Daily Papers

Modern diffusion and flow-based models are increasingly moving toward few-step, latent-free generation to bypass the computational overhead of multi-step sampling and the reconstruction bottlenecks of external autoencoders. We propose the Interval Denoiser, a theoretically rigorous framework for latent-free generation. Derived directly from the flow matching ODE, it establishes an exact analytical mapping for intermediate trajectory states. Unlike prior formulations, our prediction is shown to reside on a low-dimensional manifold across any time interval, making the regression tractable for a network operating directly on pixels. Furthermore, by avoiding empirical algebraic substitutions, our formulation correctly isolates the pure time derivative to prevent biased gradient evaluations and ensure exact first-order optimization. By analyzing this objective, we equip our framework with residual clipping and a time-sampling curriculum, enabling effective long-interval training and improving few-step performance. Trained from scratch on ImageNet 256x256, our model achieves an FID of 4.55 in one step (1-NFE) and 3.98 in two steps (2-NFE) without perceptual losses.

Modern diffusion/flow-based models for image generation typically exhibit two core characteristics: (i) using multi-step sampling, and (ii) operating in a latent space. Recent advances have made encouraging progress on each aspect individually, paving the way toward one-step diffusion/flow without latents. In this work, we take a further step towards this goal and propose "pixel MeanFlow" (pMF). Our core guideline is to formulate the network output space and the loss space separately. The network target is designed to be on a presumed low-dimensional image manifold (i.e., x-prediction), while the loss is defined via MeanFlow in the velocity space. We introduce a simple transformation between the image manifold and the average velocity field. In experiments, pMF achieves strong results for one-step latent-free generation on ImageNet at 256x256 resolution (2.22 FID) and 512x512 resolution (2.48 FID), filling a key missing piece in this regime. We hope that our study will further advance the boundaries of diffusion/flow-based generative models.

Visual counterfactual explanations aim to change classifier decisions through realistic and localized edits while preserving decision-irrelevant content. Existing DDPM-based methods typically perform classifier-guided editing along a long reverse denoising trajectory. The changing noise levels make semantic editability and spatial control difficult to balance, and the editable state is noisy, whereas the target classifier is trained on clean images. As a result, these methods require either costly recursive denoising or low-quality one-step estimates to obtain classifier-facing clean images. We propose FiRe, a Fixed-noise Refinement framework for visual counterfactual explanations. Rather than following a reverse denoising trajectory, FiRe maps the input to a fixed noise level and iteratively refines the noisy state at that level. To provide clean images for classifier guidance, FiRe first adapts Pixel Mean Flow to visual counterfactual explanation, enabling direct clean-image prediction from noisy states. To make fixed-noise refinement produce minimal and localized counterfactual edits, FiRe introduces three FiRe-specific controls: a dynamic dual-mask strategy, adaptive guidance, and early stopping, which determine where edits accumulate, which changes become visible, and when refinement stops. Experiments on five tasks across three datasets show that, compared with the strongest recent baseline, FiRe achieves about 3times faster online inference and 8times fewer FLOPs while obtaining comparable or state-of-the-art counterfactual quality.

We present PixelFlow, a family of image generation models that operate directly in the raw pixel space, in contrast to the predominant latent-space models. This approach simplifies the image generation process by eliminating the need for a pre-trained Variational Autoencoder (VAE) and enabling the whole model end-to-end trainable. Through efficient cascade flow modeling, PixelFlow achieves affordable computation cost in pixel space. It achieves an FID of 1.98 on 256times256 ImageNet class-conditional image generation benchmark. The qualitative text-to-image results demonstrate that PixelFlow excels in image quality, artistry, and semantic control. We hope this new paradigm will inspire and open up new opportunities for next-generation visual generation models. Code and models are available at https://github.com/ShoufaChen/PixelFlow.

Pixel-space diffusion models provide an appealing alternative to latent-space diffusion models by directly modeling raw images without relying on a learned tokenizer. However, scaling pixel-space models has predominantly followed dense strategies, tightly coupling model capacity with active computation. In this work, we show that standard LLM-style Mixture-of-Experts (MoE) architectures can be effectively transferred to pixel-space diffusion. Building on this finding, we introduce PixelMoE, a pixel-space generative framework that sparsely scales model capacity with standard LLM-style MoE, without diffusion-specific routing mechanisms or auxiliary routing objectives. Specifically, PixelMoE combines standard Token-Choice (TC) routing with fine-grained routed experts for input-adaptive sparse computation, a shared expert for capturing common representations, and a bias-based load-balancing strategy. To complement sparse capacity scaling, PixelMoE further introduces Pixel-Space Hierarchical Flow Matching, which varies spatial resolution along the denoising trajectory from global structure formation to fine-grained detail refinement. At comparable active parameter counts, PixelMoE consistently outperforms its dense counterparts across model scales, demonstrating effective sparse capacity scaling in pixel space. On class-conditional ImageNet-1K, PixelMoE achieves FID scores of 1.47 at 256x256 and 1.53 at 512x512 without representation alignment or perceptual losses, comparing favorably with leading pixel-space and latent-space generative models. Code and models will be released soon.

We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A well-defined identity between average and instantaneous velocities is derived and used to guide neural network training. Our method, termed the MeanFlow model, is self-contained and requires no pre-training, distillation, or curriculum learning. MeanFlow demonstrates strong empirical performance: it achieves an FID of 3.43 with a single function evaluation (1-NFE) on ImageNet 256x256 trained from scratch, significantly outperforming previous state-of-the-art one-step diffusion/flow models. Our study substantially narrows the gap between one-step diffusion/flow models and their multi-step predecessors, and we hope it will motivate future research to revisit the foundations of these powerful models.

Photo-realistic image restoration algorithms are typically evaluated by distortion measures (e.g., PSNR, SSIM) and by perceptual quality measures (e.g., FID, NIQE), where the desire is to attain the lowest possible distortion without compromising on perceptual quality. To achieve this goal, current methods typically attempt to sample from the posterior distribution, or to optimize a weighted sum of a distortion loss (e.g., MSE) and a perceptual quality loss (e.g., GAN). Unlike previous works, this paper is concerned specifically with the optimal estimator that minimizes the MSE under a constraint of perfect perceptual index, namely where the distribution of the reconstructed images is equal to that of the ground-truth ones. A recent theoretical result shows that such an estimator can be constructed by optimally transporting the posterior mean prediction (MMSE estimate) to the distribution of the ground-truth images. Inspired by this result, we introduce Posterior-Mean Rectified Flow (PMRF), a simple yet highly effective algorithm that approximates this optimal estimator. In particular, PMRF first predicts the posterior mean, and then transports the result to a high-quality image using a rectified flow model that approximates the desired optimal transport map. We investigate the theoretical utility of PMRF and demonstrate that it consistently outperforms previous methods on a variety of image restoration tasks.

Tracking pixels in videos is typically studied as an optical flow estimation problem, where every pixel is described with a displacement vector that locates it in the next frame. Even though wider temporal context is freely available, prior efforts to take this into account have yielded only small gains over 2-frame methods. In this paper, we revisit Sand and Teller's "particle video" approach, and study pixel tracking as a long-range motion estimation problem, where every pixel is described with a trajectory that locates it in multiple future frames. We re-build this classic approach using components that drive the current state-of-the-art in flow and object tracking, such as dense cost maps, iterative optimization, and learned appearance updates. We train our models using long-range amodal point trajectories mined from existing optical flow data that we synthetically augment with multi-frame occlusions. We test our approach in trajectory estimation benchmarks and in keypoint label propagation tasks, and compare favorably against state-of-the-art optical flow and feature tracking methods.

MeanFlow (MF) is a diffusion-motivated generative model that enables efficient few-step generation by learning long jumps directly from noise to data. In practice, it is often used as a latent MF by leveraging the pre-trained Stable Diffusion variational autoencoder (SD-VAE) for high-dimensional data modeling. However, MF training remains computationally demanding and is often unstable. During inference, the SD-VAE decoder dominates the generation cost, and MF depends on complex guidance hyperparameters for class-conditional generation. In this work, we develop an efficient training and sampling scheme for MF in the latent space of a Representation Autoencoder (RAE), where a pre-trained vision encoder (e.g., DINO) provides semantically rich latents paired with a lightweight decoder. We observe that naive MF training in the RAE latent space suffers from severe gradient explosion. To stabilize and accelerate training, we adopt Consistency Mid-Training for trajectory-aware initialization and use a two-stage scheme: distillation from a pre-trained flow matching teacher to speed convergence and reduce variance, followed by an optional bootstrapping stage with a one-point velocity estimator to further reduce deviation from the oracle mean flow. This design removes the need for guidance, simplifies training configurations, and reduces computation in both training and sampling. Empirically, our method achieves a 1-step FID of 2.03, outperforming vanilla MF's 3.43, while reducing sampling GFLOPS by 38% and total training cost by 83% on ImageNet 256. We further scale our approach to ImageNet 512, achieving a competitive 1-step FID of 3.23 with the lowest GFLOPS among all baselines. Code is available at https://github.com/sony/mf-rae.

Flow-based generation in high-dimensional spaces is difficult because velocity prediction requires modeling high-dimensional noise, even when data has strong low-rank structure. We present Asymmetric Flow Modeling (AsymFlow), a rank-asymmetric velocity parameterization that restricts noise prediction to a low-rank subspace while keeping data prediction full-dimensional. From this asymmetric prediction, AsymFlow analytically recovers the full-dimensional velocity without changing the network architecture or training/sampling procedures. On ImageNet 256times256, AsymFlow achieves a leading 1.57 FID, outperforming prior DiT/JiT-like pixel diffusion models by a large margin. AsymFlow also provides the first-ever route for finetuning pretrained latent flow models into pixel-space models: aligning the low-rank pixel subspace to the latent space gives a seamless initialization that preserves the latent model's high-level semantics and structure, so finetuning mainly improves low-level mismatches rather than relearning pixel generation. We show that the pixel AsymFlow model finetuned from FLUX.2 klein 9B establishes a new state of the art for pixel-space text-to-image generation, beating its latent base on HPSv3, DPG-Bench, and GenEval while qualitatively showing substantially improved visual realism.

In this work, we introduce Modulated Flows (ModFlows), a novel approach for color transfer between images based on rectified flows. The primary goal of the color transfer is to adjust the colors of a target image to match the color distribution of a reference image. Our technique is based on optimal transport and executes color transfer as an invertible transformation within the RGB color space. The ModFlows utilizes the bijective property of flows, enabling us to introduce a common intermediate color distribution and build a dataset of rectified flows. We train an encoder on this dataset to predict the weights of a rectified model for new images. After training on a set of optimal transport plans, our approach can generate plans for new pairs of distributions without additional fine-tuning. We additionally show that the trained encoder provides an image embedding, associated only with its color style. The presented method is capable of processing 4K images and achieves the state-of-the-art performance in terms of content and style similarity. Our source code is available at https://github.com/maria-larchenko/modflows

Pixel diffusion aims to generate images directly in pixel space in an end-to-end fashion. This approach avoids the limitations of VAE in the two-stage latent diffusion, offering higher model capacity. Existing pixel diffusion models suffer from slow training and inference, as they usually model both high-frequency signals and low-frequency semantics within a single diffusion transformer (DiT). To pursue a more efficient pixel diffusion paradigm, we propose the frequency-DeCoupled pixel diffusion framework. With the intuition to decouple the generation of high and low frequency components, we leverage a lightweight pixel decoder to generate high-frequency details conditioned on semantic guidance from the DiT. This thus frees the DiT to specialize in modeling low-frequency semantics. In addition, we introduce a frequency-aware flow-matching loss that emphasizes visually salient frequencies while suppressing insignificant ones. Extensive experiments show that DeCo achieves superior performance among pixel diffusion models, attaining FID of 1.62 (256x256) and 2.22 (512x512) on ImageNet, closing the gap with latent diffusion methods. Furthermore, our pretrained text-to-image model achieves a leading overall score of 0.86 on GenEval in system-level comparison. Codes are publicly available at https://github.com/Zehong-Ma/DeCo.

Unified Multimodal Models (UMMs) often rely on separate visual representations for understanding and generation, increasing visual context length and complicating integration with established vision-language pretraining pipelines. Recent advances in pixel-space modeling offer an encoder-free alternative, but extending this paradigm from images to videos is non-trivial: video understanding and generation adopt different temporal representations, leaving the design of a unified visual interface an open question. We present PixelUMM, an encoder-free model for unified image and video understanding and generation directly in pixel space. PixelUMM represents images as spatial patches and videos as spatiotemporal tubelets, connecting raw pixels to a shared multimodal backbone through single-layer linear projections. Its Mixture-of-Transformers architecture combines shared attention with task-specific parameters and extends clean-pixel prediction to video generation, jointly supporting autoregressive text prediction and pixel-space flow matching. Experiments show that PixelUMM achieves competitive performance across image and video understanding and generation tasks. We further conduct empirical studies of key design choices, including decoder design and spatial-temporal patch size, providing insights for future pixel-space unified multimodal models.

MeanFlow has recently emerged as a powerful framework for few-step generative modeling trained from scratch, but its success is not yet fully understood. In this work, we show that the MeanFlow objective naturally decomposes into two parts: trajectory flow matching and trajectory consistency. Through gradient analysis, we find that these terms are strongly negatively correlated, causing optimization conflict and slow convergence. Motivated by these insights, we introduce alpha-Flow, a broad family of objectives that unifies trajectory flow matching, Shortcut Model, and MeanFlow under one formulation. By adopting a curriculum strategy that smoothly anneals from trajectory flow matching to MeanFlow, alpha-Flow disentangles the conflicting objectives, and achieves better convergence. When trained from scratch on class-conditional ImageNet-1K 256x256 with vanilla DiT backbones, alpha-Flow consistently outperforms MeanFlow across scales and settings. Our largest alpha-Flow-XL/2+ model achieves new state-of-the-art results using vanilla DiT backbones, with FID scores of 2.58 (1-NFE) and 2.15 (2-NFE).

Studying scalable methods for visual generative modeling requires large, accessible, and stable datasets. We introduce GPIC, a Giant Permissive Image Corpus of approximately 28 trillion pixels. GPIC comprises diverse internet images captioned by a state-of-the-art vision-language model, including 100M training, 200K validation, and 1M test examples. Moreover, all GPIC images are permissively licensed for both research and commercial use. GPIC is safety-filtered, deduplicated, and centrally hosted on Hugging Face. We provide a benchmarking protocol for generative modeling on GPIC. Finally, we provide a reference baseline for pixel-space flow matching on GPIC. Our dataset, benchmark, and models are available at https://huggingface.co/datasets/stanford-vision-lab/gpic. Evaluation toolkit and code are available at https://gpic.stanford.edu

Denoising generative models, such as diffusion and flow-based models, produce high-quality samples but require many denoising steps due to discretization error. Flow maps, which estimate the average velocity between timesteps, mitigate this error and enable faster sampling. However, their training typically demands architectural changes that limit compatibility with pretrained flow models. We introduce Decoupled MeanFlow, a simple decoding strategy that converts flow models into flow map models without architectural modifications. Our method conditions the final blocks of diffusion transformers on the subsequent timestep, allowing pretrained flow models to be directly repurposed as flow maps. Combined with enhanced training techniques, this design enables high-quality generation in as few as 1 to 4 steps. Notably, we find that training flow models and subsequently converting them is more efficient and effective than training flow maps from scratch. On ImageNet 256x256 and 512x512, our models attain 1-step FID of 2.16 and 2.12, respectively, surpassing prior art by a large margin. Furthermore, we achieve FID of 1.51 and 1.68 when increasing the steps to 4, which nearly matches the performance of flow models while delivering over 100x faster inference.

This paper investigates an increasingly important topic in generative modeling: pixel-space diffusion models. Although numerous studies have explored this topic, most focus on small-scale or class-conditional settings. Consequently, a practical recipe for training pixel-space models that rival or exceed well-established latent-space counterparts remains elusive. Through a comprehensive empirical study, we first observe that direct large-scale pre-training in pixel space converges substantially more slowly than in latent space. This observation motivates a latent-to-pixel strategy that acquires generative priors efficiently in latent space and transitions to pixel space during post-training. We then systematically investigate the key design choices governing this transition, including weight initialization, data composition, prediction target, decoder architecture, and noise schedule, and identify a practical recipe that makes the resulting pixel-space models match or outperform their latent-space counterparts while delivering 3.18 to 4.75 times end-to-end inference speedups. We hope that our findings provide useful empirical insights and practical guidelines for future research on pixel-space generation.

Optical flow, which captures motion information across frames, is exploited in recent video inpainting methods through propagating pixels along its trajectories. However, the hand-crafted flow-based processes in these methods are applied separately to form the whole inpainting pipeline. Thus, these methods are less efficient and rely heavily on the intermediate results from earlier stages. In this paper, we propose an End-to-End framework for Flow-Guided Video Inpainting (E^2FGVI) through elaborately designed three trainable modules, namely, flow completion, feature propagation, and content hallucination modules. The three modules correspond with the three stages of previous flow-based methods but can be jointly optimized, leading to a more efficient and effective inpainting process. Experimental results demonstrate that the proposed method outperforms state-of-the-art methods both qualitatively and quantitatively and shows promising efficiency. The code is available at https://github.com/MCG-NKU/E2FGVI.

Pixel-space diffusion has recently emerged as a promising direction for high-fidelity image generation by modeling images directly in the original pixel domain. However, pixel-space diffusion is computationally demanding due to the extremely high dimensionality of natural images. For efficiency, existing pixel diffusion models either compromise fine details with large-patch tokenization or confine subsequent refinement within individual patches. Such intra-patch refinement inevitably restricts structural continuity across patch boundaries and long-range token interactions, limiting refinement quality. To address these issues, we propose PixSGR, a novel Pixel diffusion framework with Sparse Global Refinement tailored for modeling the distribution of natural images directly in pixel space. PixSGR starts from a supervised low-channel bottleneck to efficiently capture the low-dimensional manifold of natural images. It then progressively expands the channel dimensionality and spatial resolution to recover increasingly fine-grained structures. At the spatial refinement stage, coarse-scale attention maps preselect globally relevant interactions to pre-sparsify fine-scale attention, enabling non-local refinement beyond isolated patches without the quadratic cost of dense attention. Extensive experiments on ImageNet validate the effectiveness of PixSGR. It achieves an FID of 1.51 at 256times256 and maintains performance when scaled to 512times512, attaining an FID of 1.60.

Flow-based generative models have recently demonstrated strong performance, yet sampling typically relies on expensive numerical integration of ordinary differential equations (ODEs). Rectified Flow enables one-step sampling by learning nearly straight probability paths, but achieving such straightness requires multiple computationally intensive reflow iterations. MeanFlow achieves one-step generation by directly modeling the average velocity over time; however, when trained on highly curved flows, it suffers from slow convergence and noisy supervision. To address these limitations, we propose Rectified MeanFlow, a framework that models the mean velocity field along the rectified trajectory using only a single reflow step. This eliminates the need for perfectly straightened trajectories while enabling efficient training. Furthermore, we introduce a simple yet effective truncation heuristic that aims to reduce residual curvature and further improve performance. Extensive experiments on ImageNet at 64, 256, and 512 resolutions show that Re-MeanFlow consistently outperforms prior one-step flow distillation and Rectified Flow methods in both sample quality and training efficiency. Code is available at https://github.com/Xinxi-Zhang/Re-MeanFlow.

While recent Flow Matching models avoid the reconstruction bottlenecks of latent autoencoders by operating directly in pixel space, the lack of semantic continuity in the pixel manifold severely intertwines optimal transport paths. This induces severe trajectory conflicts near intersections, yielding sub-optimal solutions. Rather than bypassing this issue via information-lossy latent representations, we directly untangle the pixel-space trajectories by proposing Waypoint Diffusion Transformers (WiT). WiT factorizes the continuous vector field via intermediate semantic waypoints projected from pre-trained vision models. It effectively disentangles the generation trajectories by breaking the optimal transport into prior-to-waypoint and waypoint-to-pixel segments. Specifically, during the iterative denoising process, a lightweight generator dynamically infers these intermediate waypoints from the current noisy state. They then continuously condition the primary diffusion transformer via the Just-Pixel AdaLN mechanism, steering the evolution towards the next state, ultimately yielding the final RGB pixels. Evaluated on ImageNet 256x256, WiT beats strong pixel-space baselines, accelerating JiT training convergence by 2.2x. Code will be publicly released at https://github.com/hainuo-wang/WiT.git.

MeanFlow generators achieve fast few-step sampling by predicting average velocities over time intervals, making them attractive for efficient generation. Reinforcement learning (RL) has become a powerful way to align diffusion and flow models with human preferences and task-specific objectives. In particular, DiffusionNFT offers an efficient forward-process RL framework that does not require reverse-process trajectories or likelihood estimation. However, applying such RL methods to MeanFlow remains underexplored. DiffusionNFT optimizes instantaneous velocities, whereas MeanFlow samples with average velocities. To bridge this gap, we introduce MeanFlowNFT. Inspired by the MeanFlow identity, which bridges average and instantaneous velocities, we construct an induced instantaneous-velocity predictor. We apply the DiffusionNFT objective to this predictor, making reward optimization well-defined for MeanFlow. Sampling remains based on the average velocity, preserving MeanFlow's fast few-step generation. We further prove that MeanFlowNFT inherits DiffusionNFT's strict policy-improvement guarantee. Experiments on image and video generation show that MeanFlowNFT consistently improves baselines. Moreover, it outperforms prior state-of-the-art RL-tuned few-step generators on most metrics (6 of 8 on SD3.5-M), and can even surpass multi-step RL-tuned diffusion while using only a few sampling steps. For instance, on Wan 2.1, 4-step MeanFlowNFT reaches a VBench score of 84.33, surpassing 50-step LongCat-Video RL (82.57).

Flow Matching models have demonstrated strong performance across a wide range of generative tasks. However, their reliance on ODE-based iterative sampling incurs substantial computational overhead in inference, which limits their applicability in real-time scenes. While distillation is a promising solution, existing approaches largely borrow from diffusion-based score matching, often failing to exploit the intrinsic geometric structure of flows and suffering from training instability, high variance, and degraded generation quality. In this paper, we propose Mean Flow Distillation (MFD), a novel distillation framework tailored for flow matching models. We theoretically demonstrate that MFD acts as a temporal low-pass filter, effectively suppressing the high-frequency optimization noise inherent in variational score distillation (VSD) while ensuring global trajectory consistency. We further prove the Mean Flow Matching Theorem, establishing that matching expected average velocities is sufficient for strict distribution alignment. Empirically, on challenging tasks of high-dimensional manifolds including 4D occupancy forecasting and text-to-image generation, MFD achieves state-of-the-art performance, enabling high-fidelity single-step generation.

Optical flow estimation is a fundamental problem in computer vision, yet the reliance on expensive ground-truth annotations limits the scalability of supervised approaches. Although unsupervised and semi-supervised methods alleviate this issue, they often suffer from unreliable supervision signals based on brightness constancy and smoothness assumptions, leading to inaccurate motion estimation in complex real-world scenarios. To overcome these limitations, we introduce \modelname, a novel framework that synthesizes large-scale, perfectly aligned frame--flow data pairs for supervised optical flow training without human annotations. Specifically, our method leverages a pre-trained depth estimation network to generate pseudo optical flows, which serve as conditioning inputs for a next-frame generation model trained to produce high-fidelity, pixel-aligned subsequent frames. This process enables the creation of abundant, high-quality synthetic data with precise motion correspondence. Furthermore, we propose an inconsistent pixel filtering strategy that identifies and removes unreliable pixels in generated frames, effectively enhancing fine-tuning performance on real-world datasets. Extensive experiments on KITTI2012, KITTI2015, and Sintel demonstrate that \modelname achieves competitive or superior results compared to existing unsupervised and semi-supervised approaches, highlighting its potential as a scalable and annotation-free solution for optical flow learning. We will release our code upon acceptance.

Creating 4D fields of Gaussian Splatting from images or videos is a challenging task due to its under-constrained nature. While the optimization can draw photometric reference from the input videos or be regulated by generative models, directly supervising Gaussian motions remains underexplored. In this paper, we introduce a novel concept, Gaussian flow, which connects the dynamics of 3D Gaussians and pixel velocities between consecutive frames. The Gaussian flow can be efficiently obtained by splatting Gaussian dynamics into the image space. This differentiable process enables direct dynamic supervision from optical flow. Our method significantly benefits 4D dynamic content generation and 4D novel view synthesis with Gaussian Splatting, especially for contents with rich motions that are hard to be handled by existing methods. The common color drifting issue that happens in 4D generation is also resolved with improved Guassian dynamics. Superior visual quality on extensive experiments demonstrates our method's effectiveness. Quantitative and qualitative evaluations show that our method achieves state-of-the-art results on both tasks of 4D generation and 4D novel view synthesis. Project page: https://zerg-overmind.github.io/GaussianFlow.github.io/

Latent diffusion models have become the popular choice for scaling up diffusion models for high resolution image synthesis. Compared to pixel-space models that are trained end-to-end, latent models are perceived to be more efficient and to produce higher image quality at high resolution. Here we challenge these notions, and show that pixel-space models can in fact be very competitive to latent approaches both in quality and efficiency, achieving 1.5 FID on ImageNet512 and new SOTA results on ImageNet128 and ImageNet256. We present a simple recipe for scaling end-to-end pixel-space diffusion models to high resolutions. 1: Use the sigmoid loss (Kingma & Gao, 2023) with our prescribed hyper-parameters. 2: Use our simplified memory-efficient architecture with fewer skip-connections. 3: Scale the model to favor processing the image at high resolution with fewer parameters, rather than using more parameters but at a lower resolution. When combining these three steps with recently proposed tricks like guidance intervals, we obtain a family of pixel-space diffusion models we call Simple Diffusion v2 (SiD2).

Visual representations are largely developed for understanding, yet what makes them useful for generation remains unclear. We study this question in pixel diffusion transformers and uncover two key insights. First, better representation quality does not necessarily translate into greater generative utility, as externally aligned semantics can be progressively lost during pixel synthesis. Second, architectural separation with specialized pixel decoders mainly redistributes semantic and spatial modeling, without necessarily yielding representations better suited to generation. These insights suggest that a useful generative representation must be both properly formed and actively exploited. Motivated by these insights, we introduce Representation Guidance (RG), which directly forms and exploits internal representations while retaining a plain Transformer architecture. A low-dimensional bottleneck forces generation-relevant information into a compact representation, which is then explicitly used to guide decoder generation by modifying the flow-matching target according to its induced prediction offset. RG learns clearer semantic and spatial structure while scaling efficiently in both parameters and computation. On ImageNet 256x256, RG-L/16 with only 459M parameters outperforms substantially larger pixel diffusion transformers, while RG-XL/16 achieves an FID of 1.55. RG further reaches an FID of 1.74 at 512x512 and extends to text-to-image generation, achieving 0.89 on GenEval and 87.1 on DPG-Bench.

Normalizing Flows (NFs) are powerful generative models capable of exact density estimation and sampling. However, their strict invertibility often forces the model to exhaust its capacity on low-level pixel details, hindering the capture of high-level semantic structures. While Masked Image Modeling (MIM) has excelled in representation learning, its integration into generative pipelines has remained largely modular and disjointed. In this paper, we propose MIMFlow, a unified end-to-end framework that jointly optimizes latent semantics, pixel reconstruction, and generative flow. By employing a VAE encoder to infer semantic latent from masked images, MIMFlow achieves a principled decoupling of the generative task: the Normalizing Flow focuses on modeling a simplified, low-frequency semantic manifold, while a specialized decoder handles high-frequency synthesis. This design effectively resolves the inherent capacity bottleneck of NFs, allowing the model to prioritize global structural coherence over redundant noise. Empirical results on ImageNet 256times256 show that MIMFlow-L reaches 71.3\% linear probing accuracy and an FID of 2.50. Despite using only 128 tokens (50\% fewer than standard models), it yields a 32.8\% performance gain over similar-scale NF baselines. Our code is available at https://github.com/MCG-NJU/MIMFlow.

The objective of this paper is motion segmentation -- discovering and segmenting the moving objects in a video. This is a much studied area with numerous careful,and sometimes complex, approaches and training schemes including: self-supervised learning, learning from synthetic datasets, object-centric representations, amodal representations, and many more. Our interest in this paper is to determine if the Segment Anything model (SAM) can contribute to this task. We investigate two models for combining SAM with optical flow that harness the segmentation power of SAM with the ability of flow to discover and group moving objects. In the first model, we adapt SAM to take optical flow, rather than RGB, as an input. In the second, SAM takes RGB as an input, and flow is used as a segmentation prompt. These surprisingly simple methods, without any further modifications, outperform all previous approaches by a considerable margin in both single and multi-object benchmarks. We also extend these frame-level segmentations to sequence-level segmentations that maintain object identity. Again, this simple model outperforms previous methods on multiple video object segmentation benchmarks.

Semantic segmentation and semantic image synthesis are two representative tasks in visual perception and generation. While existing methods consider them as two distinct tasks, we propose a unified diffusion-based framework (SemFlow) and model them as a pair of reverse problems. Specifically, motivated by rectified flow theory, we train an ordinary differential equation (ODE) model to transport between the distributions of real images and semantic masks. As the training object is symmetric, samples belonging to the two distributions, images and semantic masks, can be effortlessly transferred reversibly. For semantic segmentation, our approach solves the contradiction between the randomness of diffusion outputs and the uniqueness of segmentation results. For image synthesis, we propose a finite perturbation approach to enhance the diversity of generated results without changing the semantic categories. Experiments show that our SemFlow achieves competitive results on semantic segmentation and semantic image synthesis tasks. We hope this simple framework will motivate people to rethink the unification of low-level and high-level vision. Project page: https://github.com/wang-chaoyang/SemFlow.

This work aims at designing a lightweight convolutional neural network for image super resolution (SR). With simplicity bare in mind, we construct a pretty concise and effective network with a newly proposed pixel attention scheme. Pixel attention (PA) is similar as channel attention and spatial attention in formulation. The difference is that PA produces 3D attention maps instead of a 1D attention vector or a 2D map. This attention scheme introduces fewer additional parameters but generates better SR results. On the basis of PA, we propose two building blocks for the main branch and the reconstruction branch, respectively. The first one - SC-PA block has the same structure as the Self-Calibrated convolution but with our PA layer. This block is much more efficient than conventional residual/dense blocks, for its twobranch architecture and attention scheme. While the second one - UPA block combines the nearest-neighbor upsampling, convolution and PA layers. It improves the final reconstruction quality with little parameter cost. Our final model- PAN could achieve similar performance as the lightweight networks - SRResNet and CARN, but with only 272K parameters (17.92% of SRResNet and 17.09% of CARN). The effectiveness of each proposed component is also validated by ablation study. The code is available at https://github.com/zhaohengyuan1/PAN.

Recent work in unsupervised multi-object segmentation shows impressive results by predicting motion from a single image despite the inherent ambiguity in predicting motion without the next image. On the other hand, the set of possible motions for an image can be constrained to a low-dimensional space by considering the scene structure and moving objects in it. We propose to model pixel-wise geometry and object motion to remove ambiguity in reconstructing flow from a single image. Specifically, we divide the image into coherently moving regions and use depth to construct flow bases that best explain the observed flow in each region. We achieve state-of-the-art results in unsupervised multi-object segmentation on synthetic and real-world datasets by modeling the scene structure and object motion. Our evaluation of the predicted depth maps shows reliable performance in monocular depth estimation.

Pixel diffusion generates images directly in pixel space in an end-to-end manner, avoiding the artifacts and bottlenecks introduced by VAEs in two-stage latent diffusion. However, it is challenging to optimize high-dimensional pixel manifolds that contain many perceptually irrelevant signals, leaving existing pixel diffusion methods lagging behind latent diffusion models. We propose PixelGen, a simple pixel diffusion framework with perceptual supervision. Instead of modeling the full image manifold, PixelGen introduces two complementary perceptual losses to guide diffusion model towards learning a more meaningful perceptual manifold. An LPIPS loss facilitates learning better local patterns, while a DINO-based perceptual loss strengthens global semantics. With perceptual supervision, PixelGen surpasses strong latent diffusion baselines. It achieves an FID of 5.11 on ImageNet-256 without classifier-free guidance using only 80 training epochs, and demonstrates favorable scaling performance on large-scale text-to-image generation with a GenEval score of 0.79. PixelGen requires no VAEs, no latent representations, and no auxiliary stages, providing a simpler yet more powerful generative paradigm. Codes are publicly available at https://github.com/Zehong-Ma/PixelGen.

At the most basic level, pixels are the source of the visual information through which we perceive the world. Pixels contain information at all levels, ranging from low-level attributes to high-level concepts. Autoencoders represent a classical and long-standing paradigm for learning representations from pixels or other raw inputs. In this work, we demonstrate that autoencoder-based self-supervised learning remains competitive today and can produce strong representations for downstream tasks, while remaining simple, stable, and efficient. Our model, codenamed "Pixio", is an enhanced masked autoencoder (MAE) with more challenging pre-training tasks and more capable architectures. The model is trained on 2B web-crawled images with a self-curation strategy with minimal human curation. Pixio performs competitively across a wide range of downstream tasks in the wild, including monocular depth estimation (e.g., Depth Anything), feed-forward 3D reconstruction (i.e., MapAnything), semantic segmentation, and robot learning, outperforming or matching DINOv3 trained at similar scales. Our results suggest that pixel-space self-supervised learning can serve as a promising alternative and a complement to latent-space approaches.

Pixel-space generative models bypass lossy latent compression, yet necessitate joint learning of global structure and fine-grained details in a high-dimensional space. Standard flow matching interpolates noise toward a fixed clean-image endpoint, leaving the spectral evolution to be learned implicitly. In this paper, we introduce Energy-Guided Flow Matching(EG-FM) that explicitly models a coarse-to-fine generative trajectory by moving endpoint. Specifically, EG-FM replaces the fixed endpoint with a heat-kernel-filtered endpoint that evolves smoothly from low-frequency image to clean image. The fraction of high-frequency signal in moving endpoint is released by an image-specific energy-guided scheduling, leading to the re-targeting of velocity in flow matching. Our framework requires no adaptation of the backbone and training data, bringing negligible cost on the training and inference stages. In our experiment, EG-FM consistently achieves lower FID on the ImageNet class-conditional image generation task at 256 times 256 with fewer epochs, reaching an FID of 1.55 at 200 epochs and 1.45 at 600 epochs. We continue training the generation task on the setting of 512 times 512 resolution, yielding a FID of 1.58 after only 40 high-resolution adaptation epochs. Furthermore, we transfer EG-FM on text-to-image generation and achieve 0.85 on GenEval score and 83.9 on DPG-Bench. Code is available at https://github.com/ysng123/EG-FM.

Latent diffusion models (LDMs) enable efficient high-resolution image synthesis by denoising in a VAE-compressed latent space. However, fixed visual tokenizers can discard fine textures and structural details, while separate representation and diffusion training creates a mismatch between reconstruction and generation objectives. These limitations have renewed interest in pixel-space diffusion, which models raw pixels directly, removes the VAE bottleneck, and supports end-to-end optimization. This formulation better matches the demands of high-fidelity generation but introduces challenges in high-dimensional modeling, including noise scheduling, loss weighting, token efficiency, and scalable architecture design. Pixel-space modeling also offers a promising basis for unified multimodal systems: raw pixels, text, and task conditions can be represented in a shared token space and jointly processed by a single Transformer, narrowing the gap between visual understanding and generation. This paper reviews Pixel-Space Diffusion Transformers (pDiTs) from the perspectives of model architecture, continuous generative mechanisms, and unified multimodal modeling. We summarize representative methods, identify key technical challenges, and discuss future directions toward high-fidelity, end-to-end vision foundation models that integrate generation and understanding.

Pixel-space diffusion models are trained on full-bandwidth noisy images, yet the useful signal available to the denoiser is strongly frequency dependent. Under rectified-flow diffusion and natural-image power-law spectra, the per-band data-to-noise contour k^{*}(t) = (1-t)^{-2/α} separates a signal-bearing low-frequency region from a noise-dominated high-frequency region at each time t. We show that this implicit coarse-to-fine structure is not merely descriptive: it induces a capacity-allocation problem. A standard pixel-space denoiser must discover the moving bandwidth boundary internally and can spend computation on frequency-time regions where the optimal prediction collapses to deterministic baselines rather than data-distribution modeling. To make this boundary explicit, we introduce Spectral Forcing, a parameter-free, time-conditional 2D-DCT low-pass operator applied to the noisy input before the patch embedder. Its cutoff expands monotonically with the diffusion time and becomes the identity at the data endpoint. Through controlled synthetic experiments, we identify the regime in which the operator is beneficial: coarse patch tokenization and data whose high-frequency content is predominantly noise rather than essential signal. On ImageNet-256 with JiT-700M/32, Spectral Forcing consistently improves both FID and Inception Score across different training epochs, demonstrating robust gains throughout training; at finer tokenization, the spectral forcing is still competitive. We further insert the unchanged operator into SenseNova-U1, a unified text-to-image model, where it improves DPG-Bench and GenEval, showing that the input-side spectral prior transfers beyond class-conditional generation. These results suggest a route to capacity-efficient pixel-space diffusion by showing the signal and hiding the noise.

This paper introduces the first two pixel retrieval benchmarks. Pixel retrieval is segmented instance retrieval. Like semantic segmentation extends classification to the pixel level, pixel retrieval is an extension of image retrieval and offers information about which pixels are related to the query object. In addition to retrieving images for the given query, it helps users quickly identify the query object in true positive images and exclude false positive images by denoting the correlated pixels. Our user study results show pixel-level annotation can significantly improve the user experience. Compared with semantic and instance segmentation, pixel retrieval requires a fine-grained recognition capability for variable-granularity targets. To this end, we propose pixel retrieval benchmarks named PROxford and PRParis, which are based on the widely used image retrieval datasets, ROxford and RParis. Three professional annotators label 5,942 images with two rounds of double-checking and refinement. Furthermore, we conduct extensive experiments and analysis on the SOTA methods in image search, image matching, detection, segmentation, and dense matching using our pixel retrieval benchmarks. Results show that the pixel retrieval task is challenging to these approaches and distinctive from existing problems, suggesting that further research can advance the content-based pixel-retrieval and thus user search experience. The datasets can be downloaded from https://github.com/anguoyuan/Pixel_retrieval-Segmented_instance_retrieval{this link}.

Flow models are effective at progressively generating realistic images, but they generally struggle to capture long-range dependencies during the generation process as they compress all the information from previous time steps into a single corrupted image. To address this limitation, we propose integrating autoregressive modeling -- known for its excellence in modeling complex, high-dimensional joint probability distributions -- into flow models. During training, at each step, we construct causally-ordered sequences by sampling multiple images from the same semantic category and applying different levels of noise, where images with higher noise levels serve as causal predecessors to those with lower noise levels. This design enables the model to learn broader category-level variations while maintaining proper causal relationships in the flow process. During generation, the model autoregressively conditions the previously generated images from earlier denoising steps, forming a contextual and coherent generation trajectory. Additionally, we design a customized hybrid linear attention mechanism tailored to our modeling approach to enhance computational efficiency. Our approach, termed ARFlow, under 400k training steps, achieves 14.08 FID scores on ImageNet at 128 * 128 without classifier-free guidance, reaching 4.34 FID with classifier-free guidance 1.5, significantly outperforming the previous flow-based model SiT's 9.17 FID. Extensive ablation studies demonstrate the effectiveness of our modeling strategy and chunk-wise attention design.

This report presents PixelBytes, an approach for unified multimodal representation learning. Drawing inspiration from sequence models like Image Transformers, PixelCNN, and Mamba-Bytes, we explore integrating text, audio, action-state, and pixelated images (sprites) into a cohesive representation. We conducted experiments on a PixelBytes Pokemon dataset and an Optimal-Control dataset. Our investigation covered various model architectures, including Recurrent Neural Networks (RNNs), State Space Models (SSMs), and Attention-based models, with a focus on bidirectional processing and our PxBy embedding technique. We evaluated models based on data reduction strategies and autoregressive learning, specifically examining Long Short-Term Memory (LSTM) networks in predictive and autoregressive modes. Our results indicate that autoregressive models perform better than predictive models in this context. Additionally, we found that diffusion models can be applied to control problems and parallelized generation. PixelBytes aims to contribute to the development of foundation models for multimodal data processing and generation. The project's code, models, and datasets are available online.

Latent-space modeling has been the standard for Diffusion Transformers (DiTs). However, it relies on a two-stage pipeline where the pretrained autoencoder introduces lossy reconstruction, leading to error accumulation while hindering joint optimization. To address these issues, we propose PixelDiT, a single-stage, end-to-end model that eliminates the need for the autoencoder and learns the diffusion process directly in the pixel space. PixelDiT adopts a fully transformer-based architecture shaped by a dual-level design: a patch-level DiT that captures global semantics and a pixel-level DiT that refines texture details, enabling efficient training of a pixel-space diffusion model while preserving fine details. Our analysis reveals that effective pixel-level token modeling is essential to the success of pixel diffusion. PixelDiT achieves 1.61 FID on ImageNet 256x256, surpassing existing pixel generative models by a large margin. We further extend PixelDiT to text-to-image generation and pretrain it at the 1024x1024 resolution in pixel space. It achieves 0.74 on GenEval and 83.5 on DPG-bench, approaching the best latent diffusion models.

Flow matching with x-prediction -- regressing the clean data point rather than the ambient velocity -- is known to exploit low-dimensional manifold structure effectively in pixel space li2025back. We ask whether a pretrained representation space, while containing a low-dimensional data manifold of comparable intrinsic dimensionality, offers a distribution more favorable for flow-matching learning. Comparing pixel, SD-VAE, and DINOv2 features along four geometric axes, we find that pixel and DINOv2 share nearly identical intrinsic dimensionalities (both d!approx!33) yet DINOv2 exhibits 7.3times higher effective rank, 35times better covariance conditioning, 11.5times lower excess kurtosis, and 1.7times lower on-manifold interpolation error; SD-VAE latents are consistently intermediate, indicating that the advantage stems from representation-learning objectives rather than mere compression. These statistical properties render the flow-matching regression well-conditioned and remove the need for the specialized prediction heads or Riemannian transport used by prior DINOv2 diffusion methods. We propose the Representation Image Transformer (RiT): a vanilla Diffusion Transformer trained by x-prediction on frozen DINOv2 features, augmented only by a dimension-aware noise schedule and joint [CLS]-patch modeling. On ImageNet 256{times}256, RiT attains FID 1.45 without guidance and 1.14 with classifier-free guidance, outperforming DiT^DH-XL with 19% fewer parameters (676M vs.\ 839M). The resulting ODE is efficiently solvable at coarse discretizations: with classifier-free guidance, 5 Heun steps already reach FID 2.0 and 10 steps reach 1.25, without distillation or consistency training. Code at https://github.com/lezhang7/RiT.

Most practical high-resolution text-to-image systems, including latent diffusion and autoregressive models, perform generation in a compact latent space, and a decoder maps the generated latents back to pixels. Yet the latent-to-pixel decoder is reconstruction-oriented, optimized to invert the encoder rather than synthesize more details, and becomes increasingly costly at megapixel scale. This drawback calls for a more expressive and efficient decoding paradigm. Motivated by recent progress in scalable pixel-space diffusion, we introduce PiD, a Pixel diffusion Decoder that reformulates latent decoding as conditional pixel diffusion, unifying decoding and upsampling into one generative module. By denoising directly in high-resolution pixel space, PiD synthesizes 4times and even 8times upscaled images with low latency. For latent conditioning, a lightweight sigma-aware adapter injects noise-corrupted latents into the pixel diffusion backbone, enabling PiD to decode partially denoised latents and terminate the latent diffusion process early. To further improve efficiency, we distill the model using DMD2, reducing inference to just 4 steps. PiD applies to both conventional VAE latents and semantic latents (e.g., SigLIP, DINOv2) used in recent RAE-based models. PiD decodes latents of 512 times 512 images into 2048 times 2048 pixels in under 1 second with 13 GB peak memory on a consumer RTX 5090, and as fast as 210 ms on a GB200 GPU, about 6times faster than cascaded diffusion-based super-resolution pipelines with better visual fidelity.

Most well-established and widely used color difference (CD) metrics are handcrafted and subject-calibrated against uniformly colored patches, which do not generalize well to photographic images characterized by natural scene complexities. Constructing CD formulae for photographic images is still an active research topic in imaging/illumination, vision science, and color science communities. In this paper, we aim to learn a deep CD metric for photographic images with four desirable properties. First, it well aligns with the observations in vision science that color and form are linked inextricably in visual cortical processing. Second, it is a proper metric in the mathematical sense. Third, it computes accurate CDs between photographic images, differing mainly in color appearances. Fourth, it is robust to mild geometric distortions (e.g., translation or due to parallax), which are often present in photographic images of the same scene captured by different digital cameras. We show that all these properties can be satisfied at once by learning a multi-scale autoregressive normalizing flow for feature transform, followed by the Euclidean distance which is linearly proportional to the human perceptual CD. Quantitative and qualitative experiments on the large-scale SPCD dataset demonstrate the promise of the learned CD metric.

Recent advances in pixel-space diffusion models have narrowed the image quality gap with latent-space diffusion, but still converge more slowly and lag behind in final image quality. We argue that a key reason is the lack of an explicit representation prior: unlike latent diffusion, which usually denoises in a compact and structured latent space, pixel diffusion needs to learn denoising-friendly representations and pixel generation simultaneously from raw RGB space. To address this problem, we propose PixelDiT2, an end-to-end pixel-space diffusion model designed to decouple representation learning from pixel generation without introducing an autoencoder or latent reconstruction bottleneck. We propose representation grounding that uses a frozen pretrained vision foundation model to provide explicit per-patch representation guidance throughout denoising, allowing the pixel diffusion transformer to focus more on pixel generation. On ImageNet-256x256, PixelDiT2 achieves an FID of 1.46 after 600 epochs; at 512x512 resolution, PixelDiT2 achieves an FID of 1.48 after 680 epochs.

Current scene flow methods broadly fail to describe motion on small objects, and current scene flow evaluation protocols hide this failure by averaging over many points, with most drawn larger objects. To fix this evaluation failure, we propose a new evaluation protocol, Bucket Normalized EPE, which is class-aware and speed-normalized, enabling contextualized error comparisons between object types that move at vastly different speeds. To highlight current method failures, we propose a frustratingly simple supervised scene flow baseline, TrackFlow, built by bolting a high-quality pretrained detector (trained using many class rebalancing techniques) onto a simple tracker, that produces state-of-the-art performance on current standard evaluations and large improvements over prior art on our new evaluation. Our results make it clear that all scene flow evaluations must be class and speed aware, and supervised scene flow methods must address point class imbalances. We release the evaluation code publicly at https://github.com/kylevedder/BucketedSceneFlowEval.

Generated images often have coherent layouts and visual content, yet local errors in small text and complex characters still limit their readability and practical use. Scene-text refinement requires accuracy, preservation, and efficiency. Existing methods based on variational autoencoders (VAEs) can lose fine strokes during reconstruction, while full-image editing can shift background colors. In this work, we introduce PixText, a model that formulates local text refinement as grouped image generation in pixel space. Conditioned on the original image, PixText generates only the target regions, preserves unedited content, and uses MeanFlow for four-step generation. We further introduce Text Refinement Bench to evaluate text correction and image preservation in generated images. On this benchmark, PixText achieves 83.06% glyph pass and 94.66% exact target-character OCR accuracy, versus 36.77% and 52.31% for the strongest baseline. Its four-step MeanFlow variant retains an 81.84% pass rate with less than one GPU-second of amortized generation cost per image.

PixelCNNs are a recently proposed class of powerful generative models with tractable likelihood. Here we discuss our implementation of PixelCNNs which we make available at https://github.com/openai/pixel-cnn. Our implementation contains a number of modifications to the original model that both simplify its structure and improve its performance. 1) We use a discretized logistic mixture likelihood on the pixels, rather than a 256-way softmax, which we find to speed up training. 2) We condition on whole pixels, rather than R/G/B sub-pixels, simplifying the model structure. 3) We use downsampling to efficiently capture structure at multiple resolutions. 4) We introduce additional short-cut connections to further speed up optimization. 5) We regularize the model using dropout. Finally, we present state-of-the-art log likelihood results on CIFAR-10 to demonstrate the usefulness of these modifications.

While large multimodal models (LMMs) have achieved remarkable progress, generating pixel-level masks for image reasoning tasks involving multiple open-world targets remains a challenge. To bridge this gap, we introduce PixelLM, an effective and efficient LMM for pixel-level reasoning and understanding. Central to PixelLM is a novel, lightweight pixel decoder and a comprehensive segmentation codebook. The decoder efficiently produces masks from the hidden embeddings of the codebook tokens, which encode detailed target-relevant information. With this design, PixelLM harmonizes with the structure of popular LMMs and avoids the need for additional costly segmentation models. Furthermore, we propose a target refinement loss to enhance the model's ability to differentiate between multiple targets, leading to substantially improved mask quality. To advance research in this area, we construct MUSE, a high-quality multi-target reasoning segmentation benchmark. PixelLM excels across various pixel-level image reasoning and understanding tasks, outperforming well-established methods in multiple benchmarks, including MUSE, single- and multi-referring segmentation. Comprehensive ablations confirm the efficacy of each proposed component. All code, models, and datasets will be publicly available.

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels K(x,y) = - |x-y|^r, r in (0,2) have exceptional properties which allow their efficient computation. We prove that the MMD of Riesz kernels, which is also known as energy distance, coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for r=1, a simple sorting algorithm can be applied to reduce the complexity from O(MN+N^2) to O((M+N)log(M+N)) for two measures with M and N support points. As another interesting follow-up result, the MMD of compactly supported measures can be estimated from above and below by the Wasserstein-1 distance. For the implementations we approximate the gradient of the sliced MMD by using only a finite number P of slices. We show that the resulting error has complexity O(d/P), where d is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for image applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10.

Image inpainting is a fundamental research area between image editing and image generation. Recent state-of-the-art (SOTA) methods have explored novel attention mechanisms, lightweight architectures, and context-aware modeling, demonstrating impressive performance. However, they often struggle with complex structure (e.g., texture, shape, spatial relations) and semantics (e.g., color consistency, object restoration, and logical correctness), leading to artifacts and inappropriate generation. To address this challenge, we design a simple yet effective inpainting paradigm called latent categories guidance, and further propose a diffusion-based model named PixelHacker. Specifically, we first construct a large dataset containing 14 million image-mask pairs by annotating foreground and background (potential 116 and 21 categories, respectively). Then, we encode potential foreground and background representations separately through two fixed-size embeddings, and intermittently inject these features into the denoising process via linear attention. Finally, by pre-training on our dataset and fine-tuning on open-source benchmarks, we obtain PixelHacker. Extensive experiments show that PixelHacker comprehensively outperforms the SOTA on a wide range of datasets (Places2, CelebA-HQ, and FFHQ) and exhibits remarkable consistency in both structure and semantics. Project page at https://hustvl.github.io/PixelHacker.

In this work, we introduce Pixelsmith, a zero-shot text-to-image generative framework to sample images at higher resolutions with a single GPU. We are the first to show that it is possible to scale the output of a pre-trained diffusion model by a factor of 1000, opening the road for gigapixel image generation at no additional cost. Our cascading method uses the image generated at the lowest resolution as a baseline to sample at higher resolutions. For the guidance, we introduce the Slider, a tunable mechanism that fuses the overall structure contained in the first-generated image with enhanced fine details. At each inference step, we denoise patches rather than the entire latent space, minimizing memory demands such that a single GPU can handle the process, regardless of the image's resolution. Our experimental results show that Pixelsmith not only achieves higher quality and diversity compared to existing techniques, but also reduces sampling time and artifacts. The code for our work is available at https://github.com/Thanos-DB/Pixelsmith.

Video analysis tasks rely heavily on identifying the pixels from different frames that correspond to the same visual target. To tackle this problem, recent studies have advocated feature learning methods that aim to learn distinctive representations to match the pixels, especially in a self-supervised fashion. Unfortunately, these methods have difficulties for tiny or even single-pixel visual targets. Pixel-wise video correspondences were traditionally related to optical flows, which however lead to deterministic correspondences and lack robustness on real-world videos. We address the problem of learning features for establishing pixel-wise correspondences. Motivated by optical flows as well as the self-supervised feature learning, we propose to use not only labeled synthetic videos but also unlabeled real-world videos for learning fine-grained representations in a holistic framework. We adopt an adversarial learning scheme to enhance the generalization ability of the learned features. Moreover, we design a coarse-to-fine framework to pursue high computational efficiency. Our experimental results on a series of correspondence-based tasks demonstrate that the proposed method outperforms state-of-the-art rivals in both accuracy and efficiency.

In many video processing tasks, leveraging large-scale image datasets is a common strategy, as image data is more abundant and facilitates comprehensive knowledge transfer. A typical approach for simulating video from static images involves applying spatial transformations, such as affine transformations and spline warping, to create sequences that mimic temporal progression. However, in tasks like video salient object detection, where both appearance and motion cues are critical, these basic image-to-video techniques fail to produce realistic optical flows that capture the independent motion properties of each object. In this study, we show that image-to-video diffusion models can generate realistic transformations of static images while understanding the contextual relationships between image components. This ability allows the model to generate plausible optical flows, preserving semantic integrity while reflecting the independent motion of scene elements. By augmenting individual images in this way, we create large-scale image-flow pairs that significantly enhance model training. Our approach achieves state-of-the-art performance across all public benchmark datasets, outperforming existing approaches.

Optical flow estimation is essential for video processing tasks, such as restoration and action recognition. The quality of videos is constantly increasing, with current standards reaching 8K resolution. However, optical flow methods are usually designed for low resolution and do not generalize to large inputs due to their rigid architectures. They adopt downscaling or input tiling to reduce the input size, causing a loss of details and global information. There is also a lack of optical flow benchmarks to judge the actual performance of existing methods on high-resolution samples. Previous works only conducted qualitative high-resolution evaluations on hand-picked samples. This paper fills this gap in optical flow estimation in two ways. We propose DPFlow, an adaptive optical flow architecture capable of generalizing up to 8K resolution inputs while trained with only low-resolution samples. We also introduce Kubric-NK, a new benchmark for evaluating optical flow methods with input resolutions ranging from 1K to 8K. Our high-resolution evaluation pushes the boundaries of existing methods and reveals new insights about their generalization capabilities. Extensive experimental results show that DPFlow achieves state-of-the-art results on the MPI-Sintel, KITTI 2015, Spring, and other high-resolution benchmarks.

Flow-based text-to-image (T2I) models excel at prompt-driven image generation, but falter on Image Restoration (IR), often "drifting away" from being faithful to the measurement. Prior work mitigate this drift with data-specific flows or task-specific adapters that are computationally heavy and not scalable across tasks. This raises the question "Can't we efficiently manipulate the existing generative capabilities of a flow model?" To this end, we introduce FlowSteer (FS), an operator-aware conditioning scheme that injects measurement priors along the sampling path,coupling a frozed flow's implicit guidance with explicit measurement constraints. Across super-resolution, deblurring, denoising, and colorization, FS improves measurement consistency and identity preservation in a strictly zero-shot setting-no retrained models, no adapters. We show how the nature of flow models and their sensitivities to noise inform the design of such a scheduler. FlowSteer, although simple, achieves a higher fidelity of reconstructed images, while leveraging the rich generative priors of flow models. All data and code will be publicly available https://tharindu-nirmal.github.io/FlowSteer/{in this link}.

The current success of diffusion transformers heavily depends on the compressed latent space shaped by the pre-trained variational autoencoder(VAE). However, this two-stage training paradigm inevitably introduces accumulated errors and decoding artifacts. To address the aforementioned problems, researchers return to pixel space at the cost of complicated cascade pipelines and increased token complexity. In contrast to their efforts, we propose to model the patch-wise decoding with neural field and present a single-scale, single-stage, efficient, end-to-end solution, coined as pixel neural field diffusion~(PixelNerd). Thanks to the efficient neural field representation in PixNerd, we directly achieved 2.15 FID on ImageNet 256times256 and 2.84 FID on ImageNet 512times512 without any complex cascade pipeline or VAE. We also extend our PixNerd framework to text-to-image applications. Our PixNerd-XXL/16 achieved a competitive 0.73 overall score on the GenEval benchmark and 80.9 overall score on the DPG benchmark.

Video inpainting, which aims at filling in missing regions of a video, remains challenging due to the difficulty of preserving the precise spatial and temporal coherence of video contents. In this work we propose a novel flow-guided video inpainting approach. Rather than filling in the RGB pixels of each frame directly, we consider video inpainting as a pixel propagation problem. We first synthesize a spatially and temporally coherent optical flow field across video frames using a newly designed Deep Flow Completion network. Then the synthesized flow field is used to guide the propagation of pixels to fill up the missing regions in the video. Specifically, the Deep Flow Completion network follows a coarse-to-fine refinement to complete the flow fields, while their quality is further improved by hard flow example mining. Following the guide of the completed flow, the missing video regions can be filled up precisely. Our method is evaluated on DAVIS and YouTube-VOS datasets qualitatively and quantitatively, achieving the state-of-the-art performance in terms of inpainting quality and speed.

Most image generation models rely on uniform tokenization, allocating the exact same computational budget to equally-sized image patches. This static paradigm cannot adapt to different resource constraints at inference time, and yields suboptimal quality-cost tradeoff by devoting the same effort to both plain backgrounds and intricate details. We propose BudgetPix, an adaptive tokenization framework that dynamically allocates compute based on visual complexity and spatial layout, enabling flexible computational budgeting at inference time. BudgetPix comprises three key components: (1) an adaptive encoder that maps a fixed-size image to a variable-length token sequence using an entropy-guided quadtree alongside a multi-scale patch embedder; (2) a scale-aware decoder reconstructs fixed-resolution images from multi-scale token sets; and (3) a flexible training and sampling schedule that enables pixel-space denoisers to operate across variable token counts. BudgetPix seamlessly integrates with existing pixel-space diffusion architectures, enabling a single checkpoint to be operated at a wide range of compute budgets. Evaluated on text-to-image generation, BudgetPix matches the fidelity of MiniT2I-L at 512^2 and PixelDiT at 1024^2 using just 25% of the original compute budget. In class-conditional generation using a MeanFlow backbone, BudgetPix requires merely 60% of the full compute budget to produce images with near-zero quality degradation, observing a marginal 0.8-point increase in FID. Comprehensive assessments by human and VLM judges confirm that BudgetPix establishes a significantly improved quality-efficiency tradeoff over prior budget-adaptive baselines. More details are available at our project page: https://karaozgur.com/BudgetPix

Scene flow estimation is a long-standing problem in computer vision, where the goal is to find the 3D motion of a scene from its consecutive observations. Recently, there have been efforts to compute the scene flow from 3D point clouds. A common approach is to train a regression model that consumes source and target point clouds and outputs the per-point translation vector. An alternative is to learn point matches between the point clouds concurrently with regressing a refinement of the initial correspondence flow. In both cases, the learning task is very challenging since the flow regression is done in the free 3D space, and a typical solution is to resort to a large annotated synthetic dataset. We introduce SCOOP, a new method for scene flow estimation that can be learned on a small amount of data without employing ground-truth flow supervision. In contrast to previous work, we train a pure correspondence model focused on learning point feature representation and initialize the flow as the difference between a source point and its softly corresponding target point. Then, in the run-time phase, we directly optimize a flow refinement component with a self-supervised objective, which leads to a coherent and accurate flow field between the point clouds. Experiments on widespread datasets demonstrate the performance gains achieved by our method compared to existing leading techniques while using a fraction of the training data. Our code is publicly available at https://github.com/itailang/SCOOP.

Diffusion and flow matching models have unlocked unprecedented capabilities for creative content creation, such as interactive image and streaming video generation. The growing demand for higher resolutions, frame rates, and context lengths, however, makes efficient generation increasingly challenging, as computational complexity grows quadratically with the number of generated tokens. Our work seeks to optimize the efficiency of the generation process in settings where the user's gaze location is known or can be estimated, for example, by using eye tracking. In these settings, we leverage the eccentricity-dependent acuity of human vision: while a user perceives very high-resolution visual information in a small region around their gaze location (the foveal region), the ability to resolve detail quickly degrades in the periphery of the visual field. Our approach starts with a mask modeling the foveated resolution to allocate tokens non-uniformly, assigning higher token density to foveal regions and lower density to peripheral regions. An image or video is generated in a mixed-resolution token setting, yielding results perceptually indistinguishable from full-resolution generation, while drastically reducing the token count and generation time. To this end, we develop a principled mechanism for constructing mixed-resolution tokens directly from high-resolution data, allowing a foveated diffusion model to be post-trained from an existing base model while maintaining content consistency across resolutions. We validate our approach through extensive analysis and a carefully designed user study, demonstrating the efficacy of foveation as a practical and scalable axis for efficient generation.

Recent advances in generative models highlight the power of geometry-aware modeling in manifold-constrained settings. Yet, for natural images, the field remains confined to Euclidean assumptions, failing to exploit the potential of intrinsic geometric structures within the data. In this work, we investigate the geometry of natural images and observe that semantic information is predominantly encoded in directional components, while norm components can be approximated by the global average. This property holds across both RGB and latent spaces, suggesting that natural images can be effectively modeled on a hypersphere. Building on this finding, we introduce Spherical Optimal Transport Flow Matching (SOT-CFM), which utilizes angular distance, and Spherical Flow Matching (SFM), which constrains dynamics directly on the manifold. Our experiments demonstrate that these geometry-aware methods achieve superior performance against Euclidean baselines. Ultimately, this work provides a novel perspective that bridges the gap between Riemannian manifold-based modeling and natural image generation.

Point clouds are naturally sparse, while image pixels are dense. The inconsistency limits feature fusion from both modalities for point-wise scene flow estimation. Previous methods rarely predict scene flow from the entire point clouds of the scene with one-time inference due to the memory inefficiency and heavy overhead from distance calculation and sorting involved in commonly used farthest point sampling, KNN, and ball query algorithms for local feature aggregation. To mitigate these issues in scene flow learning, we regularize raw points to a dense format by storing 3D coordinates in 2D grids. Unlike the sampling operation commonly used in existing works, the dense 2D representation 1) preserves most points in the given scene, 2) brings in a significant boost of efficiency, and 3) eliminates the density gap between points and pixels, allowing us to perform effective feature fusion. We also present a novel warping projection technique to alleviate the information loss problem resulting from the fact that multiple points could be mapped into one grid during projection when computing cost volume. Sufficient experiments demonstrate the efficiency and effectiveness of our method, outperforming the prior-arts on the FlyingThings3D and KITTI dataset.

In anomaly segmentation for complex driving scenes, state-of-the-art approaches utilize anomaly scoring functions to calculate anomaly scores. For these functions, accurately predicting the logits of inlier classes for each pixel is crucial for precisely inferring the anomaly score. However, in real-world driving scenarios, the diversity of scenes often results in distorted manifolds of pixel embeddings in the space. This effect is not conducive to directly using the pixel embeddings for the logit prediction during inference, a concern overlooked by existing methods. To address this problem, we propose a novel method called Random Walk on Pixel Manifolds (RWPM). RWPM utilizes random walks to reveal the intrinsic relationships among pixels to refine the pixel embeddings. The refined pixel embeddings alleviate the distortion of manifolds, improving the accuracy of anomaly scores. Our extensive experiments show that RWPM consistently improve the performance of the existing anomaly segmentation methods and achieve the best results. Code is available at: https://github.com/ZelongZeng/RWPM.

Automatic black-and-white image sequence colorization while preserving character and object identity (ID) is a complex task with significant market demand, such as in cartoon or comic series colorization. Despite advancements in visual colorization using large-scale generative models like diffusion models, challenges with controllability and identity consistency persist, making current solutions unsuitable for industrial application.To address this, we propose ColorFlow, a three-stage diffusion-based framework tailored for image sequence colorization in industrial applications. Unlike existing methods that require per-ID finetuning or explicit ID embedding extraction, we propose a novel robust and generalizable Retrieval Augmented Colorization pipeline for colorizing images with relevant color references. Our pipeline also features a dual-branch design: one branch for color identity extraction and the other for colorization, leveraging the strengths of diffusion models. We utilize the self-attention mechanism in diffusion models for strong in-context learning and color identity matching. To evaluate our model, we introduce ColorFlow-Bench, a comprehensive benchmark for reference-based colorization. Results show that ColorFlow outperforms existing models across multiple metrics, setting a new standard in sequential image colorization and potentially benefiting the art industry. We release our codes and models on our project page: https://zhuang2002.github.io/ColorFlow/.

We introduce AllTracker: a model that estimates long-range point tracks by way of estimating the flow field between a query frame and every other frame of a video. Unlike existing point tracking methods, our approach delivers high-resolution and dense (all-pixel) correspondence fields, which can be visualized as flow maps. Unlike existing optical flow methods, our approach corresponds one frame to hundreds of subsequent frames, rather than just the next frame. We develop a new architecture for this task, blending techniques from existing work in optical flow and point tracking: the model performs iterative inference on low-resolution grids of correspondence estimates, propagating information spatially via 2D convolution layers, and propagating information temporally via pixel-aligned attention layers. The model is fast and parameter-efficient (16 million parameters), and delivers state-of-the-art point tracking accuracy at high resolution (i.e., tracking 768x1024 pixels, on a 40G GPU). A benefit of our design is that we can train on a wider set of datasets, and we find that doing so is crucial for top performance. We provide an extensive ablation study on our architecture details and training recipe, making it clear which details matter most. Our code and model weights are available at https://alltracker.github.io .

Low-resolution quantized imagery, such as pixel art, is seeing a revival in modern applications ranging from video game graphics to digital design and fabrication, where creativity is often bound by a limited palette of elemental units. Despite their growing popularity, the automated generation of quantized images from raw inputs remains a significant challenge, often necessitating intensive manual input. We introduce SD-πXL, an approach for producing quantized images that employs score distillation sampling in conjunction with a differentiable image generator. Our method enables users to input a prompt and optionally an image for spatial conditioning, set any desired output size H times W, and choose a palette of n colors or elements. Each color corresponds to a distinct class for our generator, which operates on an H times W times n tensor. We adopt a softmax approach, computing a convex sum of elements, thus rendering the process differentiable and amenable to backpropagation. We show that employing Gumbel-softmax reparameterization allows for crisp pixel art effects. Unique to our method is the ability to transform input images into low-resolution, quantized versions while retaining their key semantic features. Our experiments validate SD-πXL's performance in creating visually pleasing and faithful representations, consistently outperforming the current state-of-the-art. Furthermore, we showcase SD-πXL's practical utility in fabrication through its applications in interlocking brick mosaic, beading and embroidery design.

Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models reparameterize the Gaussian mean as flow velocity. However, they underperform in few-step sampling due to discretization error and tend to produce over-saturated colors under classifier-free guidance (CFG). To address these limitations, we propose a novel Gaussian mixture flow matching (GMFlow) model: instead of predicting the mean, GMFlow predicts dynamic Gaussian mixture (GM) parameters to capture a multi-modal flow velocity distribution, which can be learned with a KL divergence loss. We demonstrate that GMFlow generalizes previous diffusion and flow matching models where a single Gaussian is learned with an L_2 denoising loss. For inference, we derive GM-SDE/ODE solvers that leverage analytic denoising distributions and velocity fields for precise few-step sampling. Furthermore, we introduce a novel probabilistic guidance scheme that mitigates the over-saturation issues of CFG and improves image generation quality. Extensive experiments demonstrate that GMFlow consistently outperforms flow matching baselines in generation quality, achieving a Precision of 0.942 with only 6 sampling steps on ImageNet 256times256.

We show how to transform a non-differentiable rasterizer into a differentiable one with minimal engineering efforts and no external dependencies (no Pytorch/Tensorflow). We rely on Stochastic Gradient Estimation, a technique that consists of rasterizing after randomly perturbing the scene's parameters such that their gradient can be stochastically estimated and descended. This method is simple and robust but does not scale in dimensionality (number of scene parameters). Our insight is that the number of parameters contributing to a given rasterized pixel is bounded. Estimating and averaging gradients on a per-pixel basis hence bounds the dimensionality of the underlying optimization problem and makes the method scalable. Furthermore, it is simple to track per-pixel contributing parameters by rasterizing ID- and UV-buffers, which are trivial additions to a rasterization engine if not already available. With these minor modifications, we obtain an in-engine optimizer for 3D assets with millions of geometry and texture parameters.

Creating high-dynamic videos such as motion-rich actions and sophisticated visual effects poses a significant challenge in the field of artificial intelligence. Unfortunately, current state-of-the-art video generation methods, primarily focusing on text-to-video generation, tend to produce video clips with minimal motions despite maintaining high fidelity. We argue that relying solely on text instructions is insufficient and suboptimal for video generation. In this paper, we introduce PixelDance, a novel approach based on diffusion models that incorporates image instructions for both the first and last frames in conjunction with text instructions for video generation. Comprehensive experimental results demonstrate that PixelDance trained with public data exhibits significantly better proficiency in synthesizing videos with complex scenes and intricate motions, setting a new standard for video generation.

Few-step generation has been a long-standing goal, with recent one-step generation methods exemplified by MeanFlow achieving remarkable results. Existing research on MeanFlow primarily focuses on class-to-image generation. However, an intuitive yet unexplored direction is to extend the condition from fixed class labels to flexible text inputs, enabling richer content creation. Compared to the limited class labels, text conditions pose greater challenges to the model's understanding capability, necessitating the effective integration of powerful text encoders into the MeanFlow framework. Surprisingly, although incorporating text conditions appears straightforward, we find that integrating powerful LLM-based text encoders using conventional training strategies results in unsatisfactory performance. To uncover the underlying cause, we conduct detailed analyses and reveal that, due to the extremely limited number of refinement steps in the MeanFlow generation, such as only one step, the text feature representations are required to possess sufficiently high discriminability. This also explains why discrete and easily distinguishable class features perform well within the MeanFlow framework. Guided by these insights, we leverage a powerful LLM-based text encoder validated to possess the required semantic properties and adapt the MeanFlow generation process to this framework, resulting in efficient text-conditioned synthesis for the first time. Furthermore, we validate our approach on the widely used diffusion model, demonstrating significant generation performance improvements. We hope this work provides a general and practical reference for future research on text-conditioned MeanFlow generation. The code is available at https://github.com/AMAP-ML/EMF.

In this paper, we introduce PixArt-\Sigma, a Diffusion Transformer model~(DiT) capable of directly generating images at 4K resolution. PixArt-\Sigma represents a significant advancement over its predecessor, PixArt-\alpha, offering images of markedly higher fidelity and improved alignment with text prompts. A key feature of PixArt-\Sigma is its training efficiency. Leveraging the foundational pre-training of PixArt-\alpha, it evolves from the `weaker' baseline to a `stronger' model via incorporating higher quality data, a process we term "weak-to-strong training". The advancements in PixArt-\Sigma are twofold: (1) High-Quality Training Data: PixArt-\Sigma incorporates superior-quality image data, paired with more precise and detailed image captions. (2) Efficient Token Compression: we propose a novel attention module within the DiT framework that compresses both keys and values, significantly improving efficiency and facilitating ultra-high-resolution image generation. Thanks to these improvements, PixArt-\Sigma achieves superior image quality and user prompt adherence capabilities with significantly smaller model size (0.6B parameters) than existing text-to-image diffusion models, such as SDXL (2.6B parameters) and SD Cascade (5.1B parameters). Moreover, PixArt-\Sigma's capability to generate 4K images supports the creation of high-resolution posters and wallpapers, efficiently bolstering the production of high-quality visual content in industries such as film and gaming.

Pixel-space diffusion Transformers (DiTs) directly operate on high-dimensional visual data, yet their hidden representations typically undergo uniform refinement across depth. Natural images, however, are inherently organized at different levels of granularity. Global structure can often be represented compactly, whereas local textures and fine details require richer representations. Motivated by this, we introduce heterogeneous refinement in pixel-space DiTs, assigning different feature groups distinct refinement budgets across depth. Consequently, an ordered feature specialization emerges: sparsely refined features predominantly encode global visual structure, whereas more frequently refined features increasingly specialize toward localized, high-frequency details. We refer to these two groups as persistent and active features, respectively. Building on this emergent specialization, we introduce Persistence Forcing (PerF), which explicitly exploits this persistent--active feature organization for pixel-space image generation. This enables persistent features to continuously condition actively refined features, allowing stable global information to guide the ongoing refinement of finer visual details. During generative sampling, this interaction further induces a meaningful guidance direction that promotes coherent global structure and naturally complements classifier-free guidance. On ImageNet 256times256, PerF-L achieves FID of 1.91, approaching 1.86 of JiT-H with only half the parameters, while PerF-H further achieves FID of 1.63 and 1.76 on ImageNet 256times256 and 512times512, respectively.

Accurate estimation of large displacement optical flow remains a critical challenge. Existing methods typically rely on iterative local search or/and domain-specific fine-tuning, which severely limits their performance in large displacement and zero-shot generalization scenarios. To overcome this, we introduce MegaFlow, a simple yet powerful model for zero-shot large displacement optical flow. Rather than relying on highly complex, task-specific architectural designs, MegaFlow adapts powerful pre-trained vision priors to produce temporally consistent motion fields. In particular, we formulate flow estimation as a global matching problem by leveraging pre-trained global Vision Transformer features, which naturally capture large displacements. This is followed by a few lightweight iterative refinements to further improve the sub-pixel accuracy. Extensive experiments demonstrate that MegaFlow achieves state-of-the-art zero-shot performance across multiple optical flow benchmarks. Moreover, our model also delivers highly competitive zero-shot performance on long-range point tracking benchmarks, demonstrating its robust transferability and suggesting a unified paradigm for generalizable motion estimation. Our project page is at: https://kristen-z.github.io/projects/megaflow.

Recent advances in diffusion and flow matching models have highlighted a shift in the preferred prediction target -- moving from noise (varepsilon) and velocity (v) to direct data (x) prediction -- particularly in high-dimensional settings. However, a formal explanation of why the optimal target depends on the specific properties of the data remains elusive. In this work, we provide a theoretical framework based on a generalized prediction formulation that accommodates arbitrary output targets, of which varepsilon-, v-, and x-prediction are special cases. We derive the analytical relationship between data's geometry and the optimal prediction target, offering a rigorous justification for why x-prediction becomes superior when the ambient dimension significantly exceeds the data's intrinsic dimension. Furthermore, while our theory identifies dimensionality as the governing factor for the optimal prediction target, the intrinsic dimension of manifold-bound data is typically intractable to estimate in practice. To bridge this gap, we propose k-Diff, a framework that employs a data-driven approach to learn the optimal prediction parameter k directly from data, bypassing the need for explicit dimension estimation. Extensive experiments in both latent-space and pixel-space image generation demonstrate that k-Diff consistently outperforms fixed-target baselines across varying architectures and data scales, providing a principled and automated approach to enhancing generative performance.

Pixel-space diffusion models avoid the lossy VAE of latent models, which suggests an advantage on downstream tasks where fine-grained detail matters. We test this claim along both routes to a pixel-space backbone. We pretrain Iris-3B, a 3B-parameter pixel-space text-to-image transformer, from scratch through a 256to512to1024 curriculum, after first ablating the prediction target and representation alignment at 256^2 to decide what to scale. We also convert a pretrained latent model, FLUX.2 Klein base 4B, to pixel space. We fine-tune both families for monocular depth estimation and for image restoration/super-resolution. We find no significant improvement from using a pixel-space generative prior. Fine-tuned for depth with one matched direct-regression recipe, Iris-3B is level with the latent FLUX.2 Klein and the converted pixel FLUX.2 Klein falls behind it, and on 4times DIV2K restoration neither pixel model beats a latent FLUX.2 Klein fine-tune, the converted one trailing it slightly. We document the recipes, the failure modes and the remaining confounds behind this negative result. Nevertheless, Iris-3B shows that pixel-space pretraining with the pixel-transformer (PiT) head of PixelDiT scales to 3B parameters and to text-to-image quality competitive with latent models, matching Qwen-Image on OneIG under the official evaluators at 1024^2. We release its weights and training code in the hope that they help pave the way for further work on pixel-space generation.

Document understanding and GUI interaction are among the highest-value applications of Vision-Language Models (VLMs), yet they impose exceptionally heavy computational burden: fine-grained text and small UI elements demand high-resolution inputs that produce tens of thousands of visual tokens. We observe that this cost is largely wasteful -- across document and GUI benchmarks, only 22--71\% of image patches are pixel-unique, the rest being exact duplicates of another patch in the same image. We propose PixelPrune, which exploits this pixel-level redundancy through predictive-coding-based compression, pruning redundant patches before the Vision Transformer (ViT) encoder. Because it operates in pixel space prior to any neural computation, PixelPrune accelerates both the ViT encoder and the downstream LLM, covering the full inference pipeline. The method is training-free, requires no learnable parameters, and supports pixel-lossless compression (τ{=}0) as well as controlled lossy compression (τ{>}0). Experiments across three model scales and document and GUI benchmarks show that PixelPrune maintains competitive task accuracy while delivering up to 4.2times inference speedup and 1.9times training acceleration. Code is available at https://github.com/OPPO-Mente-Lab/PixelPrune.

There is a bias in the inference pipeline of most diffusion models. This bias arises from a signal leak whose distribution deviates from the noise distribution, creating a discrepancy between training and inference processes. We demonstrate that this signal-leak bias is particularly significant when models are tuned to a specific style, causing sub-optimal style matching. Recent research tries to avoid the signal leakage during training. We instead show how we can exploit this signal-leak bias in existing diffusion models to allow more control over the generated images. This enables us to generate images with more varied brightness, and images that better match a desired style or color. By modeling the distribution of the signal leak in the spatial frequency and pixel domains, and including a signal leak in the initial latent, we generate images that better match expected results without any additional training.

Diffusion models have revolutionized text-to-image generation with its exceptional quality and creativity. However, its multi-step sampling process is known to be slow, often requiring tens of inference steps to obtain satisfactory results. Previous attempts to improve its sampling speed and reduce computational costs through distillation have been unsuccessful in achieving a functional one-step model. In this paper, we explore a recent method called Rectified Flow, which, thus far, has only been applied to small datasets. The core of Rectified Flow lies in its reflow procedure, which straightens the trajectories of probability flows, refines the coupling between noises and images, and facilitates the distillation process with student models. We propose a novel text-conditioned pipeline to turn Stable Diffusion (SD) into an ultra-fast one-step model, in which we find reflow plays a critical role in improving the assignment between noise and images. Leveraging our new pipeline, we create, to the best of our knowledge, the first one-step diffusion-based text-to-image generator with SD-level image quality, achieving an FID (Frechet Inception Distance) of 23.3 on MS COCO 2017-5k, surpassing the previous state-of-the-art technique, progressive distillation, by a significant margin (37.2 rightarrow 23.3 in FID). By utilizing an expanded network with 1.7B parameters, we further improve the FID to 22.4. We call our one-step models InstaFlow. On MS COCO 2014-30k, InstaFlow yields an FID of 13.1 in just 0.09 second, the best in leq 0.1 second regime, outperforming the recent StyleGAN-T (13.9 in 0.1 second). Notably, the training of InstaFlow only costs 199 A100 GPU days. Project page:~https://github.com/gnobitab/InstaFlow.

Despite recent advancements in semantic segmentation, where and what pixels are hard to segment remains largely unexplored. Existing research only separates an image into easy and hard regions and empirically observes the latter are associated with object boundaries. In this paper, we conduct a comprehensive analysis of hard pixel errors, categorizing them into three types: false responses, merging mistakes, and displacements. Our findings reveal a quantitative association between hard pixels and aliasing, which is distortion caused by the overlapping of frequency components in the Fourier domain during downsampling. To identify the frequencies responsible for aliasing, we propose using the equivalent sampling rate to calculate the Nyquist frequency, which marks the threshold for aliasing. Then, we introduce the aliasing score as a metric to quantify the extent of aliasing. While positively correlated with the proposed aliasing score, three types of hard pixels exhibit different patterns. Here, we propose two novel de-aliasing filter (DAF) and frequency mixing (FreqMix) modules to alleviate aliasing degradation by accurately removing or adjusting frequencies higher than the Nyquist frequency. The DAF precisely removes the frequencies responsible for aliasing before downsampling, while the FreqMix dynamically selects high-frequency components within the encoder block. Experimental results demonstrate consistent improvements in semantic segmentation and low-light instance segmentation tasks. The code is available at: https://github.com/Linwei-Chen/Seg-Aliasing.

This study introduces an efficient and effective method, MeDM, that utilizes pre-trained image Diffusion Models for video-to-video translation with consistent temporal flow. The proposed framework can render videos from scene position information, such as a normal G-buffer, or perform text-guided editing on videos captured in real-world scenarios. We employ explicit optical flows to construct a practical coding that enforces physical constraints on generated frames and mediates independent frame-wise scores. By leveraging this coding, maintaining temporal consistency in the generated videos can be framed as an optimization problem with a closed-form solution. To ensure compatibility with Stable Diffusion, we also suggest a workaround for modifying observed-space scores in latent-space Diffusion Models. Notably, MeDM does not require fine-tuning or test-time optimization of the Diffusion Models. Through extensive qualitative, quantitative, and subjective experiments on various benchmarks, the study demonstrates the effectiveness and superiority of the proposed approach. Project page can be found at https://medm2023.github.io

In the past, normalizing generative flows have emerged as a promising class of generative models for natural images. This type of model has many modeling advantages: the ability to efficiently compute log-likelihood of the input data, fast generation and simple overall structure. Normalizing flows remained a topic of active research but later fell out of favor, as visual quality of the samples was not competitive with other model classes, such as GANs, VQ-VAE-based approaches or diffusion models. In this paper we revisit the design of the coupling-based normalizing flow models by carefully ablating prior design choices and using computational blocks based on the Vision Transformer architecture, not convolutional neural networks. As a result, we achieve state-of-the-art quantitative and qualitative performance with a much simpler architecture. While the overall visual quality is still behind the current state-of-the-art models, we argue that strong normalizing flow models can help advancing research frontier by serving as building components of more powerful generative models.

The success of deep learning is frequently described as the ability to train all parameters of a network on a specific application in an end-to-end fashion. Yet, several design choices on the camera level, including the pixel layout of the sensor, are considered as pre-defined and fixed, and high resolution, regular pixel layouts are considered to be the most generic ones in computer vision and graphics, treating all regions of an image as equally important. While several works have considered non-uniform, \eg, hexagonal or foveated, pixel layouts in hardware and image processing, the layout has not been integrated into the end-to-end learning paradigm so far. In this work, we present the first truly end-to-end trained imaging pipeline that optimizes the size and distribution of pixels on the imaging sensor jointly with the parameters of a given neural network on a specific task. We derive an analytic, differentiable approach for the sensor layout parameterization that allows for task-specific, local varying pixel resolutions. We present two pixel layout parameterization functions: rectangular and curvilinear grid shapes that retain a regular topology. We provide a drop-in module that approximates sensor simulation given existing high-resolution images to directly connect our method with existing deep learning models. We show that network predictions benefit from learnable pixel layouts for two different downstream tasks, classification and semantic segmentation.

Flow-based generative models (Dinh et al., 2014) are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using an invertible 1x1 convolution. Using our method we demonstrate a significant improvement in log-likelihood on standard benchmarks. Perhaps most strikingly, we demonstrate that a generative model optimized towards the plain log-likelihood objective is capable of efficient realistic-looking synthesis and manipulation of large images. The code for our model is available at https://github.com/openai/glow

Pixel-space diffusion models aim to learn an end-to-end generator directly over raw pixels. This is challenging because a single model must capture both global structure and local texture in the same high-dimensional space. While recent work improves pixel diffusion through alternative prediction targets, training objectives, and architectures, these advances typically require training a new model from scratch. We show there is a cheaper, complementary strategy: a frozen, pretrained pixel diffusion model can guide itself. Our key observation is that intermediate layers of a pretrained pixel diffusion transformer can be decoded into coarse predictions that capture the main low-frequency structure, while the final layers progressively refine local, high-frequency details. We therefore attach a lightweight prediction head to an intermediate layer, keep the backbone frozen, and use the discrepancy between the intermediate and final predictions as a self-guidance direction during sampling. To train this head, we further find that real images are not necessary. Instead, model-generated samples suffice and even outperform real images for training the head, especially in enhancing the high-frequency components that pixel diffusion tends to underfit. Across multiple pixel diffusion models on ImageNet, our Synthetic Self-Guidance (SSG) consistently improves generation while adapter training requires less than 1% of full-model training compute: it reduces FID by over 50% across the evaluated JiT variants without classifier-free guidance (CFG) and further improves strong baselines with CFG, e.g., JiT-H/16 from 1.86 to 1.67 and PixelREPA-H/16 from 1.81 to 1.59. Our code is available at https://github.com/zfu006/SSG.

One-step generative modeling has emerged as a leading approach for amortizing the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and unbounded gradient variance. In this work, we establish a theory that attributes this pathology to a misuse of the conditional velocity field. We show that the conditional velocity plays two distinct statistical roles in the loss: both as an unbiased regression target and as a Monte Carlo control variate in a Jacobi-vector product, with the original MeanFlow loss assigning the wrong coefficient to the latter. We derive the optimal coefficient in closed form and show that a family of fixes in concurrent works corresponds to different practical realizations of the same optimum. A controlled sweep of this coefficient on two-dimensional benchmarks and on a latent Diffusion Transformer recovers the predicted bias-variance ordering. Our DiT experiment also reveals a quantitative FID-MSE landscape mismatch. Specifically, although the gradient-MSE is minimized at an interior coefficient value near β!=!0.94, the coefficient that minimizes FID prefers to use conditional velocity directly at the unbiased corner. Our analysis therefore explains why MeanFlow is unstable and unifies its concurrent remedies, and shows that the variance-optimal coefficient need not coincide with the quality-optimal one.

Recovering clean and accurate geometry from images is essential for robotics and augmented reality. However, existing geometry foundation models still suffer severely from flying pixels and the loss of fine details. In this paper, we present pixel-perfect visual geometry models that can predict high-quality, flying-pixel-free point clouds by leveraging generative modeling in the pixel space. We first introduce Pixel-Perfect Depth (PPD), a monocular depth foundation model built upon pixel-space diffusion transformers (DiT). To address the high computational complexity associated with pixel-space diffusion, we propose two key designs: 1) Semantics-Prompted DiT, which incorporates semantic representations from vision foundation models to prompt the diffusion process, preserving global semantics while enhancing fine-grained visual details; and 2) Cascade DiT architecture that progressively increases the number of image tokens, improving both efficiency and accuracy. To further extend PPD to video (PPVD), we introduce a new Semantics-Consistent DiT, which extracts temporally consistent semantics from a multi-view geometry foundation model. We then perform reference-guided token propagation within the DiT to maintain temporal coherence with minimal computational and memory overhead. Our models achieve the best performance among all generative monocular and video depth estimation models and produce significantly cleaner point clouds than all other models.

Diffusion and flow-based models have become the state of the art for generative AI across a wide range of data modalities, including images, videos, shapes, molecules, music, and more. This tutorial provides a self-contained introduction to diffusion and flow-based generative models from first principles. We systematically develop the necessary mathematical background in ordinary and stochastic differential equations and derive the core algorithms of flow matching and denoising diffusion models. We then provide a step-by-step guide to building image and video generators, including training methods, guidance, and architectural design. This course is ideal for machine learning researchers who want to develop a principled understanding of the theory and practice of generative AI.

Pixel diffusion models generate RGB images directly, avoiding the bottleneck of an autoencoder, yet their outputs still systematically underrepresent fine-scale natural-image statistics. We show that adversarial learning provides an effective post-training correction for this deficiency. Starting from a pretrained model, we retain its original diffusion or flow-matching objective and add an adversarial loss to the predicted output at non-high-noise timesteps, leaving the model architecture and sampling procedure unchanged. To our knowledge, this is the first systematic study of adversarial post-training for pixel diffusion. Across two pixel backbones, the method jointly improves distribution fidelity, coverage, prompt alignment, and perceptual quality. We further investigate why it works. Frequency-band and power-law analyses show that the original models systematically underproduce natural-image high-frequency content, while adversarial post-training restores this missing spectral power. In contrast, perceptual loss also increases high-frequency content but sacrifices distribution fidelity and prompt alignment. Nearest-neighbor, recall, and matched no-GAN SFT controls further rule out memorization, mode dropping, and additional optimization as simple explanations. Finally, we examine the boundary of this effect. Under the tested latent diffusion configurations, the same procedure does not produce comparable joint gains and adds almost no decoded high-frequency power. These results identify direct output access to the image statistics being corrected as a key factor governing when adversarial post-training succeeds.

There has been significant progress in Masked Image Modeling (MIM). Existing MIM methods can be broadly categorized into two groups based on the reconstruction target: pixel-based and tokenizer-based approaches. The former offers a simpler pipeline and lower computational cost, but it is known to be biased toward high-frequency details. In this paper, we provide a set of empirical studies to confirm this limitation of pixel-based MIM and propose a new method that explicitly utilizes low-level features from shallow layers to aid pixel reconstruction. By incorporating this design into our base method, MAE, we reduce the wasted modeling capability of pixel-based MIM, improving its convergence and achieving non-trivial improvements across various downstream tasks. To the best of our knowledge, we are the first to systematically investigate multi-level feature fusion for isotropic architectures like the standard Vision Transformer (ViT). Notably, when applied to a smaller model (e.g., ViT-S), our method yields significant performance gains, such as 1.2\% on fine-tuning, 2.8\% on linear probing, and 2.6\% on semantic segmentation. Code and models are available at https://github.com/open-mmlab/mmpretrain.

Flow map models such as Consistency Models (CM) and Mean Flow (MF) enable few-step generation by learning the long jump of the ODE solution of diffusion models, yet training remains unstable, sensitive to hyperparameters, and costly. Initializing from a pre-trained diffusion model helps, but still requires converting infinitesimal steps into a long-jump map, leaving instability unresolved. We introduce mid-training, the first concept and practical method that inserts a lightweight intermediate stage between the (diffusion) pre-training and the final flow map training (i.e., post-training) for vision generation. Concretely, Consistency Mid-Training (CMT) is a compact and principled stage that trains a model to map points along a solver trajectory from a pre-trained model, starting from a prior sample, directly to the solver-generated clean sample. It yields a trajectory-consistent and stable initialization. This initializer outperforms random and diffusion-based baselines and enables fast, robust convergence without heuristics. Initializing post-training with CMT weights further simplifies flow map learning. Empirically, CMT achieves state of the art two step FIDs: 1.97 on CIFAR-10, 1.32 on ImageNet 64x64, and 1.84 on ImageNet 512x512, while using up to 98% less training data and GPU time, compared to CMs. On ImageNet 256x256, CMT reaches 1-step FID 3.34 while cutting total training time by about 50% compared to MF from scratch (FID 3.43). This establishes CMT as a principled, efficient, and general framework for training flow map models.

Recently, there has been tremendous progress in visual synthesis and the underlying generative models. Here, diffusion models (DMs) stand out particularly, but lately, flow matching (FM) has also garnered considerable interest. While DMs excel in providing diverse images, they suffer from long training and slow generation. With latent diffusion, these issues are only partially alleviated. Conversely, FM offers faster training and inference but exhibits less diversity in synthesis. We demonstrate that introducing FM between the Diffusion model and the convolutional decoder offers high-resolution image synthesis with reduced computational cost and model size. Diffusion can then efficiently provide the necessary generation diversity. FM compensates for the lower resolution, mapping the small latent space to a high-dimensional one. Subsequently, the convolutional decoder of the LDM maps these latents to high-resolution images. By combining the diversity of DMs, the efficiency of FMs, and the effectiveness of convolutional decoders, we achieve state-of-the-art high-resolution image synthesis at 1024^2 with minimal computational cost. Importantly, our approach is orthogonal to recent approximation and speed-up strategies for the underlying DMs, making it easily integrable into various DM frameworks.

We present STARFlow, a scalable generative model based on normalizing flows that achieves strong performance in high-resolution image synthesis. The core of STARFlow is Transformer Autoregressive Flow (TARFlow), which combines the expressive power of normalizing flows with the structured modeling capabilities of Autoregressive Transformers. We first establish the theoretical universality of TARFlow for modeling continuous distributions. Building on this foundation, we introduce several key architectural and algorithmic innovations to significantly enhance scalability: (1) a deep-shallow design, wherein a deep Transformer block captures most of the model representational capacity, complemented by a few shallow Transformer blocks that are computationally efficient yet substantially beneficial; (2) modeling in the latent space of pretrained autoencoders, which proves more effective than direct pixel-level modeling; and (3) a novel guidance algorithm that significantly boosts sample quality. Crucially, our model remains an end-to-end normalizing flow, enabling exact maximum likelihood training in continuous spaces without discretization. STARFlow achieves competitive performance in both class-conditional and text-conditional image generation tasks, approaching state-of-the-art diffusion models in sample quality. To our knowledge, this work is the first successful demonstration of normalizing flows operating effectively at this scale and resolution.

Scene flow estimation is the task of describing the 3D motion field between temporally successive point clouds. State-of-the-art methods use strong priors and test-time optimization techniques, but require on the order of tens of seconds to process full-size point clouds, making them unusable as computer vision primitives for real-time applications such as open world object detection. Feedforward methods are considerably faster, running on the order of tens to hundreds of milliseconds for full-size point clouds, but require expensive human supervision. To address both limitations, we propose Scene Flow via Distillation, a simple, scalable distillation framework that uses a label-free optimization method to produce pseudo-labels to supervise a feedforward model. Our instantiation of this framework, ZeroFlow, achieves state-of-the-art performance on the Argoverse 2 Self-Supervised Scene Flow Challenge while using zero human labels by simply training on large-scale, diverse unlabeled data. At test-time, ZeroFlow is over 1000x faster than label-free state-of-the-art optimization-based methods on full-size point clouds (34 FPS vs 0.028 FPS) and over 1000x cheaper to train on unlabeled data compared to the cost of human annotation (\394 vs ~750,000). To facilitate further research, we will release our code, trained model weights, and high quality pseudo-labels for the Argoverse 2 and Waymo Open datasets.

We propose continuous adversarial flow models, a type of continuous-time flow model trained with an adversarial objective. Unlike flow matching, which uses a fixed mean-squared-error criterion, our approach introduces a learned discriminator to guide training. This change in objective induces a different generalized distribution, which empirically produces samples that are better aligned with the target data distribution. Our method is primarily proposed for post-training existing flow-matching models, although it can also train models from scratch. On the ImageNet 256px generation task, our post-training substantially improves the guidance-free FID of latent-space SiT from 8.26 to 3.63 and of pixel-space JiT from 7.17 to 3.57. It also improves guided generation, reducing FID from 2.06 to 1.53 for SiT and from 1.86 to 1.80 for JiT. We further evaluate our approach on text-to-image generation, where it achieves improved results on both the GenEval and DPG benchmarks.

Diffusion models face a fundamental trade-off between generation quality and computational efficiency. Latent Diffusion Models (LDMs) offer an efficient solution but suffer from potential information loss and non-end-to-end training. In contrast, existing pixel space models bypass VAEs but are computationally prohibitive for high-resolution synthesis. To resolve this dilemma, we propose DiP, an efficient pixel space diffusion framework. DiP decouples generation into a global and a local stage: a Diffusion Transformer (DiT) backbone operates on large patches for efficient global structure construction, while a co-trained lightweight Patch Detailer Head leverages contextual features to restore fine-grained local details. This synergistic design achieves computational efficiency comparable to LDMs without relying on a VAE. DiP is accomplished with up to 10times faster inference speeds than previous method while increasing the total number of parameters by only 0.3%, and achieves an 1.79 FID score on ImageNet 256times256.

Reconstructing and tracking dynamic 3D scenes remains a fundamental challenge in computer vision. Existing approaches often decouple geometry from motion: multi-view reconstruction methods assume static scenes, while dynamic tracking frameworks rely on explicit camera pose estimation or separate motion models. We propose Flow4R, a unified framework that treats camera-space scene flow as the central representation linking 3D structure, object motion, and camera motion. Flow4R predicts a minimal per-pixel property set-3D point position, scene flow, pose weight, and confidence-from two-view inputs using a Vision Transformer. This flow-centric formulation allows local geometry and bidirectional motion to be inferred symmetrically with a shared decoder in a single forward pass, without requiring explicit pose regressors or bundle adjustment. Trained jointly on static and dynamic datasets, Flow4R achieves state-of-the-art performance on 4D reconstruction and tracking tasks, demonstrating the effectiveness of the flow-central representation for spatiotemporal scene understanding.

A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed, as user-specified rewards are usually only well defined on the data distribution at the end of generation. While common workarounds to this problem are to use a denoiser to estimate what a sample would have been at the end of generation, we propose a simple solution to this problem by working directly with a flow map. By exploiting a relationship between the flow map and velocity field governing the instantaneous transport, we construct an algorithm, Flow Map Trajectory Tilting (FMTT), which provably performs better ascent on the reward than standard test-time methods involving the gradient of the reward. The approach can be used to either perform exact sampling via importance weighting or principled search that identifies local maximizers of the reward-tilted distribution. We demonstrate the efficacy of our approach against other look-ahead techniques, and show how the flow map enables engagement with complicated reward functions that make possible new forms of image editing, e.g. by interfacing with vision language models.

MeanFlow (MF) has recently been established as a framework for one-step generative modeling. However, its ``fastforward'' nature introduces key challenges in both the training objective and the guidance mechanism. First, the original MF's training target depends not only on the underlying ground-truth fields but also on the network itself. To address this issue, we recast the objective as a loss on the instantaneous velocity v, re-parameterized by a network that predicts the average velocity u. Our reformulation yields a more standard regression problem and improves the training stability. Second, the original MF fixes the classifier-free guidance scale during training, which sacrifices flexibility. We tackle this issue by formulating guidance as explicit conditioning variables, thereby retaining flexibility at test time. The diverse conditions are processed through in-context conditioning, which reduces model size and benefits performance. Overall, our improved MeanFlow (iMF) method, trained entirely from scratch, achieves 1.72 FID with a single function evaluation (1-NFE) on ImageNet 256times256. iMF substantially outperforms prior methods of this kind and closes the gap with multi-step methods while using no distillation. We hope our work will further advance fastforward generative modeling as a stand-alone paradigm.

Introduction: The paper addresses the challenging problem of predicting the short-term realized volatility of the Bitcoin price using order flow information. The inherent stochastic nature and anti-persistence of price pose difficulties in accurate prediction. Methods: To address this, we propose a method that transforms order flow data over a fixed time interval (snapshots) into images. The order flow includes trade sizes, trade directions, and limit order book, and is mapped into image colour channels. These images are then used to train both a simple 3-layer Convolutional Neural Network (CNN) and more advanced ResNet-18 and ConvMixer, with additionally supplementing them with hand-crafted features. The models are evaluated against classical GARCH, Multilayer Perceptron trained on raw data, and a naive guess method that considers current volatility as a prediction. Results: The experiments are conducted using price data from January 2021 and evaluate model performance in terms of root mean square error (RMSPE). The results show that our order flow representation with a CNN as a predictive model achieves the best performance, with an RMSPE of 0.85+/-1.1 for the model with aggregated features and 1.0+/-1.4 for the model without feature supplementation. ConvMixer with feature supplementation follows closely. In comparison, the RMSPE for the naive guess method was 1.4+/-3.0.

This paper explores higher-resolution video outpainting with extensive content generation. We point out common issues faced by existing methods when attempting to largely outpaint videos: the generation of low-quality content and limitations imposed by GPU memory. To address these challenges, we propose a diffusion-based method called Follow-Your-Canvas. It builds upon two core designs. First, instead of employing the common practice of "single-shot" outpainting, we distribute the task across spatial windows and seamlessly merge them. It allows us to outpaint videos of any size and resolution without being constrained by GPU memory. Second, the source video and its relative positional relation are injected into the generation process of each window. It makes the generated spatial layout within each window harmonize with the source video. Coupling with these two designs enables us to generate higher-resolution outpainting videos with rich content while keeping spatial and temporal consistency. Follow-Your-Canvas excels in large-scale video outpainting, e.g., from 512X512 to 1152X2048 (9X), while producing high-quality and aesthetically pleasing results. It achieves the best quantitative results across various resolution and scale setups. The code is released on https://github.com/mayuelala/FollowYourCanvas

Advances in medical imaging technologies have enabled the collection of longitudinal images, which involve repeated scanning of the same patients over time, to monitor disease progression. However, predictive modeling of such data remains challenging due to high dimensionality, irregular sampling, and data sparsity. To address these issues, we propose ImageFlowNet, a novel model designed to forecast disease trajectories from initial images while preserving spatial details. ImageFlowNet first learns multiscale joint representation spaces across patients and time points, then optimizes deterministic or stochastic flow fields within these spaces using a position-parameterized neural ODE/SDE framework. The model leverages a UNet architecture to create robust multiscale representations and mitigates data scarcity by combining knowledge from all patients. We provide theoretical insights that support our formulation of ODEs, and motivate our regularizations involving high-level visual features, latent space organization, and trajectory smoothness. We validate ImageFlowNet on three longitudinal medical image datasets depicting progression in geographic atrophy, multiple sclerosis, and glioblastoma, demonstrating its ability to effectively forecast disease progression and outperform existing methods. Our contributions include the development of ImageFlowNet, its theoretical underpinnings, and empirical validation on real-world datasets. The official implementation is available at https://github.com/KrishnaswamyLab/ImageFlowNet.

One-step generative modeling seeks to generate high-quality data samples in a single function evaluation, significantly improving efficiency over traditional diffusion or flow-based models. In this work, we introduce Modular MeanFlow (MMF), a flexible and theoretically grounded approach for learning time-averaged velocity fields. Our method derives a family of loss functions based on a differential identity linking instantaneous and average velocities, and incorporates a gradient modulation mechanism that enables stable training without sacrificing expressiveness. We further propose a curriculum-style warmup schedule to smoothly transition from coarse supervision to fully differentiable training. The MMF formulation unifies and generalizes existing consistency-based and flow-matching methods, while avoiding expensive higher-order derivatives. Empirical results across image synthesis and trajectory modeling tasks demonstrate that MMF achieves competitive sample quality, robust convergence, and strong generalization, particularly under low-data or out-of-distribution settings.

We present Neural Space-filling Curves (SFCs), a data-driven approach to infer a context-based scan order for a set of images. Linear ordering of pixels forms the basis for many applications such as video scrambling, compression, and auto-regressive models that are used in generative modeling for images. Existing algorithms resort to a fixed scanning algorithm such as Raster scan or Hilbert scan. Instead, our work learns a spatially coherent linear ordering of pixels from the dataset of images using a graph-based neural network. The resulting Neural SFC is optimized for an objective suitable for the downstream task when the image is traversed along with the scan line order. We show the advantage of using Neural SFCs in downstream applications such as image compression. Code and additional results will be made available at https://hywang66.github.io/publication/neuralsfc.

Remote sensing change detection (RSCD) aims to localise changes between two images of the same geographic region. In practice, change masks often follow region-level annotation conventions rather than purely local appearance differences, making them context-dependent and occasionally ambiguous. Most state-of-the-art methods utilise per-pixel discriminative classification, which produces a single prediction per input and fails to explicitly model the changed region as a coherent whole. A natural alternative is generative formulation, which can model a distribution of plausible masks, enabling sampling to capture ambiguity and encourage global consistency. However, existing generative RSCD approaches typically lag behind strong discriminative baselines due to the high computational cost of pixel-space generation and the complexity of their conditioning mechanisms. To address the limitations of prior discriminative and generative methods, we propose ChangeFlow, a generative framework that reformulates change detection as the synthesis of a change mask in latent space via rectified flow. ChangeFlow is guided by a structured yet lightweight conditioning signal, and its stochastic design naturally supports sampling-based prediction ensembling. Namely, aggregating multiple predicted change masks improves robustness, while sample agreement provides a practical confidence estimation that highlights ambiguous regions. Across four benchmarks, ChangeFlow achieves an average F1 of 80.4\%, improving by 1.3 points on average over the previous best method, while maintaining inference speed comparable to recent strong baselines. Project page: https://blaz-r.github.io/changeflow_cd

We propose a diffusion model-based approach, FloAtControlNet to generate cinemagraphs composed of animations of human clothing. We focus on human clothing like dresses, skirts and pants. The input to our model is a text prompt depicting the type of clothing and the texture of clothing like leopard, striped, or plain, and a sequence of normal maps that capture the underlying animation that we desire in the output. The backbone of our method is a normal-map conditioned ControlNet which is operated in a training-free regime. The key observation is that the underlying animation is embedded in the flow of the normal maps. We utilize the flow thus obtained to manipulate the self-attention maps of appropriate layers. Specifically, the self-attention maps of a particular layer and frame are recomputed as a linear combination of itself and the self-attention maps of the same layer and the previous frame, warped by the flow on the normal maps of the two frames. We show that manipulating the self-attention maps greatly enhances the quality of the clothing animation, making it look more natural as well as suppressing the background artifacts. Through extensive experiments, we show that the method proposed beats all baselines both qualitatively in terms of visual results and user study. Specifically, our method is able to alleviate the background flickering that exists in other diffusion model-based baselines that we consider. In addition, we show that our method beats all baselines in terms of RMSE and PSNR computed using the input normal map sequences and the normal map sequences obtained from the output RGB frames. Further, we show that well-established evaluation metrics like LPIPS, SSIM, and CLIP scores that are generally for visual quality are not necessarily suitable for capturing the subtle motions in human clothing animations.

Imaging is usually a mixture problem of incomplete color sampling, noise degradation, and limited resolution. This mixture problem is typically solved by a sequential solution that applies demosaicing (DM), denoising (DN), and super-resolution (SR) sequentially in a fixed and predefined pipeline (execution order of tasks), DMtoDNtoSR. The most recent work on image processing focuses on developing more sophisticated architectures to achieve higher image quality. Little attention has been paid to the design of the pipeline, and it is still not clear how significant the pipeline is to image quality. In this work, we comprehensively study the effects of pipelines on the mixture problem of learning-based DN, DM, and SR, in both sequential and joint solutions. On the one hand, in sequential solutions, we find that the pipeline has a non-trivial effect on the resulted image quality. Our suggested pipeline DNtoSRtoDM yields consistently better performance than other sequential pipelines in various experimental settings and benchmarks. On the other hand, in joint solutions, we propose an end-to-end Trinity Pixel Enhancement NETwork (TENet) that achieves state-of-the-art performance for the mixture problem. We further present a novel and simple method that can integrate a certain pipeline into a given end-to-end network by providing intermediate supervision using a detachable head. Extensive experiments show that an end-to-end network with the proposed pipeline can attain only a consistent but insignificant improvement. Our work indicates that the investigation of pipelines is applicable in sequential solutions, but is not very necessary in end-to-end networks. Code, models, and our contributed PixelShift200 dataset are available at \url{https://github.com/guochengqian/TENet

Rectified flow models have become a de facto standard in image generation due to their stable sampling trajectories and high-fidelity outputs. Despite their strong generative capabilities, they face critical limitations in image editing tasks: inaccurate inversion processes for mapping real images back into the latent space, and gradient entanglement issues during editing often result in outputs that do not faithfully reflect the target prompt. Recent efforts have attempted to directly map source and target distributions via ODE-based approaches without inversion; however,these methods still yield suboptimal editing quality. In this work, we propose a flow decomposition-and-aggregation framework built upon an inversion-free formulation to address these limitations. Specifically, we semantically decompose the target prompt into multiple sub-prompts, compute an independent flow for each, and aggregate them to form a unified editing trajectory. While we empirically observe that decomposing the original flow enhances diversity in the target space, generating semantically aligned outputs still requires consistent guidance toward the full target prompt. To this end, we design a projection and soft-aggregation mechanism for flow, inspired by gradient conflict resolution in multi-task learning. This approach adaptively weights the sub-target velocity fields, suppressing semantic redundancy while emphasizing distinct directions, thereby preserving both diversity and consistency in the final edited output. Experimental results demonstrate that our method outperforms existing zero-shot editing approaches in terms of semantic fidelity and attribute disentanglement. The code is available at https://github.com/Harvard-AI-and-Robotics-Lab/SplitFlow.

Images produced by text-to-image diffusion models might not always faithfully represent the semantic intent of the provided text prompt, where the model might overlook or entirely fail to produce certain objects. Existing solutions often require customly tailored functions for each of these problems, leading to sub-optimal results, especially for complex prompts. Our work introduces a novel perspective by tackling this challenge in a contrastive context. Our approach intuitively promotes the segregation of objects in attention maps while also maintaining that pairs of related attributes are kept close to each other. We conduct extensive experiments across a wide variety of scenarios, each involving unique combinations of objects, attributes, and scenes. These experiments effectively showcase the versatility, efficiency, and flexibility of our method in working with both latent and pixel-based diffusion models, including Stable Diffusion and Imagen. Moreover, we publicly share our source code to facilitate further research.

Existing optical flow methods broadly follow two paradigms: iterative optimization and diffusion-based estimation. Iterative methods, exemplified by RAFT, achieve high accuracy through recurrent refinement, but remain challenged by large displacements and complex motion. Diffusion-based methods introduce generative modeling and show promise in such ambiguous regions. However, existing diffusion models usually denoise the entire dense flow field from Gaussian noise, including simple regions where reliable motion can already be estimated by a lightweight network. This increases the denoising burden and may cause slow convergence and unstable training. To address this issue, we introduce FlowPainter, a diffusion-based optical flow framework that reformulates dense-flow generation as confidence-guided soft inpainting. FlowPainter employs a lightweight confidence-aware network to predict a rough flow and a pixel-wise confidence mask, distinguishing reliable simple regions from uncertain hard regions. The resulting simple-flow prior is used for confidence-based initialization and further injected into iterative denoising through confidence-gated residual guidance. With dynamically decaying guidance strength, FlowPainter stabilizes early denoising while preserving the flexibility of the diffusion model for late-stage detail refinement. Extensive experiments on public benchmarks, including Sintel, KITTI, and Spring, show that FlowPainter achieves strong accuracy under comparable training settings and converges more efficiently than existing diffusion-based optical flow methods, with notable gains on challenging benchmark splits. Our approach offers a practical way to integrate reliable discriminative priors with diffusion-based refinement for optical flow estimation. Our code is publicly available at https://github.com/mya012/FlowPainter.

Existing foundation models typically process visual input as pixels and textual input as tokens, a paradigm that contrasts with human perception, where both modalities are processed in a unified manner. With the rise of embodied and agentic AI, where inputs primarily come from camera pixels, the need for a unified perception framework becomes increasingly evident. In this paper, we propose to unify all modalities (text, tables, code, diagrams, images, etc) as pixel inputs, i.e. "Perceive Everything as Pixels" (PEAP). We introduce PixelWorld, a novel evaluation suite that unifies all the mentioned modalities into pixel space to gauge the existing models' performance. Our findings show that (1) PEAP outperforms baseline with token-based input in multimodal datasets, benefiting from unified input for better disambiguation, (2) significant declines in reasoning and coding capabilities across all models when processing pixel-based input, underscoring the need to enhance foundation models' perceptual abilities, (3) larger models can maintain strong performance on non-reasoning tasks under PEAP, while smaller models like Phi-3.5-V suffer significant performance degradation, (4) the attention pattern of PEAP is highly aligned with text token input, (5) PEAP can be accelerated significantly by exploiting the spatial sparsity. We conclude that the existing frontier models are competent in pixel perception, however, there is still headroom for improvement. Our code, dataset will be released upon acceptance.

Autoregressive video diffusion models enable streaming generation but often degrade over long rollouts: static scene layouts drift, while mechanisms that improve spatial stability tend to suppress motion, causing natural flows such as water, fire, or smoke to stagnate. We study this stability-motion trade-off in fixed-camera long-horizon nature video generation, where the two failure modes can be more clearly separated than in moving-camera settings. We propose Steady-Forcing, a memory and training framework combining a persistent visual anchor (V-Sink), an exponential moving-average motion memory (EMA-Sink), block-relative temporal encoding, periodic cache purification, and distillation from a Wan2.1-14B teacher with motion-rewarded priors under task-focused configurations. Together, these components are designed to preserve background identity while sustaining visually plausible fluid dynamics over multi-minute autoregressive rollouts. Evaluations across seven baselines show that Steady-Forcing improves long horizon background consistency and imaging quality, while a blind user study indicates stronger perceived stability and motion continuity. The benchmark evaluation further suggest that generic VBench aggregate scores under-penalize fixed-camera artifacts as well as rewarding drift-induced optical flow as Dynamic Degree while not directly penalizing texture hardening or flow stagnation - motivating future task-specific benchmarks for static-camera nature-flow evaluation. Project page: https://minar09.github.io/steadyforcing/

Recent advancements in language-guided diffusion models for image editing are often bottle-necked by cumbersome prompt engineering to precisely articulate desired changes. An intuitive alternative calls on guidance from in-the-wild image exemplars to help users bring their imagined edits to life. Contemporary exemplar-based editing methods shy away from leveraging the rich latent space learnt by pre-existing large text-to-image (TTI) models and fall back on training with curated objective functions to achieve the task. Though somewhat effective, this demands significant computational resources and lacks compatibility with diverse base models and arbitrary exemplar count. On further investigation, we also find that these techniques restrict user control to only applying uniform global changes over the entire edited region. In this paper, we introduce a novel framework for progressive exemplar-driven editing with off-the-shelf diffusion models, dubbed PIXELS, to enable customization by providing granular control over edits, allowing adjustments at the pixel or region level. Our method operates solely during inference to facilitate imitative editing, enabling users to draw inspiration from a dynamic number of reference images, or multimodal prompts, and progressively incorporate all the desired changes without retraining or fine-tuning existing TTI models. This capability of fine-grained control opens up a range of new possibilities, including selective modification of individual objects and specifying gradual spatial changes. We demonstrate that PIXELS delivers high-quality edits efficiently, leading to a notable improvement in quantitative metrics as well as human evaluation. By making high-quality image editing more accessible, PIXELS has the potential to enable professional-grade edits to a wider audience with the ease of using any open-source image generation model.

Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models. Our implementation is available at https://github.com/aravindsrinivas/flowpp

We propose a flow-guided transformer, which innovatively leverage the motion discrepancy exposed by optical flows to instruct the attention retrieval in transformer for high fidelity video inpainting. More specially, we design a novel flow completion network to complete the corrupted flows by exploiting the relevant flow features in a local temporal window. With the completed flows, we propagate the content across video frames, and adopt the flow-guided transformer to synthesize the rest corrupted regions. We decouple transformers along temporal and spatial dimension, so that we can easily integrate the locally relevant completed flows to instruct spatial attention only. Furthermore, we design a flow-reweight module to precisely control the impact of completed flows on each spatial transformer. For the sake of efficiency, we introduce window partition strategy to both spatial and temporal transformers. Especially in spatial transformer, we design a dual perspective spatial MHSA, which integrates the global tokens to the window-based attention. Extensive experiments demonstrate the effectiveness of the proposed method qualitatively and quantitatively. Codes are available at https://github.com/hitachinsk/FGT.

We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous properties like efficient computation via slicing and sorting. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows and establish an error bound for the posterior distributions. Further, we prove that our particle flow is indeed a Wasserstein gradient flow of an appropriate functional. The power of our method is demonstrated by numerical examples including conditional image generation and inverse problems like superresolution, inpainting and computed tomography in low-dose and limited-angle settings.

The recent wave of one-step generative models, which compress the multi-step trajectory of diffusion via either distillation or learned flow maps, has reached an inflection point where they can generate high-quality images. Here, we ask a natural question that follows from these advances: what happens to the denoising trajectory of multi-step diffusion when generation is compressed into a single forward pass? We offer an empirical observation we call depth as time: the denoising computation that multi-step diffusion performs across sampling steps appears to unfold across the depth of a single forward pass, and can be recovered by decoding intermediate layers with the model's own output head. Most interestingly, we show that this depthwise computation depends on the transport task a flow map is trained to solve. The most surprising case is MeanFlow, where probing shorter transport intervals reveals both denoising and renoising within a single network evaluation. In contrast, generators trained without a time-indexed transport task, such as drifting models, do not exhibit the same depthwise denoising. Consequently, we show that models that exhibit the depthwise denoising phenomenon are more compressible across the layerwise computation: a MeanFlow SiT-L/2 model can be compressed by 16.6times in parameters into a single time-conditioned block. We offer an explanation for this denoise-then-renoise behavior and show that, when we treat the layerwise computation explicitly as a flow, a single time-conditioned block can be trained to denoise across layers, compressing a MeanFlow SiT-L/2 model by 16.6times in parameters. Together, these results suggest that the temporal computation of diffusion is not eliminated by one-step generation, but reorganized across network depth.

Denoising diffusion models are widely used for high-quality image and video generation. Their performance depends on noise schedules, which define the distribution of noise levels applied during training and the sequence of noise levels traversed during sampling. Noise schedules are typically handcrafted and require manual tuning across different resolutions. In this work, we propose a principled way to design per-instance noise schedules for pixel diffusion, based on the image's spectral properties. By deriving theoretical bounds on the efficacy of minimum and maximum noise levels, we design ``tight'' noise schedules that eliminate redundant steps. During inference, we propose to conditionally sample such noise schedules. Experiments show that our noise schedules improve generative quality of single-stage pixel diffusion models, particularly in the low-step regime.

Flow matching with clean-data prediction has shown that regressing the clean point can exploit low-dimensional structure more effectively than predicting an ambient noised quantity. We ask whether this principle remains useful after images are mapped into a learned latent space, where compression has already removed much of the raw pixel variability. We introduce JLT, a 130M latent diffusion Transformer over frozen FLUX.2 VAE codes, and compare clean-latent prediction with a matched velocity-prediction DiT under the same representation, backbone, and training settings. Although the three variables x, epsilon, and v are linearly convertible for a fixed corruption time, a local Gaussian analysis shows that velocity regression inherits an isotropic target-covariance floor and amplifies low-variance latent directions, while clean prediction damps them. On ImageNet 256 x 256, JLT-B/1 obtains FID-50K 2.50 with classifier-free guidance, with a large matched-target gap over velocity prediction. These results suggest that prediction targets in latent diffusion are representation-dependent geometric choices, rather than interchangeable algebraic parameterizations.

We introduce Gaussian-Flow, a novel point-based approach for fast dynamic scene reconstruction and real-time rendering from both multi-view and monocular videos. In contrast to the prevalent NeRF-based approaches hampered by slow training and rendering speeds, our approach harnesses recent advancements in point-based 3D Gaussian Splatting (3DGS). Specifically, a novel Dual-Domain Deformation Model (DDDM) is proposed to explicitly model attribute deformations of each Gaussian point, where the time-dependent residual of each attribute is captured by a polynomial fitting in the time domain, and a Fourier series fitting in the frequency domain. The proposed DDDM is capable of modeling complex scene deformations across long video footage, eliminating the need for training separate 3DGS for each frame or introducing an additional implicit neural field to model 3D dynamics. Moreover, the explicit deformation modeling for discretized Gaussian points ensures ultra-fast training and rendering of a 4D scene, which is comparable to the original 3DGS designed for static 3D reconstruction. Our proposed approach showcases a substantial efficiency improvement, achieving a 5times faster training speed compared to the per-frame 3DGS modeling. In addition, quantitative results demonstrate that the proposed Gaussian-Flow significantly outperforms previous leading methods in novel view rendering quality. Project page: https://nju-3dv.github.io/projects/Gaussian-Flow