><td>3.45°</td><td>1.87°</td><td>2.82°</td><td>4.26°</td><td>4.59</td><td>2.68</td><td>3.81</td><td>5.53</td><td>16.7</td></tr><tr><td>Mixed-WB [5]</td><td>161.80</td><td>16.96</td><td>19.33</td><td>90.81</td><td>4.05°</td><td>1.40°</td><td>2.12°</td><td>4.88°</td><td>4.89</td><td>2.16</td><td>3.10</td><td>6.78</td><td>5.1</td></tr><tr><td>WBFlow [18]</td><td>75.39</td><td>14.22</td><td>30.90</td><td>72.91</td><td>3.34°</td><td>1.87°</td><td>2.82°</td><td>4.11°</td><td>4.28</td><td>2.68</td><td>3.77</td><td>5.21</td><td>30.2</td></tr><tr><td>SWBNet [19]</td><td>74.35</td><td>20.46</td><td>40.04</td><td>86.95</td><td>3.15°</td><td>1.33°</td><td>2.09°</td><td>4.12°</td><td>4.28</td><td>2.40</td><td>3.56</td><td>5.09</td><td>258.8</td></tr><tr><td>ABC-Former</td><td>60.60</td><td>12.15</td><td>26.92</td><td>57.20</td><td>2.99°</td><td>1.63°</td><td>2.45°</td><td>3.69°</td><td>3.95</td><td>2.35</td><td>3.40</td><td>4.86</td><td>20.2</td></tr></table>
+
+![](images/c3378122664307760f9e6a413a22ad7619238a7db1f86bea05f23afd572a65da.jpg)
+
+![](images/551cab629c1264d4c5034413d796f07d772303580bd0321e0bc3ef9de370ef9e.jpg)
+
+![](images/69c9b7b603dfb72472638fb5c3629a1a454dae2c9ace30ec0928f92db10b3bb6.jpg)  
+Input
+
+![](images/90b21a6f37be26da2b82d186d668f88fc9a76970239aaf02882730645069fbc3.jpg)
+
+![](images/274b0d8ed5c490dbb989c157e6cd37ba4165830a18f653d82013dcf2c1e3f5eb.jpg)
+
+![](images/9debd5d7045bff73cf6f43ae9b287aa5aa349b99612a69c472fac61f555c7ed0.jpg)  
+KNN
+
+![](images/a8d6b41038be2e3c006563195444320ad8b2f8cb1b0c1b17352152cf76109389.jpg)
+
+![](images/52fe869da81c3a8d34549519c14dd5829523b1f8e1cd5d824fef1f26af155959.jpg)
+
+![](images/212fdce970499e8169dde75fe208fecc2c63f118d5034dc57c0bcd20b4bd2550.jpg)  
+Deep-WB
+
+![](images/4a8103d7ed0d9d2271b26bf02ccc13fea9c3c9e460305ae0abcfc9b43e8c6464.jpg)
+
+![](images/4a7f1af5212f11c2f2a2da4296eb909272aa9df93e68395c2042987e8021674e.jpg)
+
+![](images/a116ce8cadb8fe19d639c1c63f0e2fa9a8df48fba2e99a8804f20bd49da8b763.jpg)  
+Mixed-WB  
+Figure 3. Qualitative comparisons with other sRGB-WB methods on the Rendered WB dataset [3], with the  $\Delta$ E 2000 indicated in the bottom-right corner of each image.
+
+![](images/816bbb8567944e4793334ba775b8e11f7738c51eb1f29c8c2cf843a1a8b1c998.jpg)
+
+![](images/1578e6473e3d4095fc6dc20e95f44b59944d7489d6bab7b7de44d58e920161b2.jpg)
+
+![](images/dba71879c777c4eaa2c389315803fc5fa1d3101f37d0a5fe8ca6be89f8c6d15f.jpg)  
+WBFlow
+
+![](images/6dcc78a119e3152c36728c6f826b20822c372edd29411248d6e2e8f6e6323eb6.jpg)
+
+![](images/61d8524cbfadf25a49d98c82d0001471003fc6001d52d82febe8be9c7fa8fe37.jpg)
+
+![](images/5e84cb823eda855f16fce087b5ca4795849e080d29892d97548f2378fee8f8fa.jpg)  
+Ours
+
+![](images/4c130dcc5f1dcc973e9fde452a1b89ff9d9e210238fe8db29599d8618bcac07b.jpg)
+
+![](images/f4794eb6ce4ff7737ac2b06d6440e95c88f0509c01d628b3e8bcffe08da8291f.jpg)
+
+![](images/069b3937070a01f3592c6d0ba272852ce9fc833a8312857090d40dd911351cdf.jpg)  
+GT
+
+![](images/687b9d42ba6f432d13f1b3edaaa2f1bf690bf6d0b0bb86325878ad1c95cb4593.jpg)  
+Figure 4. Qualitative comparisons with other sRGB-WB methods on the Rendered Cube+ dataset [3, 6], with the  $\Delta$ E 2000 displayed in the bottom-right corner of each image.
+
+![](images/7b18e71146036143bf058e4ad6b666f46af9f089e0d2deea7bb6e19dfa269b42.jpg)  
+Figure 5. Evaluation of the Bhattacharyya coefficient [16] for color histograms across three benchmark datasets [3, 6], showing global color accuracy for red, green, and blue histograms in sRGB-WB methods. ABC-Former achieves more consistent color distributions by leveraging global color temperature features from both sRGB and CIELab histograms.
+
+WB correction on the Rendered Cube+ dataset. We report the mean values across three evaluation metrics, along with model sizes for each combination of auxiliary models. As shown in Table 2, using only the target model (sRGB-former) without additional guidance of global color information from other modalities results in suboptimal WB accuracy. Adding a single auxiliary model (e.g.,  $\mathrm{PDF}_{\mathrm{sRGB}} + \mathrm{sRGB}$  or  $\mathrm{PDF}_{\mathrm{Lab}} + \mathrm{sRGB}$ ) improves WB performance over the target model alone. However, utilizing a single auxiliary model to jointly learn both sRGB and CIELab histograms  $(\mathrm{PDF}_{\mathrm{sRGB:Lab}} + \mathrm{sRGB})$  proves less effective, as a single
+
+model struggles to disentangle the information from both modalities. Our full ABC-Former design leverages global color temperature features from multiple modalities through two auxiliary models to guide color adjustment, achieving the highest WB accuracy. To ensure a fair comparison across these combinations, we matched the model size to that of ABC-Former by doubling the bottleneck channels in sRGBformer (Baseline) and evenly increasing channels across layers when using a single auxiliary model.
+
+Table 3 compares different loss functions that train auxiliary models for learning sRGB and CIELab histograms.
+
+Table 2. Ablation studies of ABC-Former w/ and w/o guidance from different modalities on the Rendered Cube+ dataset [3, 6]. Here, sRGB denotes sRGBformer, while  $\mathrm{PDF}_{\mathrm{sRGB}}$ , and  $\mathrm{PDF}_{\mathrm{Lab}}$  represent auxiliary PDFformer models for sRGB and CIELab histograms, respectively.  
+
+<table><tr><td>Modalities</td><td>MSE ↓</td><td>MAE ↓</td><td>ΔE 2000 ↓</td><td>Size(MB)</td></tr><tr><td>sRGB</td><td>76.56</td><td>3.35°</td><td>4.31</td><td>20.4</td></tr><tr><td>PDFLab + sRGB</td><td>73.35</td><td>3.26°</td><td>4.20</td><td>20.4</td></tr><tr><td>PDFsRGB + sRGB</td><td>68.65</td><td>3.12°</td><td>4.08</td><td>20.4</td></tr><tr><td>PDFsRGB:Lab + sRGB</td><td>72.38</td><td>3.38°</td><td>4.38</td><td>20.4</td></tr><tr><td>PDFsRGB + PDFLab + sRGB</td><td>60.60</td><td>2.99°</td><td>3.95</td><td>20.2</td></tr></table>
+
+Table 3. Ablation studies on the loss function used to train auxiliary models for learning sRGB and CIELab histograms. We compare the KL divergence, Wasserstein distance, and our chosen L2 loss on the Rendered Cube+ dataset [3, 6].  
+
+<table><tr><td>Loss function</td><td>MSE ↓</td><td>MAE ↓</td><td>ΔE 2000 ↓</td><td>Size(MB)</td></tr><tr><td>KL divergence</td><td>72.67</td><td>3.29°</td><td>4.17</td><td>20.2</td></tr><tr><td>Wasserstein distance</td><td>70.22</td><td>3.12°</td><td>4.15</td><td>20.2</td></tr><tr><td>L2 loss (Proposed)</td><td>60.60</td><td>2.99°</td><td>3.95</td><td>20.2</td></tr></table>
+
+Table 4. WB manipulation on the Rendered Cube+ dataset [3, 6].  
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">MSE ↓</td><td colspan="4">MAE ↓</td><td colspan="4">ΔE 2000 ↓</td></tr><tr><td>Mean</td><td>Q1</td><td>Q2</td><td>Q3</td><td>Mean</td><td>Q1</td><td>Q2</td><td>Q3</td><td>Mean</td><td>Q1</td><td>Q2</td><td>Q3</td></tr><tr><td>Deep-WB [2]</td><td>199.38</td><td>32.30</td><td>63.34</td><td>142.76</td><td>5.40°</td><td>2.67°</td><td>4.04°</td><td>6.36°</td><td>5.98</td><td>3.44</td><td>4.78</td><td>7.29</td></tr><tr><td>ABC-Former</td><td>82.37</td><td>0.01</td><td>17.76</td><td>65.36</td><td>2.78°</td><td>1.06°</td><td>2.85°</td><td>3.22°</td><td>2.89</td><td>0.07</td><td>2.36</td><td>4.12</td></tr></table>
+
+![](images/26fbe8e8784e5c94a3f3e9baf308d5e9b90f3978887521261dadca03bdd8f7ed.jpg)  
+Figure 6. Analysis on learned weights on Rendered Cube+ dataset [3, 6],  $\lambda_{\mathbf{i}}^{\mathbf{sRGB}}$  and  $\lambda_{\mathbf{i}}^{\mathbf{Lab}}$ , for cross-modality knowledge transfer. Here,  $i \in \{e_0, e_1, e_2, b_0, d_0, d_1, d_2\}$  represents the level of the sRGBformer block, where  $e, b,$  and  $d$  denote the encoder, bottleneck, and decoder layers, respectively.
+
+As can be seen, the L2 loss shows better performance compared to KL divergence and Wasserstein distance, at
+
+tributed to its stability and effectiveness in aligning histograms. In contrast, KL divergence may encounter issues with zero-probability bins, and Wasserstein distance can be non-smooth and challenging to optimize in high-dimensional spaces.
+
+Analyzing Learned Weights for Cross-Modality Transfer. We present the learned weights,  $\lambda_{\mathrm{i}}^{\mathrm{sRGB}}$  and  $\lambda_{\mathrm{i}}^{\mathrm{Lab}}$ , at each level of ABC-Former to illustrate how modality-complementary knowledge guides WB correction. As shown in Figure 6, the influence of calibrated global color information from sRGB and CIELab histogram modalities intensifies toward the bottleneck block, peaking at the bottleneck. This indicates that high-level WB color histogram-based features from both modalities, capturing global, semantically rich color information, are crucial for reweighting sRGB image features for accurate WB correction. Notably, the sRGB histogram modality has a slightly greater impact than CIELab, though the difference is minimal. This suggests that both color modalities collaborate effectively, allowing ABC-Former to balance raw color intensity with perceptually uniform CIELab properties.
+
+WB Manipulation. Following the setup described in [2], we conduct experiments to alter the input image's colors to match the target white balance (WB) settings. These settings correspond to the following color temperatures: tungsten  $(2850\mathrm{K})$ , fluorescent  $(3800\mathrm{K})$ , daylight  $(5500\mathrm{K})$ , cloudy  $(6500\mathrm{K})$ , and shade  $(7500\mathrm{K})$ . As shown in Table 4, ABC-Former significantly outperforms Deep-WB [2] in achieving accurate color transformations.
+
+# 5. Conclusion
+
+We presented ABC-Former, an Auxiliary Bimodal Cross-domain Transformer that enhances sRGB WB correction by leveraging complementary information from multiple modalities. ABC-Former uses Interactive Channel Attention to facilitate cross-modality knowledge transfer, integrating calibrated color features from both sRGB and CIELab histograms. This multimodal approach enables a more nuanced fusion of color information, allowing the model to handle diverse color temperatures and complex scenes with pronounced color shifts. Extensive experiments have demonstrated that ABC-Former consistently outperforms state-of-the-art methods in both quantitative and qualitative evaluations. For future work, extending into 2D histograms is a promising direction.
+
+# 6. Acknowledgments
+
+This paper was supported in part by the National Science and Technology Council, Taiwan, under grants NSTC 113-2221-E-004-001-MY3, 113-2622-E-004-001, 113-2221-E-004-006-MY2, 112-2634-F-002-005, 113-2634-F-002-008, and 113-2923-E-A49-003-MY2.
+
+# References
+
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+[2] Mahmoud Afifi and Michael S Brown. Deep white-balance editing. In CVPR, 2020. 2, 3, 5, 6, 8  
+[3] Mahmoud Afifi, Brian Price, Scott Cohen, and Michael S Brown. When color constancy goes wrong: Correcting improperly white-balanced images. In CVPR, 2019. 1, 2, 3, 5, 6, 7, 8  
+[4] Mahmoud Afifi, Jonathan T Barron, Chloe LeGendre, Yun-Ta Tsai, and Francois Bleibel. Cross-camera convolutional color constancy. In ICCV, 2021. 2  
+[5] Mahmoud Affi, Marcus A Brubaker, and Michael S Brown. Auto white-balance correction for mixed-illuminant scenes. In WACV, 2022. 2, 3, 5, 6  
+[6] Nikola Banić, Karlo Koščević, and Sven Lončarić. Unsupervised learning for color constancy. arXiv preprint arXiv:1712.00436, 2017. 5, 6, 7, 8  
+[7] Jonathan T Barron and Yun-Ta Tsai. Fast fourier color constancy. In CVPR, 2017. 2  
+[8] Simone Bianco and Claudio Cusano. Quasiunsupervised color constancy. In CVPR, 2019.  
+[9] Jonathan Cepeda-Negrete and Raul E Sanchez-Yanez. Gray-world assumption on perceptual color spaces. In PSIVT, 2014. 2  
+[10] Jiankang Deng, Jia Guo, Niannan Xue, and Stefanos Zafeiriou. Arcface: Additive angular margin loss for deep face recognition. In CVPR, 2019. 1  
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+[12] Jun Fu, Jing Liu, Hajjie Tian, Yong Li, Yongjun Bao, Zhiwei Fang, and Hanqing Lu. Dual attention network for scene segmentation. In CVPR, 2019. 1  
+[13] Sharma Gaurav. The ciede2000 color-difference formula: Implementation notes, supplementary test data,
+
+and mathematical observations. COLOR research and application, 2005. 5  
+[14] Jie Hu, Li Shen, and Gang Sun. Squeeze-andexcitation networks. In CVPR, 2018. 3  
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+[16] Thomas Kailath. The divergence and bhattacharyya distance measures in signal selection. IEEE transactions on communication technology, 1967. 5, 7  
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+[18] Chunxiao Li, Xuejing Kang, and Anlong Ming. WBFlow: Few-shot white balance for sRGB images via reversible neural flows. In IJCAI, 2023. 2, 3, 5, 6  
+[19] Chunxiao Li, Xuejing Kang, Zhifeng Zhang, and Anlong Ming. SWBNet: a stable white balance network for sRGB images. In AAAI, 2023. 2, 5, 6  
+[20] Yi-Chen Lo, Chia-Che Chang, Hsuan-Chao Chiu, Yu-Hao Huang, Chia-Ping Chen, Yu-Lin Chang, and Kevin Jou. CLCC: Contrastive learning for color constancy. In CVPR, 2021. 2  
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+# AC3D: Analyzing and Improving 3D Camera Control in Video Diffusion Transformers
+
+Sherwin Bahmani $^{1,2,3}$  Ivan Skorokhodov $^{3}$  Guocheng Qian $^{3}$  Aliaksandr Siarohin $^{3}$  Willi Menapace $^{3}$  Andrea Tagliasacchi $^{1,4}$  David B. Lindell $^{1,2}$  Sergey Tulyakov $^{3}$
+
+<sup>1</sup>University of Toronto <sup>2</sup>Vector Institute <sup>3</sup>Snap Inc. <sup>4</sup>SFU
+
+*equal contribution
+
+https://snap-research.github.io/ac3d
+
+![](images/b817cae749f12438e773bb976adf99e6f8b2a973ab4df38ce66da003d63efb02.jpg)
+
+![](images/52516c7173e4846a6846b007e2a90e43104163aca0143472ddbef4ba84c1276e.jpg)  
+Figure 1. Camera-controlled video generation. Our method enables precise camera controllability in pre-trained video diffusion transformers, allowing joint conditioning of text and camera sequences. We synthesize the same scene with two different camera trajectories as input. The inset images visualize the cameras for the videos in the corresponding columns. The left camera sequence consists of a rotation to the right, while the right camera visualizes a zoom-out and up trajectory.
+
+![](images/511171fd4800824ac854c98baa2d66ee98e1865662ef20852b5d5958d8527144.jpg)
+
+# Abstract
+
+Numerous works have recently integrated 3D camera control into foundational text-to-video models, but the resulting camera control is often imprecise, and video generation quality suffers. In this work, we analyze camera motion from a first principles perspective, uncovering insights that enable precise 3D camera manipulation without compromising synthesis quality. First, we determine that motion induced by camera movements in videos is low-frequency in nature. This motivates us to adjust train and test pose conditioning schedules, accelerating training convergence while improving visual and motion quality. Then, by probing the representations of an unconditional video diffusion transformer, we observe that they implicitly perform camera pose estimation under the hood, and only a sub-partion of their layers contain the camera information. This suggested us to limit the injection of camera conditioning to a subset of the
+
+architecture to prevent interference with other video features, leading to a  $4 \times$  reduction of training parameters, improved training speed, and  $10\%$  higher visual quality. Finally, we complement the typical dataset for camera control learning with a curated dataset of 20K diverse, dynamic videos with stationary cameras. This helps the model distinguish between camera and scene motion and improves the dynamics of generated pose-conditioned videos. We compound these findings to design the Advanced 3D Camera Control (AC3D) architecture, the new state-of-the-art model for generative video modeling with camera control.
+
+# 1. Introduction
+
+Foundational video diffusion models (VDMs) trained on internet-scale data, acquire abundant knowledge about the physical world [10]. They not only learn appearance and
+
+plausible 2D dynamics, but they also have abundant understanding of 3D structure [7]. However, most of this knowledge is stored implicitly within the model, as these models do not expose fine-grained control mechanisms, such as camera motion control. We recently witnessed a surge of works that bring 3D camera control into foundational video models [39, 149, 166], but the control they provide is not very precise, and the synthesis quality is often compromised [6]. We analyze camera motion control in video diffusion models from first principles, and develop several findings that allow us to incorporate precise 3D camera conditioning without degrading synthesis quality. To perform our analysis we train a 11.5B-parameter VDiT (video latent diffusion transformer) [100] on a dataset of 100M text/video pairs. On this model, we perform three key studies. With what we learn, we adapt the camera control solution from VD3D [6] from a pixel-based to latent-based diffusion model, and significantly improve its performance.
+
+1) The spectral properties of camera motion. To study the statistical nature of motion control, we analyze motion spectral volumes (MSV) [75] of the videos generated by a large-scale video DiT model. MSVs show the amount of energy in different portions of the frequency spectra (i.e., high energy in the low frequencies indicate smooth motion) and we measure them across 200 generated videos of different types (camera motion, scene motion, scene plus camera motion) and at various stages of the denoising synthesis process. We observe that camera motion mostly affects the lower portion of the spectrum and kicks in very early ( $\approx 10\%$ ) in the denoising trajectory. Then, as diffusion models are inherently coarse-to-fine in nature [25], we restrict our camera conditioning to only being injected on the subset of the denoising steps corresponding to low-frequencies. This results in  $\approx 15\%$  higher visual fidelity,  $\approx 30\%$  better camera following, and mitigates scene motion degradation.
+
+2) Camera motion knowledge in VDiTs. Then, we consider our text-only VDiT, and determine whether such a model possesses knowledge about cameras, and where this knowledge is expressed within its architecture. With this objective, we feed the (unseen during training) RealEstate10k [199] videos to our VDiT, and perform linear probing [27] to determine if camera poses can be recovered from its internal representation. Our analysis revealed that a video DiT implicitly performs camera pose estimation under the hood, and the presence of camera knowledge in a disentangled form peaks in its middle layers. This implies that the camera signal emerges in its early blocks to allow the later ones rely on it to build subsequent visual representations. Therefore, we adjust our conditioning scheme to only affect the first  $30\%$  of the architecture, leading to a  $\approx 4\times$  reduction in training parameters,  $15\%$  training and inference acceleration, and  $10\%$  improved visual quality.
+
+3) Re-balancing the training distribution. Finally, to supervise camera control architectures, the typical solution is to rely on the camera pose annotations provided by RealEstate10k [199]. However, this dataset contains mostly static scenes, which results in significant motion degradation of the fine-tuned video model. To overcome this problem, we curate a subset of 20K diverse videos with dynamic scenes but static cameras. As the camera conditioning branch is still activated for these videos, this helps the model disambiguate the camera from scene movement. Our experiments show that this simple adjustment in the data is sufficient to recover the scene dynamism while still enabling an effective pose-conditioned video model.
+
+Contributions. We compound the knowledge gained from these three studies into the design of the Advanced 3D Camera Control (AC3D) method. We perform extensive ablation studies and compare against state-of-the-art models for camera control, including MotionCtrl [149], CameraCtrl [39], and VD3D [6]. We demonstrate  $18\%$  higher video fidelity and  $25\%$  more precise camera steering in terms of quantitative metrics than a closest competitor, and our generated videos are favored to others in  $90\%$  of cases.
+
+# 2. Related work
+
+Our approach lies at the intersection of text-to-video, text-to-3D, and text-to-4D generation approaches. We refer to recent state-of-the-reports [101, 180] for a more thorough analysis of previous work.
+
+Text-to-video generation. Our approach builds on recent advancements in 2D video diffusion models. One prominent technique in this area enhances text-to-image models by adding temporal layers to support video generation [7, 8, 37, 119, 151]. While these methods use the U-Net architecture, more recent ones [10, 92, 93, 168] have been adapting transformer-based architectures for more scalable, realistic, and highly dynamic scene generation. We are interested in controlling the camera movements during the generation process of recent transformer-based video models based on precise camera extrinsics, i.e., cameras represented as rotation and translation sequences for each frame.
+
+4D generation. Early 4D generation works [2, 164] used 4D GANs to learn category-specific generators with an underlying dynamic 3D representation. More recent approaches [4, 5, 81, 120, 196] have tackled 4D generation by distilling motion priors from pre-trained video diffusion models into an explicit 4D representation, enabling category-agnostic 4D generation. Follow-up works investigate image or video conditioned 4D generation [33, 76, 81, 98, 109, 173, 182, 193, 196] instead of pure text inputs, improving flexibility in the generation process. While most of these works are object-centric, recent approaches [4, 159] shifted towards more complex scenes, including methods [23, 175] which
+
+![](images/7d90716174ed6253fcc66d5f7b61f599bd5530253f95e75ce8956865a8007427.jpg)  
+Figure 2. VDiT-CC model with ControlNet [71, 188] camera conditioning built on top of VDiT. Video synthesis is performed by large 4,096-dimensional DiT-XL blocks of the frozen VDiT backbone, while VDiT-CC only processes and injects the camera information through lightweight 128-dimensional DiT-XS blocks (FC stands for fully-connected layers); see Section 3.2 for details.
+
+model the background. However, all these methods are optimization-based, i.e., each scene is generated independently from scratch. Recently, L4GM [110] proposes a feed-forward 4D generator trained on object-centric synthetic 4D data. While these approaches are explicit and provide space-time control, they are limited in their photorealism compared to recent 2D video diffusion models. We investigate dynamic 3D scene generation from a different perspective by extending pre-trained video diffusion models with 3D camera control.
+
+Camera control for video models. Recently, there has been significant progress in adding camera control to video diffusion models. As the pioneering work, MotionCtrl [149] learns camera control by conditioning pre-trained video models [7, 17] with extrinsic matrices. Follow-up works [39, 65, 160] further improve the conditioning mechanisms by representing cameras as Plücker coordinates. Another line of work [49, 50, 82, 155] controls camera motion without training additional parameters. However, all of these approaches use U-Net-based architectures as their backbone. More recently, 4DiM [150] trains a space-time diffusion model from scratch for novel view synthesis from a single image input. Closely related to our work, VD3D [6] incorporates camera control into a pre-trained video diffusion transformer. While the motion and camera control improves over U-Net-based approaches, the synthesized motion in the scenes and the visual quality are still degraded compared to the base video model. In contrast to VD3D, we first thoroughly investigate the pre-trained base video model and its knowledge of camera motion. We derive an improved training and architecture design for high-quality and dynamic video generation based on our findings.
+
+Concurrent works. Concurrent approaches [68, 158, 177, 185, 194, 195] further improve camera control in U-Net-based architectures, while another work [22] tackles video diffusion transformer. However, the scene and visual quality
+
+is still limited in that approach. DimensionX [127] controls space and time in video diffusion transformers but the camera trajectories are pre-defined and not continuous. Chun-Hao et al. [51] explore pose estimation with a video DiT by pairing it with DUSt3R [145] and fine-tuning, while we perform linear probing without any training to assess its existing camera knowledge. CAT4D [152] proposes a multi-view video diffusion model fine-tuned from a multi-view model.
+
+# 3. Method
+
+We first describe our base video diffusion model (Sec. 3.1), and the baseline camera control method built on top of it (Sec. 3.2). Then, we proceed with the analysis of motion (Sec. 3.3), linear probing (Sec. 3.4) and dataset biases (Sec. 3.5), and additional insights on how to build an effective model for camera control (Sec. 3.6)
+
+# 3.1. Base model (VDiT)
+
+Following Sora [10], most modern foundational text-to-video generators use the diffusion framework [45, 122] to train a large-scale transformer [139] in the latent space of a variational autoencoder [64, 111]. We adopt the same design and, for a base video model, pre-train an 11.5B-parameter Video DiT model [100] with 32 blocks of hidden dimension 4,096 for text-to-video generation. We use the rectified flow diffusion parametrization [85] and learn in the latent space of CogVideoX [168] (using an autoencoder with a 16-channel output and compression factors of  $4 \times 8 \times 8$  in the temporal and spatial dimensions). The T5 [108] encoder produces text embeddings, which are passed into VDiT via cross-attention. We train our base model on a large-scale dataset of images and videos with text annotations, with resolutions ranging from  $17 \times 144 \times 256$  to  $121 \times 576 \times 1024$ . This design is fairly standard and followed by many existing works with little deviation [32, 102, 168, 197]; we describe our specific architectural and training setup in detail in Appendix D.
+
+# 3.2. VDiT with Camera Control (VDiT-CC)
+
+To construct a baseline architecture for camera control, we implement ControlNet [18, 188] conditioning on top of the VDiT. Similar to previous work [6, 39, 149], we use the RealEstate10k [199] dataset, consisting of  $65\mathrm{k}$  (text, video, camera trajectory) triplets  $(\pmb{t}_n,\pmb{x}_n,\pmb{c}_n)_{n = 1}^N$  and train a new set of model parameters to input the camera information into the model. Camera trajectories  $\pmb {c}\in \mathbb{R}^{f\times 25}$  are provided in the form of camera extrinsics  $\pmb {C_f}\in \mathbb{R}^{4\times 4}$  and intrinsics  $\pmb {K}_f\in \mathbb{R}^{3\times 3}$  for each  $f$ -th frame  $\pmb{x}_f$ .
+
+Camera conditioning. For base camera control, we adapt VD3D [6] since it was designed for transformer-based models and suits our setup the most, while other methods are built on top of UNet-based [112] backbones. We use Plücker camera representations [6, 16, 39, 59, 121], which are projected to the same dimensionality and resolution as the video tokens via a fully-convolutional encoder to produce camera tokens. These camera tokens are processed by a sequence of lightweight DiT-XS blocks with hidden dimension 128 and four attention heads each. To mix the camera information with the video tokens of VDiT, we use summation before each main DiT block. We also found it useful to perform cross-attention from video tokens to camera tokens as a form of a feedback connection [71]. We illustrate this model architecture, which we call VDiT-CC, in Figure 2; see implementation details in Appendix D. VDiT-CC describes the camera-controlled video model architecture used by AC3D, while AC3D describes our proposed work including analysis and additional adjustments based on the analysis.
+
+Training. Keeping the VDiT backbone frozen, we train the new parameters with a rectified flow objective [85] and standard (location of 0 and scale of 1) logit-normal noise distribution [28]. Similar to prior works [6, 150], we apply a  $10\%$  camera dropout to support classifier-free guidance (CFG) [44] later. Notably, we train VDiT-CC only at the  $256^2$  resolution: since camera motion is a low-frequency type of signal (which can be observed at lower resolutions) and the main VDiT backbone is frozen, we found that our design generalizes to higher resolutions out-of-the-box. During inference, we input text prompts and camera embeddings with classifier-free guidance at each time step.
+
+Model behavior. This baseline model, being built on top of our powerful VDiT, already achieves decent-quality camera control. However, it struggles with degraded visual quality and reduced scene motion, and sometimes, the camera control inputs are ignored. To improve the design, we analyze our VDiT backbone to understand how camera motion is modeled and represented. Then, we inspect VDiT-CC's failure cases and where they arise to address them.
+
+![](images/84e1ccc3b8c3684156cda0c6e94f1b00f3bf0f68361b47b1471f204f9c75627a.jpg)  
+Figure 3. Average magnitude of motion spectral volumes along spatial, temporal offset, and video batch dimensions for scenes with different motion types. We compute the flow of each video in a sliding window manner with temporal offsets and average the frequencies across all offsets. Videos with camera motion (purple) exhibit stronger overall motion than the videos with scene motion (orange), especially for the low-frequency range, suggesting that the motion induced by camera transitions is heavily biased towards low-frequency components. Frequency refers to the temporal frequency.
+
+# 3.3. How is camera motion modeled by diffusion?
+
+We start by analyzing how camera motion is modeled by a pre-trained video diffusion model (i.e., before camera control is incorporated). We hypothesize that the motion induced by changes in camera pose is a low-frequency type of signal and investigate the motion spectral volumes [75] of the generated videos at different steps of the denoising process. To perform this analysis, we generate 200 diverse videos with our VDiT model with 80 denoising steps and manually annotate them into four categories: videos with only scene motion, videos with only camera motion, videos with both scene and camera motion, and others; see Appendix E for details. During generation, we save the denoised predictions at each denoising step and estimate optical flow to compute the motion spectral volumes.
+
+Analysis. We visualize motion spectral volumes with  $95\%$  confidence intervals in Figure 3. Videos with camera motion exhibit higher amplitudes than scene-motion-only videos for low-frequency components while having similar characteristics for high-frequency ones. This supports the conjecture that the camera motion is a low-frequency type of signal. We also depict an example of a generated video with both scene and camera motion with four denoising steps on Fig. 4a: one can observe that the camera movement has been fully produced by  $t = 0.9$  (first  $10\%$  of the rectified flow denoising process). In contrast, scene motion details like the hand movements of the subjects are not finalized even till  $t = 0.5$ .
+
+Inspired by this finding, we pose the question: when exactly does a video diffusion model determine the camera pose? To answer this question, we plot aggregated spectral volumes for different timesteps in Figure 4b. We also show the ratio with respect to the last timestep  $t = 0$  (i.e.,
+
+![](images/8693ddc1f716218a31172eb0176c0cf1659c7715d807548d77bc27c89b978dc5.jpg)  
+(a) A generated video at different diffusion timesteps. The camera has already been decided by the model even at  $t = 0.9$  (first  $10\%$  of the denoising process) and does not change after that.
+
+![](images/9ea73aaf19caa9d407640a1ed89c9115a7296f0e1cb9290812cc347eaa8c3e6c.jpg)  
+(b) Motion spectral volumes of VDiT's generated videos for different diffusion timesteps (left) and their ratio w.r.t. the motion spectral volume at  $t = 0$  (i.e., a fully denoised video).  
+Figure 4. How camera motion is modeled by diffusion? As visualized in Figure 4a and Figure 3, the motion induced by camera transitions is a low-frequency type of motion. We observe that a video DiT creates low-frequency motion very early in the denoising trajectory: Figure 4b (left) shows that even at  $t = 0.96$  (first  $\approx 4\%$  of the steps), the low-frequency motion components have already been created, while high frequency ones do not fully unveil even till  $t = 0.5$ . We found that controlling the camera pose later in the denoising trajectory is not only unnecessary but detrimental to both scene motion and overall visual quality.
+
+![](images/23e1a2904a69fcdbc58bb5274bf44241e2989333975124d4518225d74c2d0e4e.jpg)
+
+when all motion has been generated). We then inspect when different types of motion appear during the denoising process. Figure 4b (right) shows that the low-frequency motion components fill up to  $\approx 84\%$  at  $t = 0.9$  (the first  $10\%$  of the denoising process), while high-frequency components are not well-modeled until  $t = 0.6$ .
+
+An immediate consequence of this observation is that trying to control the camera later in the denoising trajectory is simply unnecessary and will not influence the manipulation result. In this way, instead of using the standard logit-normal noise level distribution of SD3 [28] with a location of 0.0 and scale of 1.0 (which we use by default for VDiT), we switch to using truncated normal with a location of 0.8 and scale of 0.075 on the [0.6, 1] interval to cover the early steps of the denoising rectified flow trajectory. At inference time, we apply camera conditioning on the same [0.6, 1] interval. Surprisingly, we observe that not using truncation is detrimental to the scene motion and overall visual quality. Following this insight, we restrict both our train-time noise levels and test-time camera conditioning schedules to cover only the first  $40\%$  of the reverse diffusion trajectory. As Sec. 4.3 shows, this improves FID and FVD by  $14\%$  on average, and camera following by  $30\%$  on MSR-VTT (the dataset used to measure generalization to diverse, out-of-fine-tuning-distribution scenes). Further, truncated noise sampling enhances the overall scene motion.
+
+# 3.4. What does VDiT know about camera pose?
+
+Foundational video models acquire rich knowledge about the physical world, and we hypothesize that they store information about the camera pose within their representations. To investigate this, we perform linear probing of our base VDiT model on the RealEstate10k [199] dataset (not seen
+
+during training) for camera extrinsics.
+
+Specifically, we take 1,000 random 49-frame videos from RealEstate10K, feed them into VDiT under 8 noise levels  $(1/8, 2/8, \dots, 1)$ , and extract the activations for all 32 DiT blocks. Next, we split the random videos into 900 train and 100 test videos and train a linear ridge regression model to predict the rotation pitch/yaw/roll angles and translation vectors for the entire viewpoint trajectory  $(49 \times 6$  target values in total). This results in  $8 \times 32$  trained models, and we report the rotation and (normalized) translation errors [39] on a held-out test set of 100 videos in Figure 5. Surprisingly, VDiT can accurately predict the camera pose, achieving minimum test errors of  $\approx 0.025$  for rotation and for  $\approx 0.48$  translation prediction. The knowledge quality increases around layer #9 and peaks in the range of #13-21. We reason that since the camera information in block #13 is stored in such a disentangled manner, then the model is using it to build other representations; hence, conditioning the camera in this block is risky and unnecessary and would interfere with other visual features, as shown in our ablations. In this way, we propose to input the camera conditioning only in the first #8 blocks and leave the remaining 24 DiT blocks unconditioned. We find in Section 4.3 that this not only reduces the number of trainable parameters by  $\approx 4$  times and improves training speed by  $\approx 15\%$ , but also enhances the visual quality by  $\approx 10\%$ .
+
+# 3.5. Mitigating training data limitations
+
+Estimating camera parameters from in-the-wild videos remains challenging, as leading methods like [114, 115, 145, 192] frequently fail when processing videos containing dynamic scene content. This limitation results in camera-annotated datasets being heavily biased
+
+![](images/81ea02059ff1477dd730701760e70616e713378dad921b2c3c191cac9198b885.jpg)  
+Figure 5. Video DiT is secretly a camera pose estimator. We perform linear probing of camera poses in each of VDiT blocks for various noise levels and observe that video DiT performs pose estimation under the hood. Its middle blocks carry the most accurate information about the camera locations and orientations, which indicates that the camera signal emerges in the early layers to help the middle and late blocks render other visual features aligned with the viewpoint.
+
+![](images/5b13402e9380f67cf4a5cc2290fae66fa5179e151f60267cd7fe2a1dbed59fa5.jpg)
+
+toward static scenes, which is particularly evident in RealEstate10K (RE10K) [199], the predominant dataset for training camera-controlled video models [6, 39, 149]. We hypothesize that models fine-tuned on such data interpret camera position information as a signal to suppress scene dynamics. This bias persists even when jointly training on unconstrained 2D video data [150], because the camera conditioning branch is only activated when camera parameters are available, which occurs exclusively for static scenes from RE10K, as static scenes remain the only reliable source for accurate camera annotation.
+
+To address this fundamental limitation, we propose an alternative approach: rather than attempting to annotate dynamic scenes, which proved unsuccessful in our extensive preliminary research, even with state-of-the-art methods [145], we curate a collection of 20K diverse videos featuring dynamic scenes captured by stationary cameras (see Figure 6). With stationary cameras, the camera position is inherently known, (we can assign fixed arbitrary extrinsic), allowing us to maintain active camera conditioning during training. This approach enables the camera conditioning branch to remain active during training while exposing the model to dynamic content, helping it distinguish between viewpoint conditioning and scene stillness. On top of this secondary dataset, following [150], we remove the scale ambiguity in RE10K by leveraging an off-the-shelf metric depth estimator; see Appendix H. Our experiments in Sec. 4.3 demonstrate that this straightforward yet effective data curation strategy successfully mitigates the distributional limitations of RE10K, restoring much of the lost scene dynamics, while maintaining precise camera control.
+
+# 3.6. Miscellaneous improvements
+
+In addition to our core analysis, we introduce several auxiliary techniques that enhance model performance.
+
+Separate text and camera guidance. Text and camera signals require different guidance weights due to their dis
+
+![](images/68916703f5541477f8f661f8e721d18c59c45cea7bc6d959220446f4f42366a8.jpg)  
+Figure 6. RealEstate10k [199] videos (upper 2 rows) contain diverse camera trajectories, but are strongly biased towards static scenes. To mitigate this bias and also increase the concepts diversity, we curate 20K videos with stationary cameras, but dynamic content (lower 2 rows). Such datasets are easy to construct, and surprisingly effective. Section 4.3 shows that integrating the dataset into our training improves visual quality on out-of-distribution prompts by  $17\%$ .
+
+tinct nature, motivating us to separate their classifier-free guidance (CFG) [9, 44]. We formulate the equation as:
+
+$$
+\begin{array}{l} \hat {s} (\boldsymbol {x} \mid \boldsymbol {t}, \boldsymbol {c}) = (1 + w _ {y} + w _ {c}) s _ {\theta} (\boldsymbol {x} \mid \boldsymbol {t}, \boldsymbol {c}) \tag {1} \\ - w _ {y} s _ {\theta} (\boldsymbol {x} | \boldsymbol {c}) - w _ {c} s _ {\theta} (\boldsymbol {x} | \boldsymbol {t}), \\ \end{array}
+$$
+
+where  $\hat{s}(.)$  denotes the final update direction used during synthesis,  $s_{\theta}$  represents the model's predicted update direction,  $\pmb{t}$  and  $\pmb{c}$  are text and camera conditions, and  $w_{y}$  and  $w_{c}$  are their respective CFG weights. We zero-out the tensor for unconditional generation.
+
+ControlNet with feedback. Traditional ControlNet [188] conditioning, used in recent camera control methods [6, 39, 149], only processes conditioning signals without accessing the main branch. Our experiments show that using a bidirectional ControlNet produces better camera representations.
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">Human Preference</td></tr><tr><td>CA</td><td>MQ</td><td>TA</td><td>VQ</td><td>Overall</td></tr><tr><td>Ours vs. VD3D (FIT)</td><td>89.5%</td><td>79.0%</td><td>87.5%</td><td>97.5%</td><td>95.0%</td></tr><tr><td>Ours vs. VD3D (DiT)</td><td>65.0%</td><td>87.5%</td><td>83.5%</td><td>95.0%</td><td>92.5%</td></tr></table>
+
+Table 1. User study. We compare our approach to the original VD3D (FIT) and reimplemented VD3D (DiT) on top of our base model. We conduct a user study where participants indicate their preference based on camera alignment (CA), motion quality (MQ), text alignment (TA), visual quality (VQ), and overall preference (Overall).
+
+This modification behaves as a feedback mechanism [71] provided by the main synthesis branch to the camera processing branch.
+
+Dropping context in the camera branch. Applying cross-attention over the context information (text prompts, resolution, etc.) in the camera DiT-XS blocks worsens visual quality and camera steering due to harmful interference of the context embeddings with camera representations.
+
+# 4. Experiments
+
+Datasets. Our base VDiT model was trained on a large-scale dataset of text-annotated images and videos. VDiT-CC is fine-tuned from VDiT on RealEstate10K [199], contains  $\approx 65\mathrm{M}$  video clips with per-frame camera parameters since it is the setup used by existing methods [6, 39, 149].
+
+Metrics. To assess the performance, we rely on a wide range of automatic quantitative metrics. We use FID [43], FVD [136], and CLIP score [42] to evaluate visual quality, and rotation and normalized translation errors [39] of ParticleSfM [192]-reconstructed trajectories to assess camera steerability. We evaluate them both on RE10K and MSR-VTT [161], since the latter allows to assess zero-shot generalization on out-of-distribution data. Moreover, we conduct a user study with details in the appendix in Sec. J.
+
+# 4.1. Baselines
+
+We select three camera-control methods: MotionCtrl [149], CameraCtrl [39], and VD3D [6]. MotionCtrl and CameraCtrl use a UNet-based video diffusion backbone [37], while VD3D builds on top of FIT [21, 93] and as such, is easily extendable to our video DiT [100] setup. Hence, we re-implement VD3D on top of our VDiT model to obtain an additional "VD3D+DiT" baseline. Moreover, we provide comparisons for an open-source model, i.e., CogVideoX [169]. See Sec. C of the appendix for more details.
+
+# 4.2. Main results
+
+We present quantitative comparisons with the baselines in Tab. 2. One can observe that just switching from the 4B-
+
+parameter pixel-space FIT [21] backbone, employed by the original VD3D approach, to our larger 11.5B-parameter latent-space DiT yields clear improvements across most metrics. Next, the results demonstrate that AC3D establishes a new state-of-the-art in performance against all baselines. Evaluating the quality of camera motion from still images is difficult, so we instead visualize all qualitative results in the website provided within our supplementary material. Therein, we can observe that AC3D better follows pose conditioning and achieves higher visual fidelity. We conduct user studies against VD3D+FIT (the original model) and VD3D+DiT (our improved re-implementation on top of the bigger video transformer). The results are presented in Table 1: AC3D outperforms them across all qualitative aspects, achieving a  $90\%+$  overall preference score. Finally, we encourage the reader to assess the visual quality by observing videos on our website.
+
+# 4.3. Ablations
+
+No camera conditioning. The first ablation we conduct is to drop all camera conditioning, which makes the model equivalent to the vanilla VDiT. This is needed to understand the degradation of visual quality and text alignment. The results (Tab. 2, row w/o camera cond) show that our model loses less only  $\approx 7\%$  of the original visual fidelity on MSR-VTT (as measured by FVD), while (as expected) greatly improving on its in-domain RE10K data. In comparison, VD3D-DiT (the closest baseline) loses  $\approx 20\%$  of its visual fidelity on MSR-VTT.
+
+Importance of biasing the noise towards higher levels. As Sec. 3.3 shows, we use the truncated normal distribution with location of 0.8 and scale of 0.075 with the [0.6, 1] bounds for training AC3D. We ablate the importance of biasing the noise sampling towards high noise and observe higher motion, visual quality, and camera controllability.
+
+Importance of truncating the noise schedule. We change the training and inference procedure by using no truncation during noise sampling. Instead, we condition the model with camera inputs over the whole noise range and observe decreased visual quality.
+
+No camera guidance. We assess the importance of classifier-free guidance [44] on the camera conditioning in Tab. 2 (w/o camera CFG). It attains the same visual quality on both indistribution (RE10K) and out-of-distribution (MSR-VTT) data, but degrades camera following, resulting in  $\approx 5\%$  worse pose reconstruction errors.
+
+Training without our data with scene motion. To understand how well our curated data with scene motion but stationary cameras mitigates static scene bias, we train AC3D exclusively on RE10K, and report the results in Tab. 2 (w/o our dynamic data). The model maintains similar visual quality and text alignment on RE10K (in-domain data), but
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">RealEstate10K [199]</td><td colspan="5">MSR-VTT [161]</td></tr><tr><td>TransErr ↓</td><td>RotErr ↓</td><td>FID ↓</td><td>FVD ↓</td><td>CLIP ↑</td><td>TransErr ↓</td><td>RotErr ↓</td><td>FID ↓</td><td>FVD ↓</td><td>CLIP ↑</td></tr><tr><td>MotionCtrl (U-Net)</td><td>0.477</td><td>0.094</td><td>2.99</td><td>61.70</td><td>26.46</td><td>0.593</td><td>0.137</td><td>16.85</td><td>283.12</td><td>24.11</td></tr><tr><td>CameraCtrl (U-Net)</td><td>0.465</td><td>0.089</td><td>2.48</td><td>55.64</td><td>26.81</td><td>0.587</td><td>0.132</td><td>12.33</td><td>201.33</td><td>25.05</td></tr><tr><td>VD3D (FIT)</td><td>0.409</td><td>0.043</td><td>1.40</td><td>42.43</td><td>28.07</td><td>0.504</td><td>0.050</td><td>7.80</td><td>165.18</td><td>26.89</td></tr><tr><td>VD3D (CogVideoX)</td><td>0.467</td><td>0.063</td><td>1.66</td><td>43.14</td><td>28.08</td><td>0.501</td><td>0.068</td><td>7.45</td><td>148.11</td><td>27.65</td></tr><tr><td>AC3D (CogVideoX) (ours)</td><td>0.374</td><td>0.039</td><td>1.27</td><td>38.20</td><td>28.62</td><td>0.431</td><td>0.039</td><td>5.52</td><td>116.04</td><td>28.38</td></tr><tr><td>MotionCtrl (VDiT)</td><td>0.504</td><td>0.126</td><td>1.74</td><td>43.81</td><td>27.69</td><td>0.589</td><td>0.146</td><td>9.92</td><td>150.20</td><td>27.25</td></tr><tr><td>CameraCtrl (VDiT)</td><td>0.513</td><td>0.138</td><td>1.62</td><td>42.10</td><td>27.73</td><td>0.566</td><td>0.143</td><td>8.15</td><td>146.77</td><td>27.51</td></tr><tr><td>VD3D (VDiT)</td><td>0.421</td><td>0.056</td><td>1.21</td><td>38.57</td><td>28.34</td><td>0.486</td><td>0.047</td><td>6.88</td><td>137.62</td><td>27.90</td></tr><tr><td>AC3D (VDiT) (ours)</td><td>0.358</td><td>0.035</td><td>1.18</td><td>36.55</td><td>28.76</td><td>0.428</td><td>0.038</td><td>5.34</td><td>110.71</td><td>28.58</td></tr><tr><td>w/o camera cond</td><td>+0.233</td><td>+0.153</td><td>+4.02</td><td>+53.83</td><td>-1.63</td><td>+0.266</td><td>+0.157</td><td>-0.48</td><td>-8.53</td><td>+0.35</td></tr><tr><td>w/o biasing noise</td><td>+0.093</td><td>+0.015</td><td>+0.02</td><td>+1.78</td><td>-0.32</td><td>+0.138</td><td>+0.033</td><td>+0.59</td><td>+16.92</td><td>-0.54</td></tr><tr><td>w/o noise truncation</td><td>+0.020</td><td>-0.003</td><td>+0.06</td><td>+1.69</td><td>-0.20</td><td>+0.016</td><td>+0.005</td><td>+0.76</td><td>+6.63</td><td>-0.18</td></tr><tr><td>w/o camera CFG</td><td>+0.014</td><td>+0.004</td><td>+0.49</td><td>+4.57</td><td>-0.54</td><td>+0.025</td><td>+0.003</td><td>+0.03</td><td>+1.42</td><td>-0.27</td></tr><tr><td>w/o our dynamic data</td><td>-0.005</td><td>-0.004</td><td>-0.06</td><td>+0.22</td><td>-0.20</td><td>+0.004</td><td>-0.001</td><td>+0.89</td><td>+4.40</td><td>-0.55</td></tr><tr><td>w/o metric scaled data</td><td>+0.013</td><td>+0.005</td><td>+0.17</td><td>+4.65</td><td>0.00</td><td>+0.023</td><td>+0.002</td><td>-0.01</td><td>0.00</td><td>-0.12</td></tr><tr><td>w/o dropping camera context</td><td>+0.013</td><td>+0.001</td><td>+0.04</td><td>+2.46</td><td>-0.65</td><td>+0.029</td><td>+0.003</td><td>+1.25</td><td>+7.41</td><td>-0.36</td></tr><tr><td>w/o limiting camera cond to 8 blocks</td><td>-0.001</td><td>+0.001</td><td>+0.09</td><td>+0.56</td><td>-0.02</td><td>+0.003</td><td>0.000</td><td>+0.32</td><td>+9.23</td><td>-0.33</td></tr><tr><td>w/ 2D training</td><td>+0.129</td><td>+0.068</td><td>+2.60</td><td>+33.85</td><td>-1.17</td><td>+0.128</td><td>+0.093</td><td>-0.26</td><td>-3.83</td><td>+0.21</td></tr></table>
+
+Table 2. Quantitative evaluation. We evaluate all the models using camera pose and visual quality metrics based on unseen camera trajectories. We compute translation and rotation errors based on the estimated camera poses from generations using ParticleSfM [192]. We evaluate both in-distribution performance with RealEstate10K [199] and out-of-distribution performance with MSR-VTT [161].
+
+performance on out-of-distribution samples from MSR-VTT worsens ( $\approx 17\%$  worse FID and  $\approx 4\%$  worse FVD). The quality of scene motion is better assessed by referring to our qualitative video comparisons in the supplementary.
+
+Importance of metric scaled cameras. We train AC3D using the original RE10K's camera parameters without our scaling procedure and present the results in Tab. 2 (w/o metric scaled data). This is a more ambiguous conditioning signal, and results in worse visual quality ( $\approx 10\%$  FVD on RE10K) and camera following performance ( $\approx 12\%$  worse trajectory reconstruction).
+
+Providing context into the camera branch. As discussed in Sec. 3.6, we chose not to input the context information (text embeddings, resolution conditioning, etc.) into the camera branch to avoid potential interference with the camera representations. As Tab. 2 (w/o dropping camera context) shows, providing this information indeed results in  $\approx 4\%$  worse camera following and  $\approx 15\%$  lower visual quality.
+
+Importance of limiting conditioning to the first 8 VDiT blocks. Following our insights in Sec. 3.4, we condition AC3D only in the first 8 blocks. Trying to condition in all the 32 DiT blocks (w/o limiting camera cond to 8 blocks) worsens the visual quality by  $\approx 10\%$ , while keeping the quality control at the same level. This suggests that the middle and late VDiT layers indeed rely on processed camera information and conditioning them on external camera poses might lead to interference with other visual features.
+
+Joint training with 2D data. To mitigate visual quality and scene motion degradation, we attempted to perform joint fine-tuning on 2D video data (without camera annotations)
+
+which was used in base VDiT training by applying dropout on camera inputs for it. Prior work shows performance benefits with this strategy [150] and, as Tab. 2 (with  $2D$  training) shows, it indeed helps to maintain slightly higher visual fidelity in our case ( $\approx 3\%$  better FVD on MSR-VTT). However, camera steering severely deteriorates, leading to up to  $3\times$  worse results for translation/rotation errors.
+
+# 5. Conclusions
+
+Our findings demonstrate that principled analysis of camera motion in video diffusion models leads to significant improvements in control precision and efficiency. Through enhanced conditioning schedules, targeted layerspecific camera control, and better-calibrated training data, AC3D achieves state-of-the-art performance in 3D camera-controlled video synthesis while maintaining high visual quality and natural scene dynamics. This work establishes a foundation for more precise and efficient camera control in text-to-video generation. We discuss the limitations of our approach in Appendix B. In future work, we plan to focus on further improving data limitations and developing control mechanisms for camera trajectories far outside of the training distribution.
+
+# 6. Acknowledgements
+
+DBL acknowledges support from NSERC under the RGPIN program, the Canada Foundation for Innovation, and the Ontario Research Fund.
+
+# References
+
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+# ACAttack: Adaptive Cross Attacking RGB-T Tracker via Multi-Modal Response Decoupling
+
+Xinyu Xiang Qinglong Yan Hao Zhang* Jiayi Ma* Wuhan University, China
+
+xiangxinyu@whu.edu.cn, qinglong_yan@whu.edu.cn, zhpersonalbox@gmail.com, jyma2010@gmail.com
+
+# Abstract
+
+The research on adversarial attacks against trackers primarily concentrates on the RGB modality, whereas the methodology for attacking RGB-T multi-modal trackers has seldom been explored so far. This work represents an innovative attempt to develop an adaptive cross attack framework via multi-modal response decoupling, generating multi-modal adversarial patches to evade RGB-T trackers. Specifically, a modal-aware adaptive attack strategy is introduced to weaken the modality with high common information contribution alternately and iteratively, achieving the modal decoupling attack. In order to perturb the judgment of the modal balance mechanism in the tracker, we design a modal disturbance loss to increase the distance of the response map of the single-modal adversarial samples in the tracker. Besides, we also propose a novel spatio-temporal joint attack loss to progressively deteriorate the tracker's perception of the target. Moreover, the design of the shared adversarial shape enables the generated multi-modal adversarial patches to be readily deployed in real-world scenarios, effectively reducing the interference of the patch posting process on the shape attack of the infrared adversarial layer. Extensive digital and physical domain experiments demonstrate the effectiveness of our multi-modal adversarial patch attack. Our code is available at https://github.com/Xinyu-Xiang/ACAttack.
+
+# 1. Introduction
+
+The adversarial attack on visual object tracking (VOT) [1, 26] aims to mislead the prediction results of the tracker through the generated adversarial disturbance, find the model vulnerabilities, and then promote the security of the tracking model in real-life. Single-modal tracking attack methods have been extensively studied, but with the wide application of multi-modal devices [19, 20, 24], multimodal trackers are widely used in safety-critical real-world
+
+![](images/c344516e1824eddade6022528581e550f426aeec60e7d6e47551d4607884a8b0.jpg)  
+Figure 1. Our attack strategy against RGB-T trackers. An adaptive attack strategy, sensitive to modality, is introduced to alternately and iteratively suppress the modality with a high contribution of shared information. Additionally, a modal disturbance loss is crafted to enlarge the response map distance for single-modal adversarial samples within the tracker.
+
+fields such as autonomous driving and urban security [16].
+
+To address the urgent need to explore the security of trackers, adversarial attack techniques for trackers have emerged in rapid succession, including traditional gradient-based attack approaches and deep-network-based attacks. The former methods [10, 11] utilize hand-crafted parameters and apply many times of gradient ascent to maximize an adversarial loss function for misguiding deep networks. Although it can achieve certain attack effects for specific types of trackers, it is challenging to comprehensively explore and attack the potential vulnerabilities of the different trackers due to the limitations of inflexible pattern design. Nonetheless, the latter one [6] applies tremendous data to train an adversarial patches-generator including flexible architectures and optimization strategies to better automatically search for model weaknesses and realize tracker attacks. Therefore, in comparison with a traditional gradient-based attack approach, deep-network-based paradigm can more automatically and flexibly excavate the security issues within the tracker.
+
+Although prior efforts for adversarial attack methods are effective in interference trackers, several challenges still need to be addressed. Notably, existing adversarial attack methods [5, 15, 25] on tracking are designed for RGB modality, whereas the methodologies for attacking RGB-T multi-modal trackers are less explored so far. Considering the widespread deployment of multi-modal tracking technology [17, 27, 28] in several safety-critical areas, it is urgent to explore and implement adversarial attacks of multimodal tracking to understand the potential vulnerabilities of the trackers. However, as shown in Fig. 1, the unique modal coupling and structural design of RGB-T trackers make it a great challenge to successfully find model vulnerabilities. Firstly, due to the modal equilibrium mechanism and coupled multi-modal information, it is difficult to successfully jam the RGB-T tracking model itself. Specifically, the modal balancing strategy in the multi-modal tracker can effectively prevent the attack of adversarial perturbation in a single modal. Secondly, the coupling of multi-modal information can effectively weaken the attacks against the consensus region of the target. Thirdly, the deployment of patches in the physical world is also challenging because the stacked placement of multi-modal patches has a probability of compromising the expression of infrared adversarial shapes, reducing their synergy performance.
+
+Considering these challenges, we propose ACAttack, an adaptive cross attack framework via multi-modal response decoupling. It aims to generate multi-modal adversarial patches to evade RGB-T trackers in both digital and physical domains. Specifically, this framework can gradually and adaptively optimize, discover plenty of rough adversarial samples, and then map them to the high-dimensional adversarial space of different modalities according to the modal response contribution factor, forming multi-modal adversarial patches. Secondly, a modal-aware adaptive attack strategy is introduced to weaken tracker's deep semantic attention to the modality with high common information contribution according to the contribution degree of modal response alternately and iteratively, achieving the modal decoupling attack. When the contributions of two modalities are similar, we design a modal disturbance loss to search the modal imbalance vulnerabilities of the tracker, expand the distance of the response map of the single-modal adversarial samples in the tracker, and perturb the judgment of the balance modal in the tracker. We also design a spatio-temporal joint attack loss to build progressively enlarged pseudo-GT between consecutive frames, which progressively deteriorates the tracker's perception of the target. Thirdly, the design of the shared adversarial shape is deployed to eliminate the interference of visible patches on the expression of infrared adversarial shapes. After the shape is shared, it can not only reduce the consumption of the adversarial shape's inter-modal attack ability but also realize
+
+attacks other than texture in the visible modal.
+
+In summary, we make the following contributions:
+
+- We make an innovative attempt to propose an adaptive cross attack framework via multi-modal response decoupling. It can generate multi-modal adversarial patches to mislead RGB-T trackers effectively.  
+- We develop a novel modal attack flow, in which modal-aware adaptive attack strategy and modal attack constraints alternately disturb the modes with high contribution to achieve modal decoupling and destroy modal balance mechanism of tracker, respectively.  
+- We design the shape-shared stack strategy to linkage the visible and infrared adversarial shapes, reducing the attack consumption of multi-modal patches mutual deployment in physical scenarios.  
+- Experimental results show that multi-modal patches can efficiently fool RGB-T trackers in standard RGB-T tracking datasets and real scenes.
+
+# 2. Related Work
+
+# 2.1. Visual Object Tracking
+
+Given the tracked object in the first frame, object tracking aims to recognize and locate the object in subsequent frames. Many RGB tracking methods [2, 7, 14, 18, 21] have been proposed and achieved commendable tracking performance. However, RGB sensors struggle to capture objects effectively under challenging conditions such as occlusion and low light, limiting the performance of RGB trackers. To address this, the RGB-T tracking paradigm is introduced, which is not restricted to a single RGB modality but instead integrates the complementary information from both RGB and thermal modalities. This fusion enables more robust tracking capabilities. ViPT [29] introduces a vision prompt tracking framework that leverages the foundational model with strong representation capabilities, enabling interaction between the thermal and RGB modalities through a modality-complementing prompter. BAT [3] proposes a universal bidirectional adapter, which enables mutual prompt between the thermal and RGB modalities and further improves tracking performance. SDSTrack [9] designs a complementary masked patch distillation strategy based on self-distillation learning, which enhances the tracking robustness in extreme weather.
+
+# 2.2. Adversarial Attacks
+
+Currently, adversarial attacks in the tracking task primarily target RGB trackers. For instance, APYVOT [4] proposes an optimization objective function with a dual-attention mechanism to generate perturbations, disrupting tracking by interfering solely with the initial frame. MTD [8] introduces a maximum textural discrepancy loss function that misleads the visual trackers by decorrelating the template
+
+![](images/89724a5020b0aa2d41c2cccabb03770003a311051704048345ec27280933c31c.jpg)
+
+![](images/51abf7b5b1b9ea20cd809cc7842a0f6369b3ce07abf87277bc899e287d84adda.jpg)  
+Figure 2. The overall framework of our ACAttack.
+
+and search frame at hierarchical feature scales. These methods, however, fail to disrupt the significant feature enhancement resulting from the interactions between RGB and thermal modalities, which limits their effectiveness against RGB-T trackers. Therefore, it is essential to develop the attack strategy specifically designed for RGB-T tracking.
+
+# 3. Methodology
+
+# 3.1. Coarse-to-Fine Modality Attack Framework
+
+With the help of the progressive modality information integration strategy, the multi-modal trackers gradually strengthen the common scene representation and target response, thereby achieving a robust tracking performance superior to that of the single-modal trackers. Consequently, a coarse-to-fine architecture is designed to progressively degrade the modality integration capability of RGB-T models named ACAAttack, which can be divided into two stages. The overall architecture of our ACAAttack is illustrated in Fig. 2 and Algorithm 1. First, we employ projected gradient descent (PGD) in stage1 to identify a set of adversarial examples  $\{p_i\}_{i=1}^k$  with sufficient aggressiveness, narrowing the search space for refined attacks and increasing the likelihood of discovering strong adversarial examples, formulated as:
+
+$$
+\left\{p _ {i} \right\} _ {i = 1} ^ {k} = P G D \left(p _ {i} ^ {\text {i n i t}}\right), \tag {1}
+$$
+
+where  $p_i^{init}$  is randomly initialized with noise patches. The generated patches are subsequently loaded onto the visible image  $I_{vi}$  to form a visible adversarial sample  $I_{vi}^{adv}$ . This
+
+process can be formulated as follows:
+
+$$
+I _ {v i} ^ {a d v} = p _ {i} \odot M + I _ {v i} \odot (1 - M), \tag {2}
+$$
+
+where  $M$  is the binary mask for applying adversarial patch.  $\odot$  represents the element-wise Hadmard product. The adversarial visible image  $I_{vi}^{adv}$  concat with clean infrared image  $I_{ir}$  are sent to RGB-T tracker  $T(\cdot)$  to predict final bounding box  $Bbox_{pred}$  of target, which is expressed as:
+
+$$
+B b o x _ {p r e d} = T \left(I _ {v i} ^ {a d v}, I _ {i r}\right). \tag {3}
+$$
+
+We optimize this process by minimizing the conventional attack loss  $L_{att}$  relative to the center point, which is defined as:
+
+$$
+L _ {a t t} = - \left\| \left(C p (B b o x _ {p r e d}) - C p (B b o x _ {g t})\right) \right\| _ {2} ^ {2}, \tag {4}
+$$
+
+where  $C_p$  denotes the operator to obtain the center point of bounding box  $Bbox$ . Specifically, when the attack loss  $L_{att}$  reaches a predefined threshold, the iteration is halted, and a rough adversarial sample is generated. This process is repeated  $k$  times to generate a set of  $k$  rough adversarial samples. Considering the different imaging principles of infrared and visible modalities, the multi-modal patches will be specially designed according to their differences in principles. Specifically, the visible modal mainly employs the attack texture to interfere. For the infrared modal, it is difficult to detect the texture, so the adversarial shape is used to attack. Subsequently, the set of adversarial samples generated in the coarse attack stage (stage1) is fed into the
+
+subsequent fine attack process (stage2) for further refinement, resulting in the generation of multi-modal adversarial patches with strong attack performance. Finally, through continuous iterative optimization, the multi-mode patch will share the same attack shape, while the visible patch will also possess adversarial texture to confuse the tracker. The fine-grained attack phase targets the modality of the multi-modal tracker and consists of modal decoupling attacks and modal balance interference, which will be detailed in the subsequent sections.
+
+# 3.2. Modal Decoupling Attack
+
+The RGB-T tracker implicitly couples the contributions of the two modalities, thereby enhancing tracking accuracy. Given the significant role of modal contribution in the tracker, we propose a modal decoupling attack to adaptively diminish the influence of advantageous modalities. Specifically, we use the coarse adversarial samples from the stage1 as input for the stage2, feeding them simultaneously into the adversarial texture generation network  $G_{tex}^{Adv}$  and the adversarial shape generation network  $G_{shape}^{Adv}$ . For attacking the infrared modality, the rough adversarial sample set from the first stage is encoded into  $r$  dimensions via continuous downsampling and an MLP, controlling the adversarial shape. The infrared patch  $p_{ir}$  generation process can be expressed as follows:
+
+$$
+p _ {i r} = G _ {s h a p e} ^ {A d v} \left(\left\{p _ {i} \right\} _ {i = 1} ^ {k}\right). \tag {5}
+$$
+
+The adversarial texture generation network generates adversarial textures to attack the visible modality using residual connections and upsampling [23], which is defined as:
+
+$$
+p _ {v i} = \left(1 - p _ {i r}\right) \odot G _ {\text {s h a p e}} ^ {\text {A d v}} \left(\left\{p _ {i} \right\} _ {i = 1} ^ {k}\right), \tag {6}
+$$
+
+where the visible patch with adversarial textures is  $p_{vi}$ .
+
+Subsequently, the modal contribution of the current network input is calculated as the reciprocal of the difference between the response map obtained from single-modal data and the response map from dual-modal input. A larger reciprocal distance indicates that the response maps from dual-modal and single-modal inputs are more similar, suggesting a greater contribution from the current single modality to the tracker. The modal response contribution can be expressed as follows:
+
+$$
+c _ {m} = \frac {1}{\operatorname {d i s} (R (m , m) , R (v i , i r))}, \tag {7}
+$$
+
+where  $c_{m}$  represents the contribution value of  $m \in \{vi, ir\}$  modal to the tracker.  $dis$  stands for the distance function and is used to measure the Euclidean distance between response maps.  $R(\cdot, \cdot)$  shows the response map acquired by the tracker under the current input.
+
+To normalize the modal contribution, a softmax operation is applied to the reciprocal distance, yielding the final
+
+Algorithm 1: The ACAcAttack Algorithm  
+Input: Random patches  $p_i^{init}$ , parameters  $k$ ,  $M_{stage1}$ ,  $M_{stage2}$ ,  $\xi$ ,  $\zeta$   
+Output: Optimized multi-modal patches  $p_{vi}, p_{ir}$   
+1 Iteration:  
+2 Initialize a random patch  $p_i^{init}$ ;  
+3  $i = i + 1$ ;  
+4 Iteration:  
+5 Generate  $p_i$  through Eq. (1);  
+6 Use Eq. (2) to generate adversarial sample  $I_{vi}^{adv}$ ;  
+7 Calculate  $Bbox_{pred}$  using Eq. (3);  
+8 Optimize  $PGD(\cdot)$  with Eq. (4);  
+9 Until:  $L_{att} < \xi$  or iter  $\geq M_{stage1}$   
+10 Until:  $i \geq k$   
+11 Determine  $\{p_i\}_{i=1}^k$  after optimization in stage1;  
+12 Iteration:  
+13 iter  $= iter + 1$ ;  
+14 Obtain  $p_{ir}, p_{vi}$  via Eqs. (5) and (6);  
+15 Apply multi-modal patches  $p_{ir}, p_{vi}$  on  $I_{ir}, I_{vi}$ ;  
+16 Calculate  $c_{vi}, c_{ir}$  using Eq. (7);  
+17 Send to Tracker  $T(\cdot)$  to predict bounding box;  
+18 if  $|c_{vi} - c_{ir}| < \zeta$ ;  
+19 Optimize  $G_{shape}^{Adv}$  with Eq. (9);  
+20 elif  $c_{vi} - c_{ir} > \zeta$ ;  
+21 Optimize  $G_{tex}^{Adv}$  with Eqs. (4) and (10);  
+22 elif  $c_{ir} - c_{vi} > \zeta$ ;  
+23 Optimize  $G_{shape}^{Adv}$  with Eqs. (4) and (10);  
+24 Until: iter  $\geq M_{stage2}$
+
+modal contribution score, formulated as:
+
+$$
+c _ {n o r m} = \operatorname {s o f t m a x} \left(c _ {v i}, c _ {i r}\right). \tag {8}
+$$
+
+Finally, an automatic discriminant attack is executed based on the modal contribution score. As illustrated, when the visible contribution is higher in the input data, only the visible modal is attacked, specifically by optimizing the generation of adversarial textures. When the infrared contribution is higher in the input data, only the adversarial shape is modified to attack the infrared modal, thereby reducing its contribution to the tracker. Given that the tracker employs a modal balance mechanism, the contributions of the two modalities may be similar in certain scenarios, as detailed in the subsequent section.
+
+# 3.3. Modal Balance Interference
+
+Previous work on tracking attacks has attempted to design explicit attack losses to detect model vulnerabilities, but this approach often fails to account for the inherent characteristics of the model, making it challenging to execute effective attacks. Inspired by the concept of implicit attacks [25] and the multi-modal aggregation properties in
+
+RGB-T tracker [22], we develop a loss function with modal-balanced interference to target multi-modal trackers. In cases where the contributions of infrared and visible modal are similar (i.e., modal balance), the response map of single-modal input closely resembles that of dual-modal input. To disrupt this balance, we extract the response maps of the two single-modal adversarial examples and increase the distance between them. The details are provided as follows:
+
+$$
+L _ {m i} = - \left\| R \left(v i _ {a d v}, v i _ {a d v}\right) - R \left(i r _ {a d v}, i r _ {a d v}\right) \right\| _ {2} ^ {2}. \tag {9}
+$$
+
+Notably, the infrared and visible patches in our method share the same adversarial shape to achieve simultaneous attacks on both modalities. Therefore, under conditions of modal balance, only the adversarial shape is optimized. Additionally, a spatio-temporal joint attack loss  $L_{st}$  is employed in conjunction with the modal jamming loss  $L_{mi}$  to disrupt the tracker's semantic perception. The specific design is presented in the following formula:
+
+$$
+L _ {s t} = \left\| \sum_ {i = 1} ^ {s} B b o x _ {p r e d} (w, h) - r _ {i} * B b o x _ {g t} (w, h) \right\| _ {2} ^ {2}, \tag {10}
+$$
+
+where  $s$  denotes the consecutive  $s = 5$  frames extracted from a video.  $r_i$  represents the scaling factor over time to construct the pseudo-GT, which is set as [1.90, 1.95, 2.00, 2.05, 2.10].
+
+# 3.4. Implementation Process in Real-world
+
+After completing the digital domain optimization, the multimodal adversarial patches require deployment in the real world. However, during real-world deployment, visible and infrared patches are stacked, leading to inevitable interactions between the two modalities, as illustrated in Fig. 3. Specifically, the coverage of visible patches impacts the adversarial shape expression of infrared patches, while the presence of infrared patches hinders the rendering of the adversarial texture in visible modality. To address these challenges, we propose a shape-shared stacking strategy, where both the visible and infrared patches adopt the same attack shape. This design not only effectively mitigates interactions between infrared and visible patches in the real world but also enhances the attack shapes of visible patches, thereby improving overall attack performance.
+
+# 4. Experiments
+
+# 4.1. Experimental Settings
+
+# 4.1.1. Datasets and Evaluation Metrics
+
+We conduct experiments on RGBT234 [12] and LasHeR [13] datasets and assess the effectiveness of our ACAttack by evaluating precision rate (PR) and success rate (SR), both of which are commonly used metrics in tracking tasks. Taking PR as an example, we
+
+![](images/d470705f12b1b300b95534ddb97c4a2699910e4e6ccda977f227ae26d4cb9532.jpg)
+
+![](images/33fd2f375730bee087e11a98a35e6edcbe43d2da12561454172fedc8fc9231ac.jpg)  
+VI on IR
+
+![](images/f47fed5e15b83cdc966600b10b48230bac13df87d5bf3c7dd049d110db4d9ce1.jpg)
+
+![](images/92e3c6e7196ddfdb7bb345e4c518f60529abae4065d0b6b0eada7eead6b613b9.jpg)  
+IR on VI
+
+![](images/40821a79e64f48b8da64814d87a2c2c1d6b209c40f83b609db0e4879db63ce81.jpg)
+
+![](images/fa0cf77ca4b32b732a765bd36dd7bdfd3dcfd54c3d62ad0c1d21287968a7e519.jpg)  
+Ours
+
+![](images/c883cfd57486865bd20823dd356d172a367ac79998c92b08debea92727b3fbb1.jpg)  
+Figure 3. Process of physical implementation.
+
+![](images/c4eee172f1a63caf416d7705ac5c5a4cb3db0beed313dcc8d3253a8746fc10d4.jpg)  
+(a) ViPT patch  
+Figure 4. Visualization of generated patches.
+
+![](images/1f1cba12750e6777c7d348e11705f7579722488aeb97c43eb0c5ba7f185d8c9c.jpg)  
+(b) BAT patch
+
+![](images/1a25403a0068d4992e805125a13cfebb745348e2e333de0c52b4c0685aebb6dc.jpg)  
+(c) SDSTrack patch
+
+calculate the Euclidean distance of the center between the predicted bounding box and ground truth box in both RGB and thermal modalities, using the smaller distance to represent the precision RGBT234 provides 234 pairs of RGB and thermal video, with a total frame of about  $234\mathrm{K}$  and a maximum of 8K per sequence. LasHeR is comprised of 1224 visible and thermal video pairs, totaling over  $730\mathrm{K}$  frame pairs. Since the tracking performance on the background is not of interest, LasHeR performs strict alignment of the object area, allowing the object to share the same ground truth of the bounding box in both visible and thermal modalities. Therefore, we use PR and SR as evaluation metrics.
+
+# 4.1.2. Victimized Trackers and Comparison Attackers
+
+We select several state-of-the-art trackers as targets for our attack, including ViPT [29], BAT [3], and SDSTrack [9]. To demonstrate the challenges in exploiting vulnerabilities in RGB-T trackers, we use a patch composed of random noise as a baseline for comparison, emphasizing the need for meticulous exploration. Furthermore, we compare the performance of our proposed ACAttack with the representative attack method MTD [8], which is specifically designed
+
+![](images/da6a446625886f71756aead6a4e9fa99c2780b36928a437cb31b58f954fcae24.jpg)  
+(a) ViPT on RGBT234
+
+![](images/1a22cf3b0944a5bec6d422a63b67353ae6f7db902f57bf12db9a0a3abede9e4d.jpg)  
+(b) BAT on RGBT234
+
+![](images/011457f325e1dc34bddb5ac62bfa101a76791122d58e04157c92d3d0388f4432.jpg)  
+(c) SDS on RGBT234
+
+![](images/e522ecd422a23f3740a308ff9c1a063e2cb028f9532ad41a9413cd641d252e86.jpg)  
+Figure 5. Quantitative comparison of tracking performance on the RGBT234 dataset. The tracking performance of ViPT, BAT, and SDSTrack trackers is reported, including the original performance without attacks and the performance under attacks. Lower tracking metrics PR and SR represent better attack. Please zoom in for a better view.  
+Figure 6. Qualitative comparison of tracking performance on the RGBT234 dataset.
+
+for RGB trackers, highlighting the advantages of our approach in the multi-modal setting.
+
+# 4.1.3. Implementation Details
+
+The multi-spectral video in the physical domain is captured by a DJI Mavic 3T UAV equipped with thermal and RGB cameras, and the video frame rate is 30 fps. The hyperparameters in adaptive iteration  $\xi$  and  $\zeta$  is 9 and 0.02. Training epoch in stage1 is set as  $M_{\text{stage1}} = 180$ . Experiments are conducted on the RTX 3090 GPU with PyTorch.
+
+# 4.2. Comparisons in the Digital Domain
+
+We first validate the attack effectiveness of our ACAttack in the digital domain. It is important to note that we only train on the RGBT234 dataset and generate multi-modal patches  $\{p_{vi}, p_{ir}\}$ . As shown in Fig. 4, the RGB patch exhibits color and texture, while the thermal patch has an irregular shape, which aligns with the imaging characteristics of each modality. Subsequently, the patches  $\{p_{vi}, p_{ir}\}$  generated on RGBT234 are directly applied to the LasHeR dataset to verify their generalization.
+
+# 4.2.1.Quantitative Evaluation
+
+Fig. 5 illustrates a quantitative comparison of the RGBT234 dataset. The results clearly show that, under our attack, the tracking performance of existing state-of-the-art trackers suffers a significant degradation compared to clean tracking conditions. In contrast, random noise only leads to a modest decline in PR and SR, emphasizing that exploiting tracker vulnerabilities goes beyond the simplicity of random noise—it requires a more sophisticated, optimized ap
+
+proach. Additionally, the performance drop observed with MTD is smaller than that of our ACAttack, suggesting that attack methods designed specifically for RGB trackers may not effectively mitigate the feature enhancement resulting from RGB-T coupling. On the other hand, our ACAttack achieves substantial attack success. For instance, against ViPT, ACAttack reduces PR from 0.835 to 0.621 and SR from 0.617 to 0.417. Similarly, for SDSTrack, it lowers PR from 0.848 to 0.616 and SR from 0.625 to 0.426. The substantial performance drops suggest that our ACAttack succeeds in keeping the predicted bounding box far away from actual object, which will be further confirmed in subsequent qualitative results.
+
+# 4.2.2. Qualitative Evaluation
+
+As shown in Fig. 6, we present the tracking results of BAT and SDSTrack. The clean trackers perform exceptionally well in maintaining precise tracking, while our attack leads to a significant decline in tracking performance. This degradation can be attributed to our progressive generation framework, which iteratively weakens the tracker's deep semantic attention on modalities with high commonality by decoupling multi-modal responses.
+
+# 4.3. Generalization Evaluation
+
+We conduct generalization experiments on the LasHeR dataset, with quantitative and qualitative results shown in Fig. 7 and Fig. 8, respectively. Compared to random noise and MTD, our ACAttack leads to a significant drop in tracking performance across all trackers, even without training on LasHeR. Additionally, we present the IoU plots for both
+
+![](images/28049c3409491173fd313b73b9d8f4d6052356dd6d98451600c8e1c68fb1c206.jpg)  
+(a) ViPT on LasHeR
+
+![](images/eac88dcb4a67c9b330ed788edd168ef45fb74938a144720157eb3a4c466bc779.jpg)  
+(b) BAT on LasHeR
+
+![](images/441f9cb12578aae2668934ce3ac88e833dca1fd762f2b926d0004f5b281ad12a.jpg)  
+(c) SDSTrack on LasHeR
+
+![](images/0ae041af7cf0486b92cdd41c3dd040b2df52ce10d7f53dd3fa1e52eca829af99.jpg)  
+Figure 7. Quantitative comparison of tracking performance on the LasHeR dataset. The tracking performance of ViPT, BAT, and SDSTrack trackers is reported, including the original performance without attacks and the performance under attacks. Lower tracking metrics PR and SR represent better attack. Please zoom in for a better view.
+
+![](images/323f39373e80e2cf23c802d775e4e96c7945d673ba0d02d40dec1231ad08dfb8.jpg)  
+Figure 8. Qualitative comparison of tracking performance on the LasHeR dataset.  
+Figure 9. Qualitative comparison of tracking performance on the LasHeR dataset. The blue and red lines represent the IoU variation over frames of the predicted boxes under the clean trackers and the victimized trackers, respectively.
+
+clean and attacked tracking results, as shown in Fig. 9. It is clear that our ACAttack can maintain a sustained attack over extended periods. Due to the existence of our adaptive attack strategy and the modal balance interference loss, the response value of the tracker for the real target is reduced, and then the tracker is easy to deviate from the original target and is attracted by similar targets.
+
+# 4.4. Application in the Physical Domain
+
+After having verified our adversarial patches in digital scenes, we also extend experiments to demonstrate their efficacy in the physical domain. We directly apply the patches trained in the digital domain to the real world and use aero
+
+gel and paper to make thermal and RGB patches for deployment on pedestrians, respectively. A dual-spectral camera in DJI Mavic 3T is used for video capture. Thirty sets of videos of different scenes are taken as test samples. The orientation results of the test are shown in Fig. 10. It can be seen that the tracking prediction bounding box is enlarged and cannot be accurately positioned due to the interference of the multi-modal adversarial patch. Specifically, the optimization of spatio-temporal joint loss makes the patch learn the effect of expanding the tracker's prediction box. Therefore, in the physical world, the tracker will not be able to accurately locate the target after being affected by the adversarial patch.
+
+# 4.5. Ablation Studies
+
+We conduct ablation studies to assess the effectiveness of our unique design and parameter configuration, including: (I) loss function, (II) parameter K, (III) iteration mode, and (IV) applied modal. The ablation studies are performed on the RGBT234 dataset against ViPT, with quantitative results presented in Table 1.
+
+# 4.5.1. Loss Function
+
+The loss  $L_{st}$  interferes with the tracker from both temporal and spatial dimensions, while  $L_{mi}$  is used to disrupt the tracker's semantic perception. To demonstrate their effectiveness, we remove each of them individually, with the results shown in Table 1. In the absence of  $L_{st}$  or  $L_{mi}$ , the attack performance weakens, demonstrating their role in diminishing the enhanced target localization accuracy achieved through multi-modal interaction.
+
+![](images/fa1865e09e72f7edb94a1940891936ea2867a523c0a89c624cf6ced42d48b9ec.jpg)  
+Figure 10. Practical application in the physical domain.
+
+<table><tr><td rowspan="2">Metric</td><td rowspan="2">ViPT</td><td colspan="2">Config. I: loss function</td><td colspan="2">Config. II: parameter K</td><td colspan="2">Config. III: iteration mode</td><td colspan="2">Config. IV: applied modal</td><td rowspan="2">Ours</td></tr><tr><td>w/o Lst</td><td>w/o Lmi</td><td>K = 0</td><td>K = 9</td><td>cross</td><td>combine</td><td>Only RGB</td><td>Only TIR</td></tr><tr><td>PR</td><td>0.835</td><td>0.709</td><td>0.735</td><td>0.672</td><td>0.651</td><td>0.645</td><td>0.703</td><td>0.691</td><td>0.669</td><td>0.621</td></tr><tr><td>SR</td><td>0.617</td><td>0.486</td><td>0.505</td><td>0.450</td><td>0.425</td><td>0.428</td><td>0.482</td><td>0.482</td><td>0.462</td><td>0.417</td></tr></table>
+
+Table 1. Quantitative comparison of ablation studies, which is performed on the RGBT234 dataset against the ViPT tracker.
+
+# 4.5.2. Parameter K
+
+In our progressive attack framework, we first employ projected gradient descent to identify K sets of coarse adversarial examples with effective attack performance. In order to verify its effectiveness, we set the number of coarse adversarial samples K growth from 0 to 9 and 18. As shown in the Table 1, as K increases from 0 to 9 and 18, the tracker's PR and SR consistently decrease. This indicates that such coarse-grained adversarial examples can effectively narrow the search space for refined attacks, thus facilitating a more effective attack. Specifically, this progressive method for finding adversarial examples prioritizes identifying multiple sets of coarse adversarial representations from a broad spectrum of noise. Subsequently, multi-modal patch generation refines the adversarial details to produce the final adversarial patch, leveraging numerous samples that contain adversarial information. Consequently, this approach results in an enhancement in performance.
+
+# 4.5.3. Iteration Mode
+
+One of the key contributions of this paper is the adaptive iterative strategy for attacking the RGB-T tracker. To demonstrate the effectiveness of the adaptive strategy, we conduct ablation experiments using the iterative strategy. The alternating iteration strategy and the joint optimization strategy are selected for the comparison test. The former alternately optimizes the adversarial texture network and the adversarial shape network, while the latter simultaneously propagates the gradient flow to both networks. As shown in Table 1, our adaptive iteration approach can more effectively identify model vulnerabilities and generate more aggressive adversarial patches. Specifically, according to the contribution degree, our strategy can weaken deep semantic attention and break the balance of modality in tracker.
+
+# 4.5.4. Applied Modal
+
+In order to verify the multi-modal patch joint and single-modal patch attack performance, we try to conduct patch apply modal ablation experiment. Multi-modal patches  $\{p_{vi}, p_{ir}\}$  are generated to simultaneously disrupt both RGB and thermal modalities. As shown in the Table 1, we use only one of these patches in an ablation setup. The adversarial patch of a single modal produces a certain attack effect and makes the tracker confused. Evidently, our multi-modal patch achieves the best attack performance, underscoring the necessity of designing joint multi-modal attacks for RGB-T trackers.
+
+# 5. Conclusion
+
+In this work, we present a pioneering framework for adversarial attacks on RGB-T multi-modal trackers by introducing an adaptive cross-attack mechanism through multimodal response decoupling. Our approach leverages a modal-aware adaptive attack strategy and introduces novel modal disturbance loss and spatio-temporal joint attack loss to progressively impair the tracker's capability to perceive the target. The shared adversarial shape design also enhances our method's practicality, allowing seamless deployment of multi-modal patches in the real world. Experiments across digital and physical domains confirm the robustness and effectiveness of our approach in evading RGB-T trackers, highlighting the potential and significance of adaptive, multi-modal adversarial attacks in advancing the understanding of tracker vulnerabilities.
+
+# Acknowledgments
+
+This work was supported by National Natural Science Foundation of China (62276192).
+
+# References
+
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+# Acc3D: Accelerating Single Image to 3D Diffusion Models via Edge Consistency Guided Score Distillation
+
+Kendong Liu<sup>1</sup> Zhiyu Zhu<sup>1*</sup> Hui Liu<sup>2</sup> Junhui Hou<sup>1†</sup>  
+<sup>1</sup>City University of Hong Kong <sup>2</sup>Saint Francis University {kdliu2-c, zhiyuzhu2-c}@my.cityu.edu.hk h2liu@sfu.edu.hk jh.hou@cityu.edu.hk https://acc3d-object.github.io/
+
+![](images/5595a5397a1aa16bcdeab85d104e5d07d49cfb23025e04ce5305f8a3061b4206.jpg)
+
+![](images/07c71dd45aba153025ff2d7e8e8920a1b71a75a0f5859ce76339d4824715b517.jpg)  
+Input images
+
+![](images/2528d720671d4e55ef7af25ab008a54efd465b47a10aa8f1f8b11372c3220dbd.jpg)  
+Figure 1. Visual illustration of the generated high-quality multiview images and normal maps from a given single-view image by our Acc3D through fewer than four inference steps.  $\mathbb{Q}$  Zoom in for details.
+
+![](images/cbbc1b20286d3428387a09bcdcc061972eb0d66e05592571bbac39ec744920ec.jpg)  
+Generated multi-view images and normal maps
+
+![](images/bc26b08ca9dcdc5a50a19be6e357b5f7bd581d0485d90358de7d92cb431dd626.jpg)
+
+![](images/1f9bb5eace801ba6083bbadce310aa41019c36504ce4dd7dd45be8f771d73761.jpg)
+
+![](images/d2184505ea64502b4193a65c12693e279525b16ff47dadab869620427e69d0f7.jpg)
+
+![](images/8c0b5a7334523c6b56f17060471fa4a2a6963efed667000a74cc33687806b0e4.jpg)  
+Textured mesh
+
+![](images/06b7f61b2cab01f4e4e647b081740f837db236883c395448cb9349d2ce28647f.jpg)
+
+# Abstract
+
+We present Acc3D to tackle the challenge of accelerating the diffusion process to generate 3D models from single images. To derive high-quality reconstructions through few-step inferences, we emphasize the critical issue of regularizing the learning of score function in states of random noise. To this end, we propose edge consistency, i.e., consistent predictions across the high signal-to-noise ratio region, to enhance a pre-trained diffusion model, enabling a distillation-based refinement of the endpoint score function. Building on those distilled diffusion models, we propose an adversarial augmentation strategy to further enrich the gen
+
+eration detail and boost overall generation quality. The two modules complement each other, mutually reinforcing to elevate generative performance. Extensive experiments demonstrate that our Acc3D not only achieves over a  $20 \times$  increase in computational efficiency but also yields notable quality improvements, compared to the state-of-the-arts.
+
+# 1. Introduction
+
+Single image-based 3D reconstruction stands as a pivotal domain within the realms of 3D computer vision and computer graphics [5, 19, 31, 33], boasting extensive applications in virtual reality, 3D gaming, content creation, and precision robotics. Despite humans' innate ability to perceive three-dimensional structures from a single image, the swift and accurate generation of consistent content remains a formidable challenge.
+
+Diffusion models [9] have demonstrated their strong capability in image generation and video synthesis [15],
+
+paving the way for diffusion-based 3D content creation. Various studies [10, 32, 33] have been dedicated to distilling consistent 3D representations, such as neural radiance fields (NeRF) [30] or 3D Gaussian splatting [12], from 2D image diffusion models or vision language models using the Score Distillation Sampling (SDS) loss [32]. Although these methods yield visually pleasing results, the distillation process tends to be time-intensive for generating a single shape, requires intricate parameter tuning to obtain satisfactory quality, and often faces issues with unstable convergence and quality degradation. Another stream of research [7, 25] aims to directly generate 3D geometries, such as point clouds and meshes. However, the necessity for large-scale, open-source, native 3D samples inevitably hampers the development of these methods.
+
+Recent research, exemplified by Syncdreamer [19], Wonder3D [20], MVDream [38], and Era3D [14], has focused on generating multiview-consistent images directly to facilitate single-view 3D reconstruction of diverse objects. These approaches leverage the pre-trained diffusion pipeline for single image generation to model the joint probability distribution of multiview-consistent images. By improving the multiview consistency in image generation, these methods can reconstruct 3D shapes from the produced multiview images using neural reconstruction methods [46]. To improve the accuracy of 3D object reconstruction, the diffusion frameworks used in Wonder3D and Era3D directly generate normal maps and multiview images. These are then exploited in tandem with both normal maps and multiview images to reconstruct the 3D object. However, the lengthy sampling time required for the integration of the reversed differential equation burdens all these diffusion-based multiview image generation methods. This typically involves an iterative process that progressively denoises a Gaussian noise sample into an image, emphasizing the importance of sampling acceleration.
+
+In this paper, we tackle this challenge by introducing a consistency-based endpoint score-matching mechanism to achieve the few-step generation, which focuses on enhancing the accuracy of score function in low-SNR regions. Specifically, to regularize the score function for greater accuracy, we employ consistency training techniques to enforce stable score estimation in high-SNR regions, which can act as a score corrector, refining the coarse generation from the endpoint pure noise state. We subsequently introduce an adversarial training technique to further boost the alignment of the manifold of generated samples [8], where the pre-trained diffusion model is also introduced as a discriminator to fully leverage the pre-trained geometric knowledge. Our Acc3D is composed of two main components: edge consistency-guided distillation and disentangled adversarial regularization. These two components complement each other—distillation stabilizes adversarial
+
+training, reducing the risk of mode collapse, while adversarial learning enhances the perceptual richness of the model. Working in tandem, these components create a balanced and sophisticated model that delivers both stability and detail.
+
+Comprehensive experiments show that our accelerated generative model outperforms the baseline model and most other image-to-3D diffusion models. It offers high-quality 3D content across multiple views and provides faster inference. Remarkably, even with only a few iterative steps, our accelerated model can generate high-quality multiview images from a variety of 2D images with different styles.
+
+In summary, the main contributions of this work are as follows.
+
+- we have proposed an edge consistency-based paradigm to achieve distillation-based acceleration of single imaged-to-3D diffusion models, driving generation speeds up to  $20 \times$  while simultaneously elevating performance;  
+- we have conducted a comprehensive analysis, incorporating both intuitive and theoretical manners to ensure the technical soundness of the proposed method; and  
+- we have carried out extensive experiments to demonstrate the performance of the proposed algorithm on both synthetic and real datasets.
+
+# 2. Related Work
+
+Image-to-3D Generative Models. Diffusion models [9] have achieved substantial success in 2D image generation, prompting various efforts to extend pre-trained 2D diffusion models to 3D generation. DreamFusion [32] marks a pioneering endeavor in distilling a 2D image generation model to craft 3D content from a single text prompt. Building upon this groundwork, Magic3d [42] generates 3D shapes from single images, refining the 3D representation for each instance. These methods [27, 33, 44, 48] commonly employ the SDS loss to guide the optimization of their 3D representations, such as NeRF, mesh or Gaussian Splatting. Notably, NVS-Solver [28] utilizes video diffusion models integrated with data manifold constraints to directly generate consistent multi-views for both static and dynamic scenes.
+
+In order to produce 3D content without the necessity of training each sample, numerous existing studies [3, 14, 17, 19, 20, 37, 38, 49] directly generate multiview images from a single-view image. These image-to-3D diffusion models, trained on a large-scale 3D object dataset [4], exhibit impressive generalization capabilities. Syncdreamer [19] synchronizes the intermediate states of multiview images at every step of the reverse process through a 3D-aware fusion. MVDream [38] introduces self-attention into multiview images in order to improve consistency. Wonder3D [20] generates both multiview normal maps and the corresponding images under a cross-domain self-attention mechanism. Following Wonder3D, Era3D [14] implements a camera prediction module to alleviate image shape distortions and
+
+![](images/4f5c41b75b048d9582a096028047aafd3ea9b54ebc745570bd39a62bd84735fe.jpg)  
+Figure 2. Overview of our Acc3D. The training pipeline unfolds in two core components: edge consistency-guided distillation and adversarial training. Each component bolsters the other's advantages—the distillation procedure stabilizes adversarial training, mitigating the risk of mode collapse, while adversarial learning can enhance perceptual richness. Collectively, these elements craft a balanced, refined model that excels in both stability and detail.
+
+increases the image resolution up to  $512 \times 512$ . While these image-to-3D models typically demand a long inference time, our accelerated generative model stands in contrast. It can generate high-quality multiview images and normal maps with fewer iterative processes.
+
+Diffusion Model Acceleration. The iterative process of progressive denoising is a key characteristic of diffusion models, making the acceleration of the sampling process a significant area of interest [24]. Several studies [18, 26, 39, 40, 45] have focused on direct noise-to-data mapping with the objective of generating high-quality images in a single step. The study by Song et al. [40] introduces a consistency model that condenses the diffusion model process to a single step, training a one-step model to emulate the multi-step outcomes of the original model. Liu et al. [18], on the other hand, aims to keep the image generation trajectory as linear as possible between the final and current points.
+
+Generative Adversarial Networks. Several recent studies [13, 34, 35, 47, 51, 52] have adopted a generative adversarial training approach to maintain and boost the outcomes of accelerated diffusion models. Notably, [47] incorporates feedback from the discriminator by backpropagating it through the forward diffusion chain. The length of this chain is adaptively adjusted to strike a balance between noise and data levels. Kim et al. [13] combined GANs and denoising score matching loss to improve overall performance. Sauer et al. [34, 35] used the pre-trained diffusion model as the discriminator and updated the parameters in both raw and latent space. Yin et al. [52] designed the discriminator similar to [34], minimizing the difference between the generator and pre-trained model by comput
+
+ing the KL divergence of two score functions. Despite the abundance of methods aimed at achieving stable adversarial training, GANs are still prone to issues such as model collapse and unstable training, which makes scaling and adapting to different distributions challenging.
+
+# 3. Preliminary
+
+In this section, we introduce the basic knowledge of stochastic differential equation (SDE)-based formulation of diffusion models, its integrator, and consistency models.
+
+Diffusion Models. Denote by  $\mathbf{X}_t$  the latent noised variable,  $t\in [0,T]$  as the scalar indicating the time-stamp. Then, we can formulate the forward diffusion process as the following SDE, gradually shifting the clean image  $\mathbf{X}_0$  towards a random noise  $\mathbf{X}_T$ :
+
+$$
+d \mathbf {X} _ {t} = f (t) \mathbf {X} _ {t} d t + g (t) d \boldsymbol {\omega}, \tag {1}
+$$
+
+where  $d\omega$  represents the standard Wiener process, with  $f(t)$  signifying the drift coefficient function, and  $g(t)$  denoting the diffusion coefficient function. By reversing the forward SDE given in Eq. (1), we can generate the corresponding clean latent from the easily sampled random noise. This process results in the subsequent ordinary differential equation (ODE) formulations:
+
+$$
+d \mathbf {X} _ {t} = [ f (t) \mathbf {X} _ {t} - \frac {1}{2} g ^ {2} (t) \nabla_ {\mathbf {X} _ {t}} \log p (\mathbf {X} _ {t}) ] d t, \tag {2}
+$$
+
+where  $\nabla_{\mathbf{X}_t}\log p(\mathbf{X}_t)$  denote the data gradient, usually approximated by a learnable score function of  $\mathbf{S}_{\theta}(\mathbf{X}_t)$  parameterized with  $\theta$ . Consequently, the analytical solution of Eq. (2) to the arbitrary timestamp  $t$  can be expressed as
+
+$$
+\mathbf {X} _ {t} = \mathbf {X} _ {T} + \int_ {T} ^ {t} \frac {d \mathbf {X} _ {t}}{d t} d t, X _ {T} \sim \mathcal {N} (\mathbf {0}, I), \tag {3}
+$$
+
+where  $\mathcal{N}(\mathbf{0},I)$  denotes the standard Gaussian distribution.
+
+Integrators of Diffusion Models. To derive the generation samples from the differential equation-based diffusion models, we can calculate the integral of the reverse ODE trajectory in Eqs. (3) and (2) as  $\mathbf{X}_0 = \mathbf{X}_T + \int_T^0\left[f(\mathbf{X},t) - \frac{1}{2} g^2 (t)\mathbf{S}_\theta (\mathbf{X}_t)\right]dt.$  Based on the semi-linear property of the diffusion models, DPM-Solver [22, 23] gives an exact solution as
+
+$$
+\mathbf {X} _ {t - \Delta t} = \frac {\alpha_ {t - \Delta t}}{\alpha_ {t}} \mathbf {X} _ {t} - \alpha_ {t - \Delta t} \int_ {\lambda_ {t}} ^ {\lambda_ {t - \Delta t}} e ^ {- \lambda} \boldsymbol {\epsilon} _ {\boldsymbol {\theta}} (\mathbf {X} _ {\tau}, \tau) d \lambda , \tag {4}
+$$
+
+where  $\lambda := \log \left(\frac{\alpha_t}{\sigma_t}\right)$  represents the log-SNR (Signal-to-Noise Ratio);  $\epsilon_{\theta}(\cdot)$  indicates the noise estimation neural network. By computing this integral using the Taylor series, we can finally derive the reverse diffusion results.
+
+Consistency Models are introduced to train diffusion models that can consistently estimate high-quality samples from different noise levels [21, 39, 40]. Specifically, the consistency model can be parameterized as
+
+$$
+\mathcal {F} _ {\boldsymbol {\theta}} \left(\mathbf {X} _ {t}, t\right) = \mathbf {c} _ {k} (t) \mathbf {X} _ {t} + \mathbf {c} _ {o} (t) \boldsymbol {\epsilon} _ {\boldsymbol {\theta}} \left(\mathbf {X} _ {t}, t\right), \tag {5}
+$$
+
+where  $\mathbf{c}_k(\Delta t) = 1$  and  $\mathbf{c}_o(\Delta t) = 0$  ( $\Delta t > 0$  and is sufficient small) to ensure the model meets the boundary condition of  $\mathcal{F}_{\theta}(\mathbf{X}_0,0)\coloneqq \mathbf{X}_0$ ; and  $\epsilon_{\theta}(\cdot)$  represents a learnable neural network. Note that the ODE-Solver formulation in Eq. (4) can also be treated as a special case of consistency model, only if we set  $\Delta t = t$ , i.e., projecting each data point back to clean state  $t = 0$ . And we utilize this formulation in the rest of our paper. Consistency models can be trained from scratch or in a distillation manner. However, both methods aim to minimize the inconsistencies of estimations between adjacent steps, i.e.,
+
+$$
+\mathcal {L} _ {c} = d \left(\mathcal {F} _ {\boldsymbol {\theta}} \left(\mathbf {X} _ {t}, t\right), \mathcal {F} _ {\boldsymbol {\theta} ^ {-}} \left(\mathbf {X} _ {t - \Delta t}, t - \Delta t\right)\right), \tag {6}
+$$
+
+where  $\mathbf{X}_{t - \Delta t}$  can be derived by solving inverse steps from  $\mathbf{X}_t$  using a pre-trained diffusion model or be directly interpolated with the same noise sample as  $\mathbf{X}_t$ ;  $\theta^{-}$  indicates to apply the stop gradient operation on the running mean of  $\theta$ ; and  $d(\cdot)$  represents a discrepancy measurement, e.g., Frobenius Norm [2] or LPIPS [53].
+
+# 4. Proposed Method
+
+Accurately estimating the score function is particularly challenging in states of pure random noise (i.e., the low-SNR edge). As a result, in existing diffusion-based single image-to-3D models, the few-step reverse process suffers from accumulated errors in the score function, leading to imprecise results at the final stage of denoising and significantly degrading generation performance. To address this issue, we propose Acc3D, which progressively improves the estimation of the score function at the endpoint (low-SNR side) during training, thus enhancing generative per
+
+![](images/c5d3db269b96c3a00205b32d586ded931187d297cd6039fa7981afd2705383aa.jpg)  
+Figure 3. Illustration of the progressive score matching by our edge consistency distillation, in a data manifold view, where  $\mathcal{M}_t$  indicates the data manifold with the timestamp  $t$ , e.g.,  $\mathcal{M}_T$  and  $\mathcal{M}_0$  represent the manifolds of pure noise and clean samples, respectively;  $\mathbf{X}_{0|T}$  represents the few-step estimation of the clean sample from Gaussian noise  $\mathbf{X}_T$ ;  $\widetilde{\mathbf{X}}_0$  represents a relatively accurate training target of  $\mathbf{X}_{0|T}$ , refined by the edge consistency region; and  $\mathcal{E}(\cdot)$  is the generation error, e.g., distance between its corresponding manifold surface. (a) shows the single-step reverse trajectory by the endpoint (pure noise) score function; (b) represents the noised latent interpolation using noise  $\mathbf{X}_T$  and  $\mathbf{X}_{0|T}$ ; and (c) indicates the score estimation in the region with consistency characteristic. The left subfigure illustrates that before being adapted by the proposed strategy. The right subfigure shows that after being trained by our method, the error of the score function at the initial pure noise state is gradually decreased as  $\mathcal{E}(\mathbf{X}_{0|T}) > \mathcal{E}(\mathbf{X}_{0|T}')$ . It indicates that the result  $\mathbf{X}_{0|T}$  can gradually approach the data manifold.
+
+formance in a few-step generation. To be specific, we propose an edge consistency model as a score corrector, enabling regularization and distillation for enhanced accuracy of score estimation at endpoints, as outlined in Sec. 4.1. Building on these insights, we introduce an adversarial regularization process in Sec. 4.2, aimed at further minimizing the discrepancy between generated and real samples. These two modules work in synergy, strengthening each other to improve generative performance.
+
+# 4.1. Edge Consistency-guided Distillation
+
+In this section, we propose edge consistency-guided distillation to reduce integral errors in the one-step inference outcomes of diffusion models.
+
+Technically, let  $\mathbf{X}_{0|T}$  be the one-step coarse generation result from noisy latent at timestamp  $T$  to 0 through the first-order approximation of ODE-Solver in Eq. (4), written as
+
+$$
+\mathbf {X} _ {0 \mid T} = \mathcal {F} _ {\boldsymbol {\theta} _ {G}} \left(\mathbf {X} _ {T}, T\right), \tag {7}
+$$
+
+where  $\theta_{G}$  represents the parameters of the generator. Let  $\mathbf{X}_0^*$  be the on-manifold sample corresponding to  $\mathbf{X}_{0|T}$ , and  $\mathcal{E}(\mathbf{X}_{0|T}) = \| \mathbf{X}_{0|T} - \mathbf{X}_0^*\| _F$  the error between  $\mathbf{X}_{0|T}$  and  $\mathbf{X}_0^*$ , as depicted on the left side of Fig. 3. Effectively and accurately minimizing the value of  $\mathcal{E}$  thus becomes
+
+the paramount objective to improve the quality of  $\mathbf{X}_{0|T}$ . However, obtaining  $\mathbf{X}_0^*$  directly is challenging or even intractable: (1) taking the clean image  $\mathbf{X}_0$  as  $\mathbf{X}_0^*$  causes the model to predict blurry values, approximating a weighted average of  $\mathbf{X}_0^*$ , since multiple  $\mathbf{X}_0^*$  can be denoised by the diffusion model to produce the same noise; and (2) preparing the noise- $\mathbf{X}_0^*$  pairs by generating the entire training dataset from noise is a computationally intensive process. Thus, instead of directly deriving the sample  $\mathbf{X}_0^*$ , we draw inspiration from the reward lifting process in reinforcement learning and propose to regularize  $\mathbf{X}_{0|T}$  to approach a feasible sample  $\widetilde{\mathbf{X}}_0$  with a reduced error, i.e.,  $\mathcal{E}(\widetilde{\mathbf{X}}_0) < \mathcal{E}(\mathbf{X}_{0|T})$ . With the progression of model iterations, the sample  $\widetilde{\mathbf{X}}_0$  is expected to gradually improve to be closer to the data manifold surface  $\mathcal{M}_0$ , while the coarse estimation  $\mathbf{X}_{0|T}$  steadily approaches  $\widetilde{\mathbf{X}}_0$ , leading to continuous refinement. Such a process is intuitively depicted in the right sub-figure of Fig. 3.
+
+Building on this progressive refinement intuition, the focus shifts to obtaining an accurate sample  $\widetilde{\mathbf{X}}_0$ . Leveraging the consistency model's ability to generate high-quality outputs directly from the latent space with varying noise levels, we train our accelerated model with consistency constraints in Eq. (6) within the edge region (i.e., the region with high SNR), which we term "edge consistency." The accelerated model is trained to generate the refined estimation  $\widetilde{\mathbf{X}}_0$  under the guidance of edge consistency constraints. As  $\widetilde{\mathbf{X}}_0$  experiences the additional denoising step, it becomes more accurate and closer to  $\mathbf{X}_0^*$  compared to the coarse estimation  $\mathbf{X}_{0|T}$ . Specifically, the feasible refined estimation  $\widetilde{\mathbf{X}}_0$  is computed as follows:
+
+$$
+\widetilde {\mathbf {X}} _ {0} = \mathcal {F} _ {\boldsymbol {\theta} _ {G} ^ {-}} \left(\mathbf {X} _ {t | 0, T}, t\right), \tag {8}
+$$
+
+where  $\mathbf{X}_{t|0,T}$  denotes the forward diffusion process to evolve  $\mathbf{X}_{0|T}$  to timestamp  $t$  using the initial noise  $\mathbf{X}_T$ . Here we utilize the same noise of  $\mathbf{X}_T$  to keep the correspondence of data points between the noise and data manifolds. Through distilling the  $\mathbf{X}_{0|T}$ , we can progressively correct the coarse estimation to approach the more accurate sample  $\widetilde{\mathbf{X}}_0$ , i.e.,
+
+$$
+\mathcal {L} _ {d} = d \left(\widetilde {\mathbf {X}} _ {0}, \mathbf {X} _ {0 | T}\right). \tag {9}
+$$
+
+Distilling the coarse estimation with consistency guidance enhances the accuracy of the score function in the one-step accelerated model, ultimately facilitating the generation of high-quality samples.
+
+Remark. We are not aimed at devising novel consistency training techniques. Instead, we utilize consistency constraints to train the high-SNR edge region as an effective refinement tool to guide the learning of the score function in the pure noise state (endpoint), which can give reasonable regularization and preserve generation diversity. Our edge consistency-guided score distillation method strategi-
+
+Algorithm 1 Training Pipeline of the Proposed Algorithm  
+Input: Pre-trained diffusion model parameterized with  $\theta$ ; training dataset  $S$ ; number of iterations  $K$ ; learning rate  $\eta_{G}$  and  $\eta_{D}$ .  
+Output: Optimized generation model parameters  $\theta_{G}^{*}$   
+1:  $\theta_{G} \gets \theta$  ▷ Initialize  $G$  from pre-trained model  
+2: Initialize discriminator  $\theta_{D}$  randomly.  
+3: for  $k = 1$  to  $K$  do  
+4: Sample data  $\mathbf{X}_0$  from  $S$ , draw gaussian noise  $\epsilon \sim \mathcal{N}(0, \mathbf{I})$ , draw gaussian noise  $\mathbf{X}_T \sim \mathcal{N}(0, \mathbf{I})$   
+5: Sample timestep  $t \sim \mathcal{U}(0, N)$  where  $N < T$  and interval  $\Delta t \sim \mathcal{U}(0, \delta]$  ▷ sample  $t$  and  $\Delta t$  for edge consistency  
+6: Interpolate noised latent:  $\mathbf{X}_t = \alpha_t \mathbf{X}_0 + \sigma_t \epsilon$  and corresponding  $\mathbf{X}_{t - \Delta t} = \alpha_{t - \Delta t} \mathbf{X}_0 + \sigma_{t - \Delta t} \epsilon$   
+7: Compute edge consistency loss  $\mathcal{L}_c$  Eq. (6)  
+8: Calculate coarse target using Eq. (7)  
+9: Calculate refined target  $\widetilde{\mathbf{X}}_0$  using Eq. (8)  
+10: Compute score distillation loss  $\mathcal{L}_d$  using Eq. (9)  
+11: Evaluate adversarial loss  $\mathcal{L}_{GAN}$  using Eq. (10)  
+12: Update  $G$ :  $\theta_{G} \gets \theta_{G} - \eta_{G} \nabla_{\theta_{G}} (\mathcal{L}_{c} + \mathcal{L}_{d} + \mathcal{L}_{GAN})$   
+13: Update  $D$ :  $\theta_{D} \gets \theta_{D} + \eta_{D} \nabla_{\theta_{D}} \mathcal{L}_{GAN}$   
+14: return  $\theta_{G}^{*}$
+
+cally avoids consistency regularization in low-SNR challenging regions, potentially reducing the learning burden and thus enhancing generative performance. See the results in Table 3 for the advantage of our edge consistency over the traditional consistency model that applies consistency regularization to the entire region. We also refer readers to Sec. A of the Supplementary Material for a detailed theoretical analysis.
+
+# 4.2. Disentangled Adversarial Regularization
+
+To further calibrate the distribution of the generated data, in this section, we introduce the adversarial training technique to directly measure the error of generation by a learnable discriminator [36]. As shown in Fig. 2, to leverage the pre-trained geometric knowledge in the diffusion model, we utilize the pre-trained diffusion model as the discriminator. However, due to the huge distribution gap between the geometric (normal) and texture components, in this process, we separate the discriminative learning processes via introducing a dual-discriminator, as shown in Fig. 2. Moreover, the adversarial learning objective can be formulated as
+
+$$
+\mathcal {L} _ {G A N} = \mathcal {D} _ {\boldsymbol {\theta} _ {D}} \left(\mathcal {F} _ {\boldsymbol {\theta} _ {G}} \left(\mathbf {X} _ {T}, T\right)\right) - \mathcal {D} _ {\boldsymbol {\theta} _ {D}} \left(\mathbf {X} ^ {*}\right), \tag {10}
+$$
+
+where  $\theta_{\mathcal{G}}$  and  $\theta_{\mathcal{D}}$  are the network parameters of the generator and discriminator, respectively,  $\mathcal{F}_{\theta_G}(\mathbf{X}_T,T) = \mathbf{X}_{0|T}$  and  $\mathbf{X}^*$  indicates the real images and normal.
+
+Remark. Decoupling the learning of geometry and tex
+
+![](images/0896b15a4741d337f665ce0f76b0c47d532a91b672144a8969b726e2e3499fd0.jpg)  
+Figure 4. Visual comparisons of our Acc3D, Era3D [14], and Wonder3D [20] on the GSO [6] dataset. For each sample, we provide the generated view, normal map, and reconstructed 3D mesh, displayed from left to right, respectively.
+
+ture information is a simple yet effective strategy that enhances the adversarial training process. We also want to highlight that while leveraging adversarial training can significantly enhance generative capabilities, without robust guidance—such as our edge consistency-guided progressive distillation detailed in Sec. 4.1—adversarial learning is prone to instability and mode collapse, as demonstrated in the ablation studies outlined in Table 3 and Fig. 7. In essence, the decoupled adversarial regularization and edge consistency complement each other, mutually reinforcing to elevate generative performance.
+
+In all, Algorithm 1 summarizes the training pipeline of the proposed method.
+
+# 5. Experiments
+
+# 5.1. Experimental Settings
+
+Dataset. Our model was trained on the Objaverse [4] dataset. We have aligned our training dataset with that of Wonder3D [20], which includes approximately 35,000 objects. We prepared our rendered multiview images and normal maps with Blender protocols. The rendered results consist of six views, all adjusted to the same scale as Era3D, including the front, back, left, right, front-right, and front-left views. For the evaluation dataset, we adopt the Google Scanned Object dataset, following prior works [19, 20]. For the quantitative evaluation, we initially rendered the input image at a resolution of  $512 \times 512$ , subsequently obtaining multiview results and 3D assets.
+
+Evaluation Metrics. We evaluated our Acc3D from multiple perspectives, including the quality of novel view synthesis and the consistency of 3D reconstruction. Following Liu et al. [19], we used common metrics for image quality assessment to evaluate the performance of generated multiview outputs, such as PSNR, LPIPS, and SSIM. Additionally, we utilize more unpaired and perceptual scores, e.g., MUSIQ, CLIPIQA and MANIQA, to validate the performance of our model. For single-view 3D reconstruction,
+
+Table 1. Quantitative comparison of different methods for single view reconstruction. The best and second-best results are highlighted in bold and underlined, respectively.  
+
+<table><tr><td>Metrics</td><td>Ze.123 [17]</td><td>Sync. [19]</td><td>Wo.3D [20]</td><td>Era3D [14]</td><td>One23 [16]</td><td>Acc3D Ours</td><td>Acc3D Ours</td></tr><tr><td>NFE ↓</td><td>50</td><td>50</td><td>40</td><td>40</td><td>50</td><td>2</td><td>4</td></tr><tr><td></td><td colspan="5">GSO Dataset [6]</td><td></td><td></td></tr><tr><td>MUSIQ ↑</td><td>60.39</td><td>64.46</td><td>58.19</td><td>63.64</td><td>61.79</td><td>67.85</td><td>69.26</td></tr><tr><td>CLIPQA ↑</td><td>0.48</td><td>0.52</td><td>0.45</td><td>0.53</td><td>0.43</td><td>0.62</td><td>0.65</td></tr><tr><td>MANIQA ↑</td><td>0.56</td><td>0.63</td><td>0.55</td><td>0.42</td><td>0.54</td><td>0.59</td><td>0.64</td></tr><tr><td></td><td colspan="5">DTC Dataset [29]</td><td></td><td></td></tr><tr><td>PSNR ↑</td><td>17.84</td><td>22.31</td><td>23.02</td><td>23.36</td><td>16.01</td><td>23.06</td><td>24.01</td></tr><tr><td>SSIM ↑</td><td>0.78</td><td>0.24</td><td>0.86</td><td>0.87</td><td>0.75</td><td>0.87</td><td>0.88</td></tr><tr><td>LPIPS ↓</td><td>0.25</td><td>0.10</td><td>0.14</td><td>0.14</td><td>0.35</td><td>0.14</td><td>0.12</td></tr><tr><td>MUSIQ ↑</td><td>58.15</td><td>56.67</td><td>55.24</td><td>60.13</td><td>59.39</td><td>64.46</td><td>65.52</td></tr><tr><td>CLIPQA ↑</td><td>0.51</td><td>0.55</td><td>0.47</td><td>0.56</td><td>0.46</td><td>0.63</td><td>0.65</td></tr><tr><td>MANIQA ↑</td><td>0.56</td><td>0.64</td><td>0.54</td><td>0.42</td><td>0.53</td><td>0.56</td><td>0.59</td></tr></table>
+
+we reported Chamfer Distances (CD) and Volume IoU between reconstructed shapes and ground-truth shapes. This demonstrated the rationality and multiview consistency of the image-to-3D diffusion model.
+
+Baselines. We compared our Acc3D with 11 state-of-the-art image-to-3D models, including Zero123 [17], RealFusion [27], Magic123 [33], One-2-3-45 [16], PointE [31], Shap-E [11], SyncDreamer [19], Wonder3D [20], Era3D [14], as well as two accelerated image-to-3D models, Stable-Fast-3D [1] and TripoSR [43]. RealFusion and Magic123 use SDS loss on Stable Diffusion for single-view reconstruction. Zero123, SyncDreamer, Wonder3D, and Era3D generate consistent multiview images, with Wonder3D and Era3D also producing normal maps.
+
+Implementation Details. We adapt the proposed model on the recent effective 3D generation method Era3D [14], which can concurrently generate normal maps and multiview images at a high resolution of  $512 \times 512$ . We used AdamW as the optimizer with an initial learning rate set to  $5e - 6$ , and the number of gradient accumulation steps of 8. The training process generally necessitates 24 hours on
+
+"A boy wearing a baseball cap."
+
+![](images/02c22c5f27fa13aa0e5b1424d8828fd74db2ef566c2f0bd54087869bbfe8ab9c.jpg)
+
+![](images/cd20b6641e68110760325e80ec06b3d82cc8486ce121286ee0ea56e2e59392b2.jpg)
+
+![](images/40cd0dbec5666b013f0632cac07ce6878ed625b7b3a86bfe92e53d4fa06c18a9.jpg)
+
+![](images/747ce0a5ab9e3d0f5c554058bf5ae0cca5cd8c4add6450c900838e7eebd813c8.jpg)
+
+![](images/f51e0f8c02d0b5c2d1d31cac6709884b37711c26d1f41028090e288f606aa536.jpg)
+
+"A crocodile in cowboy costume."
+
+![](images/582ee98ea92fa9d96c5488d9b470a564841286fff0ca32b4882890e170b67082.jpg)
+
+![](images/87992c217d0cd4220e7272cd75ed01bf595a9da82194f9b2cdc3367b32eb1082.jpg)
+
+![](images/d68b009fc1aefe09390ce1875433650064c37311038fc8244da7d375dcb09634.jpg)
+
+![](images/1b7090ec28bfa64fffb2200cc177785dce925912cd20e722a60d43d0fbca433f.jpg)
+
+"A mouse in chef hat."
+
+![](images/9e4f64f3016692848227998b7d5fa1fc0f886215957fd58b73a506e25621f341.jpg)
+
+![](images/9608342c26991af91bdd4d3cfc343329b5b2623603833e6af4eea1b652b03f0f.jpg)
+
+![](images/9c0ce0ee634f51eec1d802ccd4f8b18db82bc32bc5693cef362d45e6dda42935.jpg)
+
+"An elephant in circus performer outfit."
+
+![](images/807a79d553d905211c839d31137b94c326d9a44bf4a2657cb82b7e4b6c1544c0.jpg)
+
+![](images/bb2673fa311dae5778e015982d891a8d6199b973e9c127cb245c0d81bdb9ae3c.jpg)
+
+![](images/86ad0522e85beaea885c1d6d95c47b87a2c465562ca28a7a71ac083860fe4ceb.jpg)
+
+"A graceful robot with red hair."
+
+![](images/d349aa06f683b26a284c8726c9bec8e2a013bed2e3d2c14dbf108ad5fd80aff3.jpg)  
+Input images
+
+![](images/40a9f67659f8d3816584180dbdcd45f7bf630903d6f866b9d06354f38a795c14.jpg)
+
+![](images/e8ea377f55b59266a98639c5b6ae2eb17cf22ccb3c04879770ab1a924e2cf896.jpg)  
+Zero123  
+(NFE=50)
+
+![](images/ba0198044fabae244f9f29fc8da10f7816f58e480003544faa028590a87b8be1.jpg)
+
+![](images/9fa7a87a2b64f6bb007bf2bb2eac3c817e2c93ae2ae7e73977229a07939a1abe.jpg)
+
+![](images/3142b2e02f12d533a89c366a69e4de811b46c568e686e166b2dc6042faf1eeb7.jpg)
+
+![](images/0c1fc7cf216cdd7b4a8cbbdaa224a490dfcbe7a06a53a47a7eb97d1657a31155.jpg)
+
+![](images/b0c18f32bb7cfb53e2faf205e7eaf0e787e15ceec92ecb5e0a0e51239a315076.jpg)  
+Magic123
+
+![](images/2ca4c4c500be4d7f4e63e2cafb9a12cccb40f9685d50105b995c2bb95f07a162.jpg)
+
+![](images/8c0da267a0085f7b60064c582aa5ad98289b357b9310d0729b16860891d2dfbd.jpg)
+
+![](images/08c27a02ee523b060e7982dc8cafe9783ad5f3d4b31c729374aa86564c8966e0.jpg)
+
+![](images/be6f6b77ed21722ef0fcdf9edf9ead32ca8f891e97dea2eed72b7dc31dbf0967.jpg)
+
+![](images/73dac9e181640224df15df03717ff910424ec0ba70a25ad4c7300822ae16f726.jpg)
+
+![](images/96eeb761c1eec5f7b28a4cbad15b076434c47e462ff1561952b74f6a551aad18.jpg)
+
+![](images/e8a1b78d4442c3d0ef67e7f6e351f717344ddb6c502de0636ba36bfd006f183e.jpg)
+
+![](images/9df2593e3d395bee4e28766b2af336c8f2c66d3701c059b408c44d87553afcd0.jpg)
+
+![](images/7250e88bcc7bfe52cba98bd4f078035f81b7e86561340b88243cc7bea8dfb8e7.jpg)
+
+![](images/311cb41adbd03f583b8b0af49a68ed0ab87b95661256471575d2e74a8e847517.jpg)
+
+![](images/b08da0ddb4911dd35b2194d5cf0cf208585db4643ca1cbb2f13e983fc2376354.jpg)
+
+![](images/6947e31c5831fda425d5e3e7720c1d36e0d9c2afb830aeacdb0325af44d56c92.jpg)
+
+![](images/685d17bc8c803d6133550ae418e60e5845aa3f68569a3ef026cd478604c807b0.jpg)
+
+![](images/fc6fdda234b7ca73373c491435b9ab10ece8bf99e549577f6a5aa45aab2562c2.jpg)
+
+![](images/6aa204cbe5f3a85f103b73c85c1a82140f7109cd220a6fe2f4416b64802f5ec1.jpg)
+
+![](images/64c87f1e0fa10f5cf1eebdc4ddca1a2b393f523317054815cb14640289a597d7.jpg)
+
+![](images/0075b1492022cf28872bb90d6ef9f0001b3c6ec5a054e0eddfa1d098d2a91da3.jpg)
+
+![](images/3e391bc3472b727ac1b9536c6caf8b8424803d2ec7d512ee672e36c95898e6f1.jpg)
+
+![](images/6a6846a572f419f8601eb91f8175294dbc685b134b0d439bd769351683333246.jpg)
+
+![](images/198b54fa129edacc39823d49d8a2003b2e939d7bb999a4be5e56404cabe85a7b.jpg)
+
+![](images/e0d6782243955107649291a60f56d97adeed81243ccb3921149ded9abdcb297e.jpg)
+
+![](images/30d17de8ee953b293e75ca653f51bb0804c5b62563f5199ca1b5543e496b0512.jpg)
+
+![](images/264ae613e8829d890456a2e8c3210b62d0d2e0d9b3ea195ab0309bbb892a18f0.jpg)
+
+![](images/d4e643c755ea5b5b649ae8cd8d5c8d526a39f7db72078dbd36963cb4e7aa7dcc.jpg)  
+Ours (NFE=2)
+
+![](images/5e4bfd00a3cf7ff5902e15fef607307678eb20d6dbba546c799dd0f4e82bd6e5.jpg)  
+Textured mesh
+
+![](images/02d405fb7647ec2bb2e58d37d55a1707bbcf3d1e2eb0e09711b0d101e08def96.jpg)
+
+![](images/74d684db3f85618916c334c14061f2e804a1ace2c1447ee3aa5d6e9a0f5430ec.jpg)  
+Figure 5. The qualitative results generated by Acc3D on various styles of images generated by text-to-image model Flux [41]. Please refer to Fig. 6 for more comprehensive comparisons between our Acc3D and baseline model Era3D. Q Zoom in for details.  
+Figure 6. Visual results of our Acc3D and Era3D (baseline model).
+
+a cluster equipped with four 40GB NVIDIA GeForce RTX A6000 GPUs. For 3D reconstruction, we followed Era3D to generate 3D assets using NeuS [46].
+
+# 5.2. Experimental Results
+
+Novel View Synthesis Results. We present the numerical results in Table 1 to quantitatively evaluate the quality of generated novel views. Our model is assessed on both the GSO [6] and DTC [29] datasets, with the DTC dataset being the most recent collection that offers a high degree of granularity and intricate 3D details. Acc3D achieves the
+
+Table 2. Quantitative results for 3D reconstruction on GSO. Symbol  ${}^{ \dagger  }$  indicates the method that directly generates 3D meshes.  
+
+<table><tr><td>Metrics</td><td>CD↓</td><td>IoU↑</td><td>NFE↓</td></tr><tr><td>Realfusion [27]</td><td>0.0819</td><td>0.2741</td><td>-</td></tr><tr><td>One-2-3-45 [16]</td><td>0.0629</td><td>0.4086</td><td>50</td></tr><tr><td>Point-E [31]</td><td>0.0426</td><td>0.2875</td><td>64</td></tr><tr><td>Shap-E [11]</td><td>0.0436</td><td>0.3584</td><td>64</td></tr><tr><td>Magic123 [33]</td><td>0.0516</td><td>0.4528</td><td>-</td></tr><tr><td>Zero123 [17]</td><td>0.0339</td><td>0.5035</td><td>50</td></tr><tr><td>SyncDreamer [19]</td><td>0.0261</td><td>0.5421</td><td>50</td></tr><tr><td>Wonder3D [20]</td><td>0.0199</td><td>0.6244</td><td>40</td></tr><tr><td>Era3D [14]</td><td>0.0217</td><td>0.5973</td><td>40</td></tr><tr><td>InstantMesh [50]</td><td>0.0406</td><td>0.4778</td><td>75</td></tr><tr><td>Stable-Fast-3D†[1]</td><td>0.0421</td><td>0.5141</td><td>-</td></tr><tr><td>TripoSR†[43]</td><td>0.0326</td><td>0.5326</td><td>-</td></tr><tr><td>Acc3D (Ours)</td><td>0.0191</td><td>0.6681</td><td>2</td></tr></table>
+
+highest average scores on most metrics, especially in natural image quality, highlighting our framework's superiority in novel view synthesis. We further visually compare different examples from the GSO dataset in Fig. 4. Our method achieves superior visualization results while reducing inference time. Besides those aforementioned datasets with reference multiviews, we also evaluate our method in the wild using T2I-generated images in Fig. 5. Our method consistently generates high-definition, detailed results compared to other methods, especially on the challenging samples of the crocodile  $(2^{nd}$  row) and the face of the elephant  $(4^{th}$
+
+Table 3. Quantitative results of ablation studies on the GSO dataset.  $\checkmark$  (resp.  $\times$ ) indicates the presence (resp. absence) of the corresponding component.  $\uparrow$  (resp.  $\downarrow$ ) means the larger (resp. the smaller), the better. "Distill." stands for score distillation with Eq. (8). "Consis." represents the timestamp region of consistency loss, corresponding to  $[0, N]$  in Alg. 1.  $[0, T]$  indicates the consistency regularization is applied to all noise levels during training. "Adv." refers to adversarial learning. "Single" indicates the utilization of only one discriminator for both normal and texture components. The metrics were obtained under two-step inference.  
+
+<table><tr><td></td><td colspan="2">Distill.Consis.</td><td>Adv.</td><td>PSNR↑</td><td>CD↓</td><td>MUSI.↑</td><td>CLIPI.↑</td></tr><tr><td>(a)</td><td>×</td><td>[0, T]</td><td>×</td><td>18.11</td><td>0.060</td><td>61.01</td><td>0.55</td></tr><tr><td>(b)</td><td>×</td><td>[0, T]</td><td>✓</td><td>20.79</td><td>0.021</td><td>67.22</td><td>0.62</td></tr><tr><td>(c)</td><td>✓</td><td>[0, T]</td><td>✓</td><td>21.10</td><td>0.025</td><td>65.39</td><td>0.60</td></tr><tr><td>(d)</td><td>✓</td><td>×</td><td>✓</td><td>20.47</td><td>0.026</td><td>63.08</td><td>0.58</td></tr><tr><td>(e)</td><td>×</td><td>[0, 0.4T]</td><td>✓</td><td>20.32</td><td>0.027</td><td>66.57</td><td>0.62</td></tr><tr><td>(f)</td><td>✓</td><td>[0, 0.2T]</td><td>✓</td><td>21.22</td><td>0.027</td><td>67.24</td><td>0.58</td></tr><tr><td>(g)</td><td>✓</td><td>[0, 0.6T]</td><td>✓</td><td>22.13</td><td>0.022</td><td>66.87</td><td>0.59</td></tr><tr><td>(h)</td><td>✓</td><td>[0, 0.8T]</td><td>✓</td><td>21.23</td><td>0.024</td><td>65.06</td><td>0.61</td></tr><tr><td>(i)</td><td>✓</td><td>[0, 0.4T]</td><td>×</td><td>21.09</td><td>0.029</td><td>51.05</td><td>0.45</td></tr><tr><td>(j)</td><td>✓</td><td>[0, 0.4T]</td><td>single</td><td>21.37</td><td>0.022</td><td>66.41</td><td>0.57</td></tr><tr><td rowspan="2">Era3D[14]-Ours</td><td rowspan="2">✓</td><td>-</td><td>-</td><td>20.17</td><td>0.023</td><td>53.81</td><td>0.46</td></tr><tr><td>[0, 0.4T]</td><td>✓</td><td>22.47</td><td>0.019</td><td>67.85</td><td>0.62</td></tr></table>
+
+row). We also compare our method with base model Era3D in Fig. 6. Our accelerated model achieves better results with NFE of 2, while Era3D struggles with few steps.
+
+3D Reconstruction Results. We conduct both quantitative and qualitative evaluations of the reconstructed geometry as presented in Table 2 and Fig. 4. In Table 2, our method attains excellent reconstruction results with the least number of function evaluations (NFE). Fig. 4 shows that Wonder3D is highly sensitive to the facing direction of input images; for instance, it fails to generate novel views for the sample of elephant in the left pose. Despite boasting a higher resolution of 512, Era3D still produces relatively coarse mesh outputs.
+
+# 5.3. Ablation Studies
+
+We perform comprehensive ablation studies (Table 3), training all models similarly except for the ablation term and evaluating on GSO dataset.
+
+Disentangled Adversarial Learning. Through comparing Table 3 (j) and "Ours", we find that separately learning different modalities can help stabilize adversarial learning and get better quantitative results. As depicted in Fig. 7 (3) and "Ours", the fusing of these two modalities adversely affect the discriminator/model's performance, shown obviously for the  $1^{st}$  and  $3^{rd}$  samples.
+
+Various Distillation Settings. We evaluate the effectiveness of our consistency-guided score distillation. Specifically, comparisons between Table 3 (e) and "Ours" validate
+
+![](images/14ae3d1d429b1225959958b8e68a6dc8e653906d3d2ac01bf452702ccf04bb87.jpg)  
+Figure 7. Visualizations of the ablation study conducted on GSO. All results are generated in two steps. The results (1), (2), and (3) correspond to the experimental configurations (b), (g), and (i) outlined in Table 3, respectively.
+
+the necessity of distillation. Without distillation loss, being solely trained with adversarial learning is hard to derive high-quality results. Table 3 (a)/(b) V.S. "Ours" also indicates the superiority of our edge consistency-guided distillation compared with full consistency model [39, 40]. We can also visually compared with Fig. 7 (1) and "Ours" that the setting of (b) generates strange samples, especially for the bag in the  $1^{st}$  row. This suggests that GANs are prone to mode collapse without robust regularization.
+
+Parameter selections of consistency constraints. By comparing Table 3 (c), (d), (f), (g), (h) and "Ours", we can conclude that using a consistency model to guide score matching at the endpoint is more effective than directly utilizing the original diffusion model. Additionally, the choice of the region for the consistency constraint is crucial. Selecting an appropriate edge consistency region can significantly enhance the generation results
+
+# 6. Conclusion
+
+We introduced Acc3D, a novel and streamlined method designed to accelerate single image-to-3D diffusion models. Acc3D integrates a consistency-guided distillation process and an adversarial augmentation strategy. Our model significantly improves computational efficiency, achieving a speed increase of over  $20\times$ , while also enhancing the quality of the generated 3D models. Our method outperforms the baseline and most other image-to-3D models in metrics, such as CD and IoU. The effectiveness and efficiency of our proposed approach highlight its potential for broad adoption. All the code and datasets utilized in our research are publicly available, fostering further investigation and refinement by the broader scientific community.
+
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