Daily Papers

The remarkable advances in deep learning have led to the emergence of many off-the-shelf classifiers, e.g., large pre-trained models. However, since they are typically trained on clean data, they remain vulnerable to adversarial attacks. Despite this vulnerability, their superior performance and transferability make off-the-shelf classifiers still valuable in practice, demanding further work to provide adversarial robustness for them in a post-hoc manner. A recently proposed method, denoised smoothing, leverages a denoiser model in front of the classifier to obtain provable robustness without additional training. However, the denoiser often creates hallucination, i.e., images that have lost the semantics of their originally assigned class, leading to a drop in robustness. Furthermore, its noise-and-denoise procedure introduces a significant distribution shift from the original distribution, causing the denoised smoothing framework to achieve sub-optimal robustness. In this paper, we introduce Fine-Tuning with Confidence-Aware Denoised Image Selection (FT-CADIS), a novel fine-tuning scheme to enhance the certified robustness of off-the-shelf classifiers. FT-CADIS is inspired by the observation that the confidence of off-the-shelf classifiers can effectively identify hallucinated images during denoised smoothing. Based on this, we develop a confidence-aware training objective to handle such hallucinated images and improve the stability of fine-tuning from denoised images. In this way, the classifier can be fine-tuned using only images that are beneficial for adversarial robustness. We also find that such a fine-tuning can be done by updating a small fraction of parameters of the classifier. Extensive experiments demonstrate that FT-CADIS has established the state-of-the-art certified robustness among denoised smoothing methods across all ell_2-adversary radius in various benchmarks.

Diffusion models are highly developed in continuous spaces for image and video domains. Recently, major advances have been made for discrete diffusion models for categorical data, specifically in the language domain. In contrast, diffusion models for discrete integer-valued data are less developed, despite the prevalence of this modality, ranging from images and music to gene counts. We introduce Jumping Up and Down (JUD)---a new family of denoiser-based diffusion models for discrete ordinal data. This is the first family of diffusion models for ordinal data which centers around training denoisers, which at the same time allows for bi-directional (up and down) perturbations of the data. The simplicity of the training objective, combined with the flexibility of bi-directional perturbations, leads us to obtain competitive results across different data modalities.

Vision-Language-Action (VLA) models offer a unified framework for robotic manipulation by integrating visual perception, language understanding, and control generation. Yet existing VLA models still struggle to generalize across diverse tasks, scenes, and camera viewpoints, and often produce coarse or unstable actions. We introduce E0, a continuized discrete diffusion framework that formulates action generation as iterative denoising over quantized action tokens. Compared with continuous diffusion policies, E0 offers two key advantages: (1) discrete action tokens align naturally with the symbolic structure of pretrained VLM/VLA backbones, enabling stronger semantic conditioning; and 2. discrete diffusion matches the true quantized nature of real-world robot control-whose hardware constraints (e.g., encoder resolution, control frequency, actuation latency) inherently discretize continuous signals-and therefore benefits from a Bayes-optimal denoiser that models the correct discrete action distribution, leading to stronger generalization. Compared with discrete autoregressive and mask-based discrete diffusion models, E0 supports a significantly larger and finer-grained action vocabulary and avoids the distributional mismatch introduced by masking-based corruptions-yielding more accurate fine-grained action control. We further introduce a spherical viewpoint perturbation augmentation method to improve robustness to camera shifts without additional data. Experiments on LIBERO, VLABench, and ManiSkill show that E0 achieves state-of-the-art performance across 14 diverse environments, outperforming strong baselines by 10.7% on average. Real-world evaluation on a Franka arm confirms that E0 delivers precise, robust, and transferable manipulation, establishing discrete diffusion as a promising direction for generalizable VLA policy learning.

Robotic manipulation is inherently multi-frame: local actions may be simple in an end-effector frame, while transport, upright-object handling, and whole-body coordination are better represented in a base-aligned frame. However, modern diffusion-based visuomotor policies typically commit to a single predefined action frame, forcing one denoiser to model action distributions that are often unnecessarily complex in that frame. We propose Mixture of Frames Policy (MoF), a diffusion policy that performs synchronized action denoising across multiple coordinate frames. MoF maintains a single canonical diffusion state, re-expresses it in several task-relevant frames, applies frame-specialized denoisers, and fuses their noise predictions back in the canonical frame. To make this possible for intermediate noisy diffusion states, we introduce a column-based 6D rotation representation within an SE(3) action parameterization that supports exact, differentiable frame transformations without requiring noisy rotations to lie on the SO(3) manifold. Across nine simulated bimanual manipulation tasks, we show that the best action frame is task-dependent and that MoF improves over oracle frame selection and standard Mixture-of-Experts (MoE) baselines. We further evaluate MoF on two real-world bimanual mobile manipulation tasks, demonstrating that it outperforms all constituent single-frame baselines. Project homepage: https://mofpo.github.io

Single-cell RNA-seq profiles are high-dimensional, sparse, and unordered, causing autoregressive generation to impose an artificial ordering bias and suffer from error accumulation. To address this, we propose scDiVa, a masked discrete diffusion foundation model that aligns generation with the dropout-like corruption process by defining a continuous-time forward masking mechanism in token space. ScDiVa features a bidirectional denoiser that jointly models discrete gene identities and continuous values, utilizing entropy-normalized serialization and a latent anchor token to maximize information efficiency and preserve global cell identity. The model is trained via depth-invariant time sampling and a dual denoising objective to simulate varying sparsity levels while ensuring precise recovery of both identity and magnitude. Pre-trained on 59 million cells, scDiVa achieves strong transfer performance across major benchmarks, including batch integration, cell type annotation, and perturbation response prediction. These results suggest that masked discrete diffusion serves as a biologically coherent and effective alternative to autoregression.

We present TexFusion (Texture Diffusion), a new method to synthesize textures for given 3D geometries, using large-scale text-guided image diffusion models. In contrast to recent works that leverage 2D text-to-image diffusion models to distill 3D objects using a slow and fragile optimization process, TexFusion introduces a new 3D-consistent generation technique specifically designed for texture synthesis that employs regular diffusion model sampling on different 2D rendered views. Specifically, we leverage latent diffusion models, apply the diffusion model's denoiser on a set of 2D renders of the 3D object, and aggregate the different denoising predictions on a shared latent texture map. Final output RGB textures are produced by optimizing an intermediate neural color field on the decodings of 2D renders of the latent texture. We thoroughly validate TexFusion and show that we can efficiently generate diverse, high quality and globally coherent textures. We achieve state-of-the-art text-guided texture synthesis performance using only image diffusion models, while avoiding the pitfalls of previous distillation-based methods. The text-conditioning offers detailed control and we also do not rely on any ground truth 3D textures for training. This makes our method versatile and applicable to a broad range of geometry and texture types. We hope that TexFusion will advance AI-based texturing of 3D assets for applications in virtual reality, game design, simulation, and more.

Iterative sampling in diffusion models can lead to error accumulation due to exposure bias. The denoiser is trained on real images interpolated with noise, but at inference its inputs are constructed from its own imperfect predictions from the earlier steps, something it has never seen at training time. This might be one reason diffusion models often struggle without additional help, such as CFG. We introduce a correction step for diffusion models which attempts to reduce this training-inference gap. The corrector takes the base model's prediction as input and is trained against the same ground-truth target. This makes correction an explicit learning task, with training inputs provided by the base model. During sampling, at each denoising step, we iteratively refine the denoiser's clean-sample prediction. This allows us to correct predictions at intermediate denoising steps, preventing early artifacts from persisting into the final sample. Although the corrector is trained only on predictions from the base denoiser, it can be applied repeatedly to its own outputs at inference for better results. This simple framework leads to substantial improvement in sample quality while largely preserving diversity. We evaluate our method across DiT, SiT, and JiT. Our method substantially improves upon previously reported FID scores for unguided generation and, notably, unconditional generation, where producing high-quality samples without guidance has been particularly challenging. Our method achieves performance competitive with classifier-free guidance (CFG), and combining correction with CFG further improves diversity and reduces oversaturation typical of CFG. Finally, we show that the additional inference cost of correction can be amortized by distilling the refined predictions back into the base diffusion model, retaining the quality gains without additional inference-time overhead.

Despite recent advances in hardware acceleration of ray tracing, real-time ray budgets remain stubbornly limited at a handful of samples per pixel (spp) on commodity hardware, placing the onus on denoising algorithms to achieve high visual quality for path traced global illumination. Neural network-based solutions give excellent result quality at the cost of increased execution time relative to hand-engineered methods, making them less suitable for deployment on resource-constrained systems. We therefore propose incorporating a neural network into a computationally-efficient local linear model-based denoiser, and demonstrate faithful single-frame reconstruction of global illumination for Lambertian scenes at very low sample counts (1spp) and for low computational cost. Other contributions include improving the quality and performance of local linear model-based denoising through a simplified mathematical treatment, and demonstration of the surprising usefulness of ambient occlusion as a guide channel. We also show how our technique is straightforwardly extensible to joint denoising and upsampling of path traced renders with reference to low-cost, rasterized guide channels.

Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy inspired by the structure of the MSE-optimal conditional mean estimator (CME). The resulting DM-based denoiser can be conveniently employed using a pre-trained DM, being particularly fast by truncating reverse diffusion steps and not requiring stochastic re-sampling. We present a comprehensive (non-)asymptotic optimality analysis of the proposed diffusion-based denoiser, demonstrating polynomial-time convergence to the CME under mild conditions. Our analysis also derives a novel Lipschitz constant that depends solely on the DM's hyperparameters. Further, we offer a new perspective on DMs, showing that they inherently combine an asymptotically optimal denoiser with a powerful generator, modifiable by switching re-sampling in the reverse process on or off. The theoretical findings are thoroughly validated with experiments based on various benchmark datasets

Among generative models, diffusion models are uniquely intriguing due to the existence of a closed-form optimal minimizer of their training objective, often referred to as the optimal denoiser. However, diffusion using this optimal denoiser merely reproduces images in the training set and hence fails to capture the behavior of deep diffusion models. Recent work has attempted to characterize this gap between the optimal denoiser and deep diffusion models, proposing analytical, training-free models that can generate images that resemble those generated by a trained UNet. The best-performing method hypothesizes that shift equivariance and locality inductive biases of convolutional neural networks are the cause of the performance gap, hence incorporating these assumptions into its analytical model. In this work, we present evidence that the locality in deep diffusion models emerges as a statistical property of the image dataset, not due to the inductive bias of convolutional neural networks. Specifically, we demonstrate that an optimal parametric linear denoiser exhibits similar locality properties to the deep neural denoisers. We further show, both theoretically and experimentally, that this locality arises directly from the pixel correlations present in natural image datasets. Finally, we use these insights to craft an analytical denoiser that better matches scores predicted by a deep diffusion model than the prior expert-crafted alternative.

Being one of the oldest and most basic problems in image processing, image denoising has seen a resurgence spurred by rapid advances in deep learning. Yet, most modern denoising architectures make limited use of the technical knowledge acquired researching the classical denoisers that came before the mainstream use of neural networks, instead relying on depth and large parameter counts. This poses a challenge not only for understanding the properties of such networks, but also for deploying them on real devices which may present resource constraints and diverse noise profiles. Tackling both issues, we propose an architecture dedicated to RAW-to-RAW denoising that incorporates the interpretable structure of classical self-similarity-based denoisers into a fully learnable neural network. Our design centers on a novel nonlocal block that parallels the established pipeline of neighbor matching, collaborative filtering and aggregation popularized by nonlocal patch-based methods, operating on learned multiscale feature representations. This built-in nonlocality efficiently expands the receptive field, sufficing a single block per scale with a moderate number of neighbors to obtain high-quality results. Training the network on a curated dataset with clean real RAW data and modeled synthetic noise while conditioning it on a noise level map yields a sensor-agnostic denoiser that generalizes effectively to unseen devices. Both quantitative and visual results on benchmarks and in-the-wild photographs position our method as a practical and interpretable solution for real-world RAW denoising, achieving results competitive with state-of-the-art convolutional and transformer-based denoisers while using significantly fewer parameters. The code is available at https://github.com/MIA-UIB/nonlocal-matchfilter .

It is widely believed that noise conditioning is indispensable for denoising diffusion models to work successfully. This work challenges this belief. Motivated by research on blind image denoising, we investigate a variety of denoising-based generative models in the absence of noise conditioning. To our surprise, most models exhibit graceful degradation, and in some cases, they even perform better without noise conditioning. We provide a theoretical analysis of the error caused by removing noise conditioning and demonstrate that our analysis aligns with empirical observations. We further introduce a noise-unconditional model that achieves a competitive FID of 2.23 on CIFAR-10, significantly narrowing the gap to leading noise-conditional models. We hope our findings will inspire the community to revisit the foundations and formulations of denoising generative models.

Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not always the case in real-world applications. For example, in inverse graphics, the goal is to generate samples from a distribution of 3D scenes that align with a given image, but ground-truth 3D scenes are unavailable and only 2D images are accessible. To address this limitation, we propose a novel class of denoising diffusion probabilistic models that learn to sample from distributions of signals that are never directly observed. Instead, these signals are measured indirectly through a known differentiable forward model, which produces partial observations of the unknown signal. Our approach involves integrating the forward model directly into the denoising process. This integration effectively connects the generative modeling of observations with the generative modeling of the underlying signals, allowing for end-to-end training of a conditional generative model over signals. During inference, our approach enables sampling from the distribution of underlying signals that are consistent with a given partial observation. We demonstrate the effectiveness of our method on three challenging computer vision tasks. For instance, in the context of inverse graphics, our model enables direct sampling from the distribution of 3D scenes that align with a single 2D input image.

The denoising process of diffusion models can be interpreted as an approximate projection of noisy samples onto the data manifold. Moreover, the noise level in these samples approximates their distance to the underlying manifold. Building on this insight, we propose a novel method to enhance sample generation by aligning the estimated noise level with the true distance of noisy samples to the manifold. Specifically, we introduce a noise level correction network, leveraging a pre-trained denoising network, to refine noise level estimates during the denoising process. Additionally, we extend this approach to various image restoration tasks by integrating task-specific constraints, including inpainting, deblurring, super-resolution, colorization, and compressed sensing. Experimental results demonstrate that our method significantly improves sample quality in both unconstrained and constrained generation scenarios. Notably, the proposed noise level correction framework is compatible with existing denoising schedulers (e.g., DDIM), offering additional performance improvements.

Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed over several steps by adding Gaussian noise and then learns to reverse the diffusion process to retrieve the desired noise-free data from noisy data samples. Diffusion models are widely appreciated for their strong mode coverage and quality of the generated samples despite their known computational burdens. Capitalizing on the advances in computer vision, the field of medical imaging has also observed a growing interest in diffusion models. To help the researcher navigate this profusion, this survey intends to provide a comprehensive overview of diffusion models in the discipline of medical image analysis. Specifically, we introduce the solid theoretical foundation and fundamental concepts behind diffusion models and the three generic diffusion modelling frameworks: diffusion probabilistic models, noise-conditioned score networks, and stochastic differential equations. Then, we provide a systematic taxonomy of diffusion models in the medical domain and propose a multi-perspective categorization based on their application, imaging modality, organ of interest, and algorithms. To this end, we cover extensive applications of diffusion models in the medical domain. Furthermore, we emphasize the practical use case of some selected approaches, and then we discuss the limitations of the diffusion models in the medical domain and propose several directions to fulfill the demands of this field. Finally, we gather the overviewed studies with their available open-source implementations at https://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.

Denoising diffusion models have recently shown impressive results in generative tasks. By learning powerful priors from huge collections of training images, such models are able to gradually modify complete noise to a clean natural image via a sequence of small denoising steps, seemingly making them well-suited for single image denoising. However, effectively applying denoising diffusion models to removal of realistic noise is more challenging than it may seem, since their formulation is based on additive white Gaussian noise, unlike noise in real-world images. In this work, we present SVNR, a novel formulation of denoising diffusion that assumes a more realistic, spatially-variant noise model. SVNR enables using the noisy input image as the starting point for the denoising diffusion process, in addition to conditioning the process on it. To this end, we adapt the diffusion process to allow each pixel to have its own time embedding, and propose training and inference schemes that support spatially-varying time maps. Our formulation also accounts for the correlation that exists between the condition image and the samples along the modified diffusion process. In our experiments we demonstrate the advantages of our approach over a strong diffusion model baseline, as well as over a state-of-the-art single image denoising method.

Denoising diffusion models represent a recent emerging topic in computer vision, demonstrating remarkable results in the area of generative modeling. A diffusion model is a deep generative model that is based on two stages, a forward diffusion stage and a reverse diffusion stage. In the forward diffusion stage, the input data is gradually perturbed over several steps by adding Gaussian noise. In the reverse stage, a model is tasked at recovering the original input data by learning to gradually reverse the diffusion process, step by step. Diffusion models are widely appreciated for the quality and diversity of the generated samples, despite their known computational burdens, i.e. low speeds due to the high number of steps involved during sampling. In this survey, we provide a comprehensive review of articles on denoising diffusion models applied in vision, comprising both theoretical and practical contributions in the field. First, we identify and present three generic diffusion modeling frameworks, which are based on denoising diffusion probabilistic models, noise conditioned score networks, and stochastic differential equations. We further discuss the relations between diffusion models and other deep generative models, including variational auto-encoders, generative adversarial networks, energy-based models, autoregressive models and normalizing flows. Then, we introduce a multi-perspective categorization of diffusion models applied in computer vision. Finally, we illustrate the current limitations of diffusion models and envision some interesting directions for future research.

Image denoising is a well studied problem with an extensive activity that has spread over several decades. Despite the many available denoising algorithms, the quest for simple, powerful and fast denoisers is still an active and vibrant topic of research. Leading classical denoising methods are typically designed to exploit the inner structure in images by modeling local overlapping patches, while operating in an unsupervised fashion. In contrast, recent newcomers to this arena are supervised and universal neural-network-based methods that bypass this modeling altogether, targeting the inference goal directly and globally, while tending to be very deep and parameter heavy. This work proposes a novel lightweight learnable architecture for image denoising, and presents a combination of supervised and unsupervised training of it, the first aiming for a universal denoiser and the second for adapting it to the incoming image. Our architecture embeds in it several of the main concepts taken from classical methods, relying on patch processing, leveraging non-local self-similarity, exploiting representation sparsity and providing a multiscale treatment. Our proposed universal denoiser achieves near state-of-the-art results, while using a small fraction of the typical number of parameters. In addition, we introduce and demonstrate two highly effective ways for further boosting the denoising performance, by adapting this universal network to the input image.

Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (\ie the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory-efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ .

Supervised training for real-world denoising presents challenges due to the difficulty of collecting large datasets of paired noisy and clean images. Recent methods have attempted to address this by utilizing unpaired datasets of clean and noisy images. Some approaches leverage such unpaired data to train denoisers in a supervised manner by generating synthetic clean-noisy pairs. However, these methods often fall short due to the distribution gap between synthetic and real noisy images. To mitigate this issue, we propose a solution based on input sparsification, specifically using random input masking. Our method, which we refer to as Mask, Inpaint and Denoise (MID), trains a denoiser to simultaneously denoise and inpaint synthetic clean-noisy pairs. On one hand, input sparsification reduces the gap between synthetic and real noisy images. On the other hand, an inpainter trained in a supervised manner can still accurately reconstruct sparse inputs by predicting missing clean pixels using the remaining unmasked pixels. Our approach begins with a synthetic Gaussian noise sampler and iteratively refines it using a noise dataset derived from the denoiser's predictions. The noise dataset is created by subtracting predicted pseudo-clean images from real noisy images at each iteration. The core intuition is that improving the denoiser results in a more accurate noise dataset and, consequently, a better noise sampler. We validate our method through extensive experiments on real-world noisy image datasets, demonstrating competitive performance compared to existing unsupervised denoising methods.

Large reasoning models (LRMs) generate long reasoning traces before producing final answers. While these traces may contain useful signals for hallucination detection, harnessing them is non-trivial because long trajectories often include noisy steps that obscure the cues relevant to truthfulness assessment. In this paper, we identify two prevalent forms of reasoning noises, i.e., irrelevant steps and repetitive steps, and show that both substantially degrade hallucination detection performance. Existing confidence-based scores and naive embedding-based filtering fail to reliably separate noisy from informative steps. To address this challenge, we propose REDE, a novel learning framework for denoising reasoning traces for hallucination detection. Specifically, REDE leverages final-answer attention as an automatic supervision signal to shape the step-level representation space, yielding refined embeddings in which noisy steps can be reliably identified and filtered. REDE can be readily plugged into diverse hallucination detectors by operating on the filtered reasoning trajectory after removing noisy steps. Extensive experiments on multiple reasoning benchmarks show that REDE consistently improves detection performance over competitive baselines.

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this paper, we use this observation to reinterpret denoising diffusion models as approximate gradient descent applied to the Euclidean distance function. We then provide straight-forward convergence analysis of the DDIM sampler under simple assumptions on the projection-error of the denoiser. Finally, we propose a new sampler based on two simple modifications to DDIM using insights from our theoretical results. In as few as 5-10 function evaluations, our sampler achieves state-of-the-art FID scores on pretrained CIFAR-10 and CelebA models and can generate high quality samples on latent diffusion models.

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In this paper, we establish the interpretation of DDMs in terms of image restoration (IR). Integrating IR literature allows us to use an alternative objective and diverse forward processes, not confining to the diffusion process. By imposing prior knowledge on the loss function grounded on MAP-based estimation, we eliminate the need for the expensive sampling of DDMs. Also, we propose a multi-scale training, which improves the performance compared to the diffusion process, by taking advantage of the flexibility of the forward process. Experimental results demonstrate that our model improves the quality and efficiency of both training and inference. Furthermore, we show the applicability of our model to inverse problems. We believe that our framework paves the way for designing a new type of flexible general generative model.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

We describe a novel method for training high-quality image denoising models based on unorganized collections of corrupted images. The training does not need access to clean reference images, or explicit pairs of corrupted images, and can thus be applied in situations where such data is unacceptably expensive or impossible to acquire. We build on a recent technique that removes the need for reference data by employing networks with a "blind spot" in the receptive field, and significantly improve two key aspects: image quality and training efficiency. Our result quality is on par with state-of-the-art neural network denoisers in the case of i.i.d. additive Gaussian noise, and not far behind with Poisson and impulse noise. We also successfully handle cases where parameters of the noise model are variable and/or unknown in both training and evaluation data.

Recent works on plug-and-play image restoration have shown that a denoiser can implicitly serve as the image prior for model-based methods to solve many inverse problems. Such a property induces considerable advantages for plug-and-play image restoration (e.g., integrating the flexibility of model-based method and effectiveness of learning-based methods) when the denoiser is discriminatively learned via deep convolutional neural network (CNN) with large modeling capacity. However, while deeper and larger CNN models are rapidly gaining popularity, existing plug-and-play image restoration hinders its performance due to the lack of suitable denoiser prior. In order to push the limits of plug-and-play image restoration, we set up a benchmark deep denoiser prior by training a highly flexible and effective CNN denoiser. We then plug the deep denoiser prior as a modular part into a half quadratic splitting based iterative algorithm to solve various image restoration problems. We, meanwhile, provide a thorough analysis of parameter setting, intermediate results and empirical convergence to better understand the working mechanism. Experimental results on three representative image restoration tasks, including deblurring, super-resolution and demosaicing, demonstrate that the proposed plug-and-play image restoration with deep denoiser prior not only significantly outperforms other state-of-the-art model-based methods but also achieves competitive or even superior performance against state-of-the-art learning-based methods. The source code is available at https://github.com/cszn/DPIR.

Advancements in neural implicit representations and differentiable rendering have markedly improved the ability to learn animatable 3D avatars from sparse multi-view RGB videos. However, current methods that map observation space to canonical space often face challenges in capturing pose-dependent details and generalizing to novel poses. While diffusion models have demonstrated remarkable zero-shot capabilities in 2D image generation, their potential for creating animatable 3D avatars from 2D inputs remains underexplored. In this work, we introduce 3D^2-Actor, a novel approach featuring a pose-conditioned 3D-aware human modeling pipeline that integrates iterative 2D denoising and 3D rectifying steps. The 2D denoiser, guided by pose cues, generates detailed multi-view images that provide the rich feature set necessary for high-fidelity 3D reconstruction and pose rendering. Complementing this, our Gaussian-based 3D rectifier renders images with enhanced 3D consistency through a two-stage projection strategy and a novel local coordinate representation. Additionally, we propose an innovative sampling strategy to ensure smooth temporal continuity across frames in video synthesis. Our method effectively addresses the limitations of traditional numerical solutions in handling ill-posed mappings, producing realistic and animatable 3D human avatars. Experimental results demonstrate that 3D^2-Actor excels in high-fidelity avatar modeling and robustly generalizes to novel poses. Code is available at: https://github.com/silence-tang/GaussianActor.

Discrete diffusion models are often trained through clean-data prediction, but the prediction can be used in different ways to define the reverse dynamics. In Masked Diffusion Models (MDM) these choices largely coincide, whereas in Uniform Diffusion Models (UDM) they do not. We show that the standard plug-in bridge parameterization for UDM is not optimized by the denoising posterior, but by a leave-one-out posterior that predicts each clean token without using its own noisy observation. This identifies a mismatch between the plug-in ELBO and the usual cross-entropy denoising objective. We characterize the leave-one-out target and derive exact conversions between the denoiser, the leave-one-out posterior, and the score. These conversions allow us to disentangle parameterization and training objective. Our results also lead to inference improvements without any additional training through an informed predictor-corrector sampler and improved temperature sampling based on the leave-one-out predictor. We further introduce an absorbing-state reformulation of uniform diffusion that preserves the UDM joint law while decomposing it into masked-diffusion-like sampling operations, with simpler denoising posteriors, carry-over unmasking, and a natural remasking mechanism. On language modeling, leave-one-out parameterizations consistently improve UDM generation, while the absorbing construction matches or surpasses masked diffusion. These results suggest that the empirical gap between masked and uniform diffusion is driven less by the choice of marginals themselves than by parameterization and sampling design. The code and models can be found at https://github.com/samsongourevitch/rev_udm.

Reinforcement learning (RL) can be used to improve the policy (denoiser) of diffusion large language models (dLLMs), while being hindered by the intractability of the policy likelihood. A dominant and efficient family of methods replaces the likelihood in standard RL with its evidence lower bound (ELBO), estimated from randomly masked sequences. Despite being well aligned with pre-training, these approaches introduce bias through training--inference mismatch by using the ELBO as a likelihood surrogate, which can degrade performance. In this work, we propose Guided Denoiser Self-Distillation (GDSD) to directly distill the denoiser of dLLMs from an advantage-guided self-teacher, derived from the closed-form optimum of reverse-KL regularized RL. GDSD matches the dLLM's denoiser logits to the teacher's via a normalization-free objective, which reduces RL to likelihood-free self-distillation and thus bypasses the TIM biases. Recent ELBO-based methods emerge as instances of applying different distillation divergences, but with diagnosable pathologies that GDSD avoids. On planning, math, and coding benchmarks with LLaDA-8B and Dream-7B, GDSD consistently outperforms prior state-of-the-art ELBO-based methods with a more stable training reward dynamics, achieving test-accuracy improvements of up to +19.6%. These results suggest that direct denoiser self-distillation, without relying on an ELBO likelihood surrogate, can provide a more stable and effective RL procedure for dLLMs. Code is available at https://github.com/GaryBall/GDSD.

Generative denoising models, such as diffusion and flow-matching, learn to sample from complex distributions by training a deep neural network denoiser to recover clean data from noise-corrupted samples. While such models are typically compared on the quality of their synthesized samples, these metrics provide limited insight into how the underlying denoiser, which drives generation, differs. In this work, we propose to analyze the spectrum of the denoiser Jacobian as a tool to characterize these differences. Across pre-trained denoising models, we observe that better generative performance is associated with larger Jacobian eigenvalues. Motivated by this, we introduce a regularization scheme that controls the Jacobian spectrum by training the denoiser on perturbed inputs, with perturbations suppressing or amplifying Jacobian responses. On ImageNet, we test whether directly modifying the Jacobian spectral properties leads to improved generations. Our findings suggest that denoisers benefit from both strengthening responses along data-relevant principal eigen-directions and suppressing the noisy, data-irrelevant ones. This establishes the denoiser Jacobian as a useful tool for identifying differences between generative denoising models.

Recently, the mainstream practice for training low-light raw image denoising methods has shifted towards employing synthetic data. Noise modeling, which focuses on characterizing the noise distribution of real-world sensors, profoundly influences the effectiveness and practicality of synthetic data. Currently, physics-based noise modeling struggles to characterize the entire real noise distribution, while learning-based noise modeling impractically depends on paired real data. In this paper, we propose a novel strategy: learning the noise model from dark frames instead of paired real data, to break down the data dependency. Based on this strategy, we introduce an efficient physics-guided noise neural proxy (PNNP) to approximate the real-world sensor noise model. Specifically, we integrate physical priors into neural proxies and introduce three efficient techniques: physics-guided noise decoupling (PND), physics-guided proxy model (PPM), and differentiable distribution loss (DDL). PND decouples the dark frame into different components and handles different levels of noise flexibly, which reduces the complexity of noise modeling. PPM incorporates physical priors to constrain the generated noise, which promotes the accuracy of noise modeling. DDL provides explicit and reliable supervision for noise distribution, which promotes the precision of noise modeling. PNNP exhibits powerful potential in characterizing the real noise distribution. Extensive experiments on public datasets demonstrate superior performance in practical low-light raw image denoising. The code will be available at https://github.com/fenghansen/PNNP.

Real-world image noise removal is a long-standing yet very challenging task in computer vision. The success of deep neural network in denoising stimulates the research of noise generation, aiming at synthesizing more clean-noisy image pairs to facilitate the training of deep denoisers. In this work, we propose a novel unified framework to simultaneously deal with the noise removal and noise generation tasks. Instead of only inferring the posteriori distribution of the latent clean image conditioned on the observed noisy image in traditional MAP framework, our proposed method learns the joint distribution of the clean-noisy image pairs. Specifically, we approximate the joint distribution with two different factorized forms, which can be formulated as a denoiser mapping the noisy image to the clean one and a generator mapping the clean image to the noisy one. The learned joint distribution implicitly contains all the information between the noisy and clean images, avoiding the necessity of manually designing the image priors and noise assumptions as traditional. Besides, the performance of our denoiser can be further improved by augmenting the original training dataset with the learned generator. Moreover, we propose two metrics to assess the quality of the generated noisy image, for which, to the best of our knowledge, such metrics are firstly proposed along this research line. Extensive experiments have been conducted to demonstrate the superiority of our method over the state-of-the-arts both in the real noise removal and generation tasks. The training and testing code is available at https://github.com/zsyOAOA/DANet.

Image denoising is a fundamental problem in computational photography, where achieving high perception with low distortion is highly demanding. Current methods either struggle with perceptual quality or suffer from significant distortion. Recently, the emerging diffusion model has achieved state-of-the-art performance in various tasks and demonstrates great potential for image denoising. However, stimulating diffusion models for image denoising is not straightforward and requires solving several critical problems. For one thing, the input inconsistency hinders the connection between diffusion models and image denoising. For another, the content inconsistency between the generated image and the desired denoised image introduces distortion. To tackle these problems, we present a novel strategy called the Diffusion Model for Image Denoising (DMID) by understanding and rethinking the diffusion model from a denoising perspective. Our DMID strategy includes an adaptive embedding method that embeds the noisy image into a pre-trained unconditional diffusion model and an adaptive ensembling method that reduces distortion in the denoised image. Our DMID strategy achieves state-of-the-art performance on both distortion-based and perception-based metrics, for both Gaussian and real-world image denoising.The code is available at https://github.com/Li-Tong-621/DMID.

Learning to denoise has emerged as a prominent paradigm to design state-of-the-art deep generative models for natural images. How to use it to model the distributions of both continuous real-valued data and categorical data has been well studied in recently proposed diffusion models. However, it is found in this paper to have limited ability in modeling some other types of data, such as count and non-negative continuous data, that are often highly sparse, skewed, heavy-tailed, and/or overdispersed. To this end, we propose learning to jump as a general recipe for generative modeling of various types of data. Using a forward count thinning process to construct learning objectives to train a deep neural network, it employs a reverse count thickening process to iteratively refine its generation through that network. We demonstrate when learning to jump is expected to perform comparably to learning to denoise, and when it is expected to perform better. For example, learning to jump is recommended when the training data is non-negative and exhibits strong sparsity, skewness, heavy-tailedness, and/or heterogeneity.

In this work, we present CleanUNet, a causal speech denoising model on the raw waveform. The proposed model is based on an encoder-decoder architecture combined with several self-attention blocks to refine its bottleneck representations, which is crucial to obtain good results. The model is optimized through a set of losses defined over both waveform and multi-resolution spectrograms. The proposed method outperforms the state-of-the-art models in terms of denoised speech quality from various objective and subjective evaluation metrics. We release our code and models at https://github.com/nvidia/cleanunet.

Today's denoising diffusion models do not "denoise" in the classical sense, i.e., they do not directly predict clean images. Rather, the neural networks predict noise or a noised quantity. In this paper, we suggest that predicting clean data and predicting noised quantities are fundamentally different. According to the manifold assumption, natural data should lie on a low-dimensional manifold, whereas noised quantities do not. With this assumption, we advocate for models that directly predict clean data, which allows apparently under-capacity networks to operate effectively in very high-dimensional spaces. We show that simple, large-patch Transformers on pixels can be strong generative models: using no tokenizer, no pre-training, and no extra loss. Our approach is conceptually nothing more than "Just image Transformers", or JiT, as we call it. We report competitive results using JiT with large patch sizes of 16 and 32 on ImageNet at resolutions of 256 and 512, where predicting high-dimensional noised quantities can fail catastrophically. With our networks mapping back to the basics of the manifold, our research goes back to basics and pursues a self-contained paradigm for Transformer-based diffusion on raw natural data.

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

Denoising diffusion models have emerged as a powerful tool for various image generation and editing tasks, facilitating the synthesis of visual content in an unconditional or input-conditional manner. The core idea behind them is learning to reverse the process of gradually adding noise to images, allowing them to generate high-quality samples from a complex distribution. In this survey, we provide an exhaustive overview of existing methods using diffusion models for image editing, covering both theoretical and practical aspects in the field. We delve into a thorough analysis and categorization of these works from multiple perspectives, including learning strategies, user-input conditions, and the array of specific editing tasks that can be accomplished. In addition, we pay special attention to image inpainting and outpainting, and explore both earlier traditional context-driven and current multimodal conditional methods, offering a comprehensive analysis of their methodologies. To further evaluate the performance of text-guided image editing algorithms, we propose a systematic benchmark, EditEval, featuring an innovative metric, LMM Score. Finally, we address current limitations and envision some potential directions for future research. The accompanying repository is released at https://github.com/SiatMMLab/Awesome-Diffusion-Model-Based-Image-Editing-Methods.

We present a dynamic model in which the weights are conditioned on an input sample x and are learned to match those that would be obtained by finetuning a base model on x and its label y. This mapping between an input sample and network weights is approximated by a denoising diffusion model. The diffusion model we employ focuses on modifying a single layer of the base model and is conditioned on the input, activations, and output of this layer. Since the diffusion model is stochastic in nature, multiple initializations generate different networks, forming an ensemble, which leads to further improvements. Our experiments demonstrate the wide applicability of the method for image classification, 3D reconstruction, tabular data, speech separation, and natural language processing. Our code is available at https://github.com/ShaharLutatiPersonal/OCD

There have been many image denoisers using deep neural networks, which outperform conventional model-based methods by large margins. Recently, self-supervised methods have attracted attention because constructing a large real noise dataset for supervised training is an enormous burden. The most representative self-supervised denoisers are based on blind-spot networks, which exclude the receptive field's center pixel. However, excluding any input pixel is abandoning some information, especially when the input pixel at the corresponding output position is excluded. In addition, a standard blind-spot network fails to reduce real camera noise due to the pixel-wise correlation of noise, though it successfully removes independently distributed synthetic noise. Hence, to realize a more practical denoiser, we propose a novel self-supervised training framework that can remove real noise. For this, we derive the theoretic upper bound of a supervised loss where the network is guided by the downsampled blinded output. Also, we design a conditional blind-spot network (C-BSN), which selectively controls the blindness of the network to use the center pixel information. Furthermore, we exploit a random subsampler to decorrelate noise spatially, making the C-BSN free of visual artifacts that were often seen in downsample-based methods. Extensive experiments show that the proposed C-BSN achieves state-of-the-art performance on real-world datasets as a self-supervised denoiser and shows qualitatively pleasing results without any post-processing or refinement.

In this paper, we propose a state-of-the-art video denoising algorithm based on a convolutional neural network architecture. Until recently, video denoising with neural networks had been a largely under explored domain, and existing methods could not compete with the performance of the best patch-based methods. The approach we introduce in this paper, called FastDVDnet, shows similar or better performance than other state-of-the-art competitors with significantly lower computing times. In contrast to other existing neural network denoisers, our algorithm exhibits several desirable properties such as fast runtimes, and the ability to handle a wide range of noise levels with a single network model. The characteristics of its architecture make it possible to avoid using a costly motion compensation stage while achieving excellent performance. The combination between its denoising performance and lower computational load makes this algorithm attractive for practical denoising applications. We compare our method with different state-of-art algorithms, both visually and with respect to objective quality metrics.

Diffusion models are a family of generative models that yield record-breaking performance in tasks such as image synthesis, video generation, and molecule design. Despite their capabilities, their efficiency, especially in the reverse denoising process, remains a challenge due to slow convergence rates and high computational costs. In this work, we introduce an approach that leverages continuous dynamical systems to design a novel denoising network for diffusion models that is more parameter-efficient, exhibits faster convergence, and demonstrates increased noise robustness. Experimenting with denoising probabilistic diffusion models, our framework operates with approximately a quarter of the parameters and 30% of the Floating Point Operations (FLOPs) compared to standard U-Nets in Denoising Diffusion Probabilistic Models (DDPMs). Furthermore, our model is up to 70% faster in inference than the baseline models when measured in equal conditions while converging to better quality solutions.

A prominent family of methods for learning data distributions relies on density ratio estimation (DRE), where a model is trained to classify between data samples and samples from some reference distribution. DRE-based models can directly output the likelihood for any given input, a highly desired property that is lacking in most generative techniques. Nevertheless, to date, DRE methods have failed in accurately capturing the distributions of complex high-dimensional data, like images, and have thus been drawing reduced research attention in recent years. In this work we present classification diffusion models (CDMs), a DRE-based generative method that adopts the formalism of denoising diffusion models (DDMs) while making use of a classifier that predicts the level of noise added to a clean signal. Our method is based on an analytical connection that we derive between the MSE-optimal denoiser for removing white Gaussian noise and the cross-entropy-optimal classifier for predicting the noise level. Our method is the first DRE-based technique that can successfully generate images beyond the MNIST dataset. Furthermore, it can output the likelihood of any input in a single forward pass, achieving state-of-the-art negative log likelihood (NLL) among methods with this property. Code is available on the project's webpage in https://shaharYadin.github.io/CDM/ .

Most existing Image Restoration (IR) models are task-specific, which can not be generalized to different degradation operators. In this work, we propose the Denoising Diffusion Null-Space Model (DDNM), a novel zero-shot framework for arbitrary linear IR problems, including but not limited to image super-resolution, colorization, inpainting, compressed sensing, and deblurring. DDNM only needs a pre-trained off-the-shelf diffusion model as the generative prior, without any extra training or network modifications. By refining only the null-space contents during the reverse diffusion process, we can yield diverse results satisfying both data consistency and realness. We further propose an enhanced and robust version, dubbed DDNM+, to support noisy restoration and improve restoration quality for hard tasks. Our experiments on several IR tasks reveal that DDNM outperforms other state-of-the-art zero-shot IR methods. We also demonstrate that DDNM+ can solve complex real-world applications, e.g., old photo restoration.

We present Midicoth, a lossless compression system that introduces a micro-diffusion denoising layer for improving probability estimates produced by adaptive statistical models. In compressors such as Prediction by Partial Matching (PPM), probability estimates are smoothed by a prior to handle sparse observations. When contexts have been seen only a few times, this prior dominates the prediction and produces distributions that are significantly flatter than the true source distribution, leading to compression inefficiency. Midicoth addresses this limitation by treating prior smoothing as a shrinkage process and applying a reverse denoising step that corrects predicted probabilities using empirical calibration statistics. To make this correction data-efficient, the method decomposes each byte prediction into a hierarchy of binary decisions along a bitwise tree. This converts a single 256-way calibration problem into a sequence of binary calibration tasks, enabling reliable estimation of correction terms from relatively small numbers of observations. The denoising process is applied in multiple successive steps, allowing each stage to refine residual prediction errors left by the previous one. The micro-diffusion layer operates as a lightweight post-blend calibration stage applied after all model predictions have been combined, allowing it to correct systematic biases in the final probability distribution. Midicoth combines five fully online components: an adaptive PPM model, a long-range match model, a trie-based word model, a high-order context model, and the micro-diffusion denoiser applied as the final stage.

Enhancing the sound quality of historical music recordings is a long-standing problem. This paper presents a novel denoising method based on a fully-convolutional deep neural network. A two-stage U-Net model architecture is designed to model and suppress the degradations with high fidelity. The method processes the time-frequency representation of audio, and is trained using realistic noisy data to jointly remove hiss, clicks, thumps, and other common additive disturbances from old analog discs. The proposed model outperforms previous methods in both objective and subjective metrics. The results of a formal blind listening test show that real gramophone recordings denoised with this method have significantly better quality than the baseline methods. This study shows the importance of realistic training data and the power of deep learning in audio restoration.

Denoising diffusion probabilistic models (DDPMs) employ a sequence of white Gaussian noise samples to generate an image. In analogy with GANs, those noise maps could be considered as the latent code associated with the generated image. However, this native noise space does not possess a convenient structure, and is thus challenging to work with in editing tasks. Here, we propose an alternative latent noise space for DDPM that enables a wide range of editing operations via simple means, and present an inversion method for extracting these edit-friendly noise maps for any given image (real or synthetically generated). As opposed to the native DDPM noise space, the edit-friendly noise maps do not have a standard normal distribution and are not statistically independent across timesteps. However, they allow perfect reconstruction of any desired image, and simple transformations on them translate into meaningful manipulations of the output image (e.g., shifting, color edits). Moreover, in text-conditional models, fixing those noise maps while changing the text prompt, modifies semantics while retaining structure. We illustrate how this property enables text-based editing of real images via the diverse DDPM sampling scheme (in contrast to the popular non-diverse DDIM inversion). We also show how it can be used within existing diffusion-based editing methods to improve their quality and diversity.

Denoising and filtering are widely used in routine seismic-data-processing to improve the signal-to-noise ratio (SNR) of recorded signals and by doing so to improve subsequent analyses. In this paper we develop a new denoising/decomposition method, DeepDenoiser, based on a deep neural network. This network is able to learn simultaneously a sparse representation of data in the time-frequency domain and a non-linear function that maps this representation into masks that decompose input data into a signal of interest and noise (defined as any non-seismic signal). We show that DeepDenoiser achieves impressive denoising of seismic signals even when the signal and noise share a common frequency band. Our method properly handles a variety of colored noise and non-earthquake signals. DeepDenoiser can significantly improve the SNR with minimal changes in the waveform shape of interest, even in presence of high noise levels. We demonstrate the effect of our method on improving earthquake detection. There are clear applications of DeepDenoiser to seismic imaging, micro-seismic monitoring, and preprocessing of ambient noise data. We also note that potential applications of our approach are not limited to these applications or even to earthquake data, and that our approach can be adapted to diverse signals and applications in other settings.

Previous raw image-based low-light image enhancement methods predominantly relied on feed-forward neural networks to learn deterministic mappings from low-light to normally-exposed images. However, they failed to capture critical distribution information, leading to visually undesirable results. This work addresses the issue by seamlessly integrating a diffusion model with a physics-based exposure model. Different from a vanilla diffusion model that has to perform Gaussian denoising, with the injected physics-based exposure model, our restoration process can directly start from a noisy image instead of pure noise. As such, our method obtains significantly improved performance and reduced inference time compared with vanilla diffusion models. To make full use of the advantages of different intermediate steps, we further propose an adaptive residual layer that effectively screens out the side-effect in the iterative refinement when the intermediate results have been already well-exposed. The proposed framework can work with both real-paired datasets, SOTA noise models, and different backbone networks. Note that, the proposed framework is compatible with real-paired datasets, real/synthetic noise models, and different backbone networks. We evaluate the proposed method on various public benchmarks, achieving promising results with consistent improvements using different exposure models and backbones. Besides, the proposed method achieves better generalization capacity for unseen amplifying ratios and better performance than a larger feedforward neural model when few parameters are adopted.

Diffusion models have recently achieved great success in the synthesis of high-quality images and videos. However, the existing denoising techniques in diffusion models are commonly based on step-by-step noise predictions, which suffers from high computation cost, resulting in a prohibitive latency for interactive applications. In this paper, we propose AdaptiveDiffusion to relieve this bottleneck by adaptively reducing the noise prediction steps during the denoising process. Our method considers the potential of skipping as many noise prediction steps as possible while keeping the final denoised results identical to the original full-step ones. Specifically, the skipping strategy is guided by the third-order latent difference that indicates the stability between timesteps during the denoising process, which benefits the reusing of previous noise prediction results. Extensive experiments on image and video diffusion models demonstrate that our method can significantly speed up the denoising process while generating identical results to the original process, achieving up to an average 2~5x speedup without quality degradation.

Diffusion Probabilistic Models have demonstrated remarkable performance across a wide range of generative tasks. However, we have observed that these models often suffer from a Signal-to-Noise Ratio-timestep (SNR-t) bias. This bias refers to the misalignment between the SNR of the denoising sample and its corresponding timestep during the inference phase. Specifically, during training, the SNR of a sample is strictly coupled with its timestep. However, this correspondence is disrupted during inference, leading to error accumulation and impairing the generation quality. We provide comprehensive empirical evidence and theoretical analysis to substantiate this phenomenon and propose a simple yet effective differential correction method to mitigate the SNR-t bias. Recognizing that diffusion models typically reconstruct low-frequency components before focusing on high-frequency details during the reverse denoising process, we decompose samples into various frequency components and apply differential correction to each component individually. Extensive experiments show that our approach significantly improves the generation quality of various diffusion models (IDDPM, ADM, DDIM, A-DPM, EA-DPM, EDM, PFGM++, and FLUX) on datasets of various resolutions with negligible computational overhead. The code is at https://github.com/AMAP-ML/DCW.

Denoising diffusion models (DDMs) have led to staggering performance leaps in image generation, editing and restoration. However, existing DDMs use very large datasets for training. Here, we introduce a framework for training a DDM on a single image. Our method, which we coin SinDDM, learns the internal statistics of the training image by using a multi-scale diffusion process. To drive the reverse diffusion process, we use a fully-convolutional light-weight denoiser, which is conditioned on both the noise level and the scale. This architecture allows generating samples of arbitrary dimensions, in a coarse-to-fine manner. As we illustrate, SinDDM generates diverse high-quality samples, and is applicable in a wide array of tasks, including style transfer and harmonization. Furthermore, it can be easily guided by external supervision. Particularly, we demonstrate text-guided generation from a single image using a pre-trained CLIP model.

Current diffusion-based image restoration methods feed degraded input images as conditions into the noise estimation network. However, interpreting this diffusion process is challenging since it essentially generates the target image from the noise. To establish a unified and more interpretable model for image generation and restoration, we propose residual denoising diffusion models (RDDM). In contrast to existing diffusion models (e.g., DDPM or DDIM) that focus solely on noise estimation, our RDDM predicts residuals to represent directional diffusion from the target domain to the input domain, while concurrently estimating noise to account for random perturbations in the diffusion process. The introduction of residuals allows us to redefine the forward diffusion process, wherein the target image progressively diffuses into a purely noisy image or a noise-carrying input image, thus unifying image generation and restoration. We demonstrate that our sampling process is consistent with that of DDPM and DDIM through coefficient transformation, and propose a partially path-independent generation process to better understand the reverse process. Notably, with native support for conditional inputs, our RDDM enables a generic UNet, trained with only an ell _1 loss and a batch size of 1, to compete with state-of-the-art image restoration methods. We provide code and pre-trained models to encourage further exploration, application, and development of our innovative framework (https://github.com/nachifur/RDDM).

The vast work in Deep Learning (DL) has led to a leap in image denoising research. Most DL solutions for this task have chosen to put their efforts on the denoiser's architecture while maximizing distortion performance. However, distortion driven solutions lead to blurry results with sub-optimal perceptual quality, especially in immoderate noise levels. In this paper we propose a different perspective, aiming to produce sharp and visually pleasing denoised images that are still faithful to their clean sources. Formally, our goal is to achieve high perceptual quality with acceptable distortion. This is attained by a stochastic denoiser that samples from the posterior distribution, trained as a generator in the framework of conditional generative adversarial networks (CGAN). Contrary to distortion-based regularization terms that conflict with perceptual quality, we introduce to the CGAN objective a theoretically founded penalty term that does not force a distortion requirement on individual samples, but rather on their mean. We showcase our proposed method with a novel denoiser architecture that achieves the reformed denoising goal and produces vivid and diverse outcomes in immoderate noise levels.

While diffusion models excel in video restoration, their reliance on extensive iterative steps limits efficiency. Conversely, aggressive single-step distillation often compromises fine texture recovery. To achieve an optimal balance, we present SATB-VR, a few-step paradigm that jump-starts the denoising process via an auxiliary predictor, explicitly bypassing early low signal-to-noise ratio (SNR) steps. However, naive joint training of the predictor and the denoiser inherently introduces a severe train-inference discrepancy. To resolve this, we propose the SNR-Aware Trajectory Blending (SATB) strategy. During the forward process, SATB constructs the noisy input by dynamically blending the predictor's output with the ground-truth trajectory based on the SNRs. This forces the denoiser to robustly compensate for initial prediction errors while smoothly converging to the clean data manifold. Furthermore, we introduce a Denoiser-Driven Consistency (DDC) loss, leveraging the concurrently updated denoiser as a dynamic evaluator to explicitly align internal features and boost predictor accuracy. Extensive experiments demonstrate that, under flexible few-step inference regimes (\eg, le 5 steps), SATB-VR performs favorably against existing approaches on synthetic, real-world, and AIGC benchmarks.

Diffusion models have become the dominant tool for high-fidelity image and video generation, yet are critically bottlenecked by their inference speed due to the numerous iterative passes of Diffusion Transformers. To reduce the exhaustive compute, recent works resort to the feature caching and reusing scheme that skips network evaluations at selected diffusion steps by using cached features in previous steps. However, their preliminary design solely relies on local approximation, causing errors to grow rapidly with large skips and leading to degraded sample quality at high speedups. In this work, we propose spectral diffusion feature forecaster (Spectrum), a training-free approach that enables global, long-range feature reuse with tightly controlled error. In particular, we view the latent features of the denoiser as functions over time and approximate them with Chebyshev polynomials. Specifically, we fit the coefficient for each basis via ridge regression, which is then leveraged to forecast features at multiple future diffusion steps. We theoretically reveal that our approach admits more favorable long-horizon behavior and yields an error bound that does not compound with the step size. Extensive experiments on various state-of-the-art image and video diffusion models consistently verify the superiority of our approach. Notably, we achieve up to 4.79times speedup on FLUX.1 and 4.67times speedup on Wan2.1-14B, while maintaining much higher sample quality compared with the baselines.

To achieve promising results on removing noise from real-world images, most of existing denoising networks are formulated with complex network structure, making them impractical for deployment. Some attempts focused on reducing the number of filters and feature channels but suffered from large performance loss, and a more practical and lightweight denoising network with fast inference speed is of high demand. To this end, a Thumbnail based Denoising Network dubbed Thunder, is proposed and implemented as a lightweight structure for fast restoration without comprising the denoising capabilities. Specifically, the Thunder model contains two newly-established modules: (1) a wavelet-based Thumbnail Subspace Encoder (TSE) which can leverage sub-bands correlation to provide an approximate thumbnail based on the low-frequent feature; (2) a Subspace Projection based Refine Module (SPR) which can restore the details for thumbnail progressively based on the subspace projection approach. Extensive experiments have been carried out on two real-world denoising benchmarks, demonstrating that the proposed Thunder outperforms the existing lightweight models and achieves competitive performance on PSNR and SSIM when compared with the complex designs.

Deep learning methods have shown remarkable performance in image denoising, particularly when trained on large-scale paired datasets. However, acquiring such paired datasets for real-world scenarios poses a significant challenge. Although unsupervised approaches based on generative adversarial networks offer a promising solution for denoising without paired datasets, they are difficult in surpassing the performance limitations of conventional GAN-based unsupervised frameworks without significantly modifying existing structures or increasing the computational complexity of denoisers. To address this problem, we propose a SC strategy for multiple denoisers. This strategy can achieve significant performance improvement without increasing the inference complexity of the GAN-based denoising framework. Its basic idea is to iteratively replace the previous less powerful denoiser in the filter-guided noise extraction module with the current powerful denoiser. This process generates better synthetic clean-noisy image pairs, leading to a more powerful denoiser for the next iteration. This baseline ensures the stability and effectiveness of the training network. The experimental results demonstrate the superiority of our method over state-of-the-art unsupervised methods.

When capturing and storing images, devices inevitably introduce noise. Reducing this noise is a critical task called image denoising. Deep learning has become the de facto method for image denoising, especially with the emergence of Transformer-based models that have achieved notable state-of-the-art results on various image tasks. However, deep learning-based methods often suffer from a lack of generalization ability. For example, deep models trained on Gaussian noise may perform poorly when tested on other noise distributions. To address this issue, we present a novel approach to enhance the generalization performance of denoising networks, known as masked training. Our method involves masking random pixels of the input image and reconstructing the missing information during training. We also mask out the features in the self-attention layers to avoid the impact of training-testing inconsistency. Our approach exhibits better generalization ability than other deep learning models and is directly applicable to real-world scenarios. Additionally, our interpretability analysis demonstrates the superiority of our method.

With its significant performance improvements, the deep learning paradigm has become a standard tool for modern image denoisers. While promising performance has been shown on seen noise distributions, existing approaches often suffer from generalisation to unseen noise types or general and real noise. It is understandable as the model is designed to learn paired mapping (e.g. from a noisy image to its clean version). In this paper, we instead propose to learn to disentangle the noisy image, under the intuitive assumption that different corrupted versions of the same clean image share a common latent space. A self-supervised learning framework is proposed to achieve the goal, without looking at the latent clean image. By taking two different corrupted versions of the same image as input, the proposed Multi-view Self-supervised Disentanglement (MeD) approach learns to disentangle the latent clean features from the corruptions and recover the clean image consequently. Extensive experimental analysis on both synthetic and real noise shows the superiority of the proposed method over prior self-supervised approaches, especially on unseen novel noise types. On real noise, the proposed method even outperforms its supervised counterparts by over 3 dB.

Deep learning-based denoising models have been widely employed in vision tasks, functioning as filters to eliminate noise while retaining crucial semantic information. Additionally, they play a vital role in defending against adversarial perturbations that threaten downstream tasks. However, these models can be intrinsically susceptible to adversarial attacks due to their dependence on specific noise assumptions. Existing attacks on denoising models mainly aim at deteriorating visual clarity while neglecting semantic manipulation, rendering them either easily detectable or limited in effectiveness. In this paper, we propose Mutual Information-Guided Attack (MIGA), the first method designed to directly attack deep denoising models by strategically disrupting their ability to preserve semantic content via adversarial perturbations. By minimizing the mutual information between the original and denoised images, a measure of semantic similarity. MIGA forces the denoiser to produce perceptually clean yet semantically altered outputs. While these images appear visually plausible, they encode systematically distorted semantics, revealing a fundamental vulnerability in denoising models. These distortions persist in denoised outputs and can be quantitatively assessed through downstream task performance. We propose new evaluation metrics and systematically assess MIGA on four denoising models across five datasets, demonstrating its consistent effectiveness in disrupting semantic fidelity. Our findings suggest that denoising models are not always robust and can introduce security risks in real-world applications.

A diffusion model, which is formulated to produce an image using thousands of denoising steps, usually suffers from a slow inference speed. Existing acceleration algorithms simplify the sampling by skipping most steps yet exhibit considerable performance degradation. By viewing the generation of diffusion models as a discretized integrating process, we argue that the quality drop is partly caused by applying an inaccurate integral direction to a timestep interval. To rectify this issue, we propose a timestep aligner that helps find a more accurate integral direction for a particular interval at the minimum cost. Specifically, at each denoising step, we replace the original parameterization by conditioning the network on a new timestep, which is obtained by aligning the sampling distribution to the real distribution. Extensive experiments show that our plug-in design can be trained efficiently and boost the inference performance of various state-of-the-art acceleration methods, especially when there are few denoising steps. For example, when using 10 denoising steps on the popular LSUN Bedroom dataset, we improve the FID of DDIM from 9.65 to 6.07, simply by adopting our method for a more appropriate set of timesteps. Code will be made publicly available.

Low-light photography produces images with low signal-to-noise ratios due to limited photons. In such conditions, common approximations like the Gaussian noise model fall short, and many denoising techniques fail to remove noise effectively. Although deep-learning methods perform well, they require large datasets of paired images that are impractical to acquire. As a remedy, synthesizing realistic low-light noise has gained significant attention. In this paper, we investigate the ability of diffusion models to capture the complex distribution of low-light noise. We show that a naive application of conventional diffusion models is inadequate for this task and propose three key adaptations that enable high-precision noise generation without calibration or post-processing: a two-branch architecture to better model signal-dependent and signal-independent noise, the incorporation of positional information to capture fixed-pattern noise, and a tailored diffusion noise schedule. Consequently, our model enables the generation of large datasets for training low-light denoising networks, leading to state-of-the-art performance. Through comprehensive analysis, including statistical evaluation and noise decomposition, we provide deeper insights into the characteristics of the generated data.

A diffusion probabilistic model (DPM), which constructs a forward diffusion process by gradually adding noise to data points and learns the reverse denoising process to generate new samples, has been shown to handle complex data distribution. Despite its recent success in image synthesis, applying DPMs to video generation is still challenging due to high-dimensional data spaces. Previous methods usually adopt a standard diffusion process, where frames in the same video clip are destroyed with independent noises, ignoring the content redundancy and temporal correlation. This work presents a decomposed diffusion process via resolving the per-frame noise into a base noise that is shared among all frames and a residual noise that varies along the time axis. The denoising pipeline employs two jointly-learned networks to match the noise decomposition accordingly. Experiments on various datasets confirm that our approach, termed as VideoFusion, surpasses both GAN-based and diffusion-based alternatives in high-quality video generation. We further show that our decomposed formulation can benefit from pre-trained image diffusion models and well-support text-conditioned video creation.

In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation ability of idealised denoising diffusion models for high-dimensional target data, implementations introduce thresholding procedures for the generating process to overcome issues arising from the unbounded state space of such models. This mismatch between theoretical design and implementation of diffusion models has been addressed empirically by using a reflected diffusion process as the driver of noise instead. In this paper, we study statistical guarantees of these denoising reflected diffusion models. In particular, we establish minimax optimal rates of convergence in total variation, up to a polylogarithmic factor, under Sobolev smoothness assumptions. Our main contributions include the statistical analysis of this novel class of denoising reflected diffusion models and a refined score approximation method in both time and space, leveraging spectral decomposition and rigorous neural network analysis.

In recent years, large convolutional neural networks have been widely used as tools for image deblurring, because of their ability in restoring images very precisely. It is well known that image deblurring is mathematically modeled as an ill-posed inverse problem and its solution is difficult to approximate when noise affects the data. Really, one limitation of neural networks for deblurring is their sensitivity to noise and other perturbations, which can lead to instability and produce poor reconstructions. In addition, networks do not necessarily take into account the numerical formulation of the underlying imaging problem, when trained end-to-end. In this paper, we propose some strategies to improve stability without losing to much accuracy to deblur images with deep-learning based methods. First, we suggest a very small neural architecture, which reduces the execution time for training, satisfying a green AI need, and does not extremely amplify noise in the computed image. Second, we introduce a unified framework where a pre-processing step balances the lack of stability of the following, neural network-based, step. Two different pre-processors are presented: the former implements a strong parameter-free denoiser, and the latter is a variational model-based regularized formulation of the latent imaging problem. This framework is also formally characterized by mathematical analysis. Numerical experiments are performed to verify the accuracy and stability of the proposed approaches for image deblurring when unknown or not-quantified noise is present; the results confirm that they improve the network stability with respect to noise. In particular, the model-based framework represents the most reliable trade-off between visual precision and robustness.

Supervised neural networks are known to achieve excellent results in various image restoration tasks. However, such training requires datasets composed of pairs of corrupted images and their corresponding ground truth targets. Unfortunately, such data is not available in many applications. For the task of image denoising in which the noise statistics is unknown, several self-supervised training methods have been proposed for overcoming this difficulty. Some of these require knowledge of the noise model, while others assume that the contaminating noise is uncorrelated, both assumptions are too limiting for many practical needs. This work proposes a novel self-supervised training technique suitable for the removal of unknown correlated noise. The proposed approach neither requires knowledge of the noise model nor access to ground truth targets. The input to our algorithm consists of easily captured bursts of noisy shots. Our algorithm constructs artificial patch-craft images from these bursts by patch matching and stitching, and the obtained crafted images are used as targets for the training. Our method does not require registration of the images within the burst. We evaluate the proposed framework through extensive experiments with synthetic and real image noise.

Plug-and-play Image Restoration (IR) has been widely recognized as a flexible and interpretable method for solving various inverse problems by utilizing any off-the-shelf denoiser as the implicit image prior. However, most existing methods focus on discriminative Gaussian denoisers. Although diffusion models have shown impressive performance for high-quality image synthesis, their potential to serve as a generative denoiser prior to the plug-and-play IR methods remains to be further explored. While several other attempts have been made to adopt diffusion models for image restoration, they either fail to achieve satisfactory results or typically require an unacceptable number of Neural Function Evaluations (NFEs) during inference. This paper proposes DiffPIR, which integrates the traditional plug-and-play method into the diffusion sampling framework. Compared to plug-and-play IR methods that rely on discriminative Gaussian denoisers, DiffPIR is expected to inherit the generative ability of diffusion models. Experimental results on three representative IR tasks, including super-resolution, image deblurring, and inpainting, demonstrate that DiffPIR achieves state-of-the-art performance on both the FFHQ and ImageNet datasets in terms of reconstruction faithfulness and perceptual quality with no more than 100 NFEs. The source code is available at {https://github.com/yuanzhi-zhu/DiffPIR}

Denoising diffusion (score-based) generative models have recently achieved significant accomplishments in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data into noise and a backward denoising process for sampling data from noise. Unfortunately, the generation process of current denoising diffusion models is notoriously slow due to the lengthy iterative noise estimations, which rely on cumbersome neural networks. It prevents the diffusion models from being widely deployed, especially on edge devices. Previous works accelerate the generation process of diffusion model (DM) via finding shorter yet effective sampling trajectories. However, they overlook the cost of noise estimation with a heavy network in every iteration. In this work, we accelerate generation from the perspective of compressing the noise estimation network. Due to the difficulty of retraining DMs, we exclude mainstream training-aware compression paradigms and introduce post-training quantization (PTQ) into DM acceleration. However, the output distributions of noise estimation networks change with time-step, making previous PTQ methods fail in DMs since they are designed for single-time step scenarios. To devise a DM-specific PTQ method, we explore PTQ on DM in three aspects: quantized operations, calibration dataset, and calibration metric. We summarize and use several observations derived from all-inclusive investigations to formulate our method, which especially targets the unique multi-time-step structure of DMs. Experimentally, our method can directly quantize full-precision DMs into 8-bit models while maintaining or even improving their performance in a training-free manner. Importantly, our method can serve as a plug-and-play module on other fast-sampling methods, e.g., DDIM. The code is available at https://github.com/42Shawn/PTQ4DM .

We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies diffusion-based probabilistic regression methods. Within this framework, FALDA leverages Fourier-based decomposition to incorporate a component-specific architecture, enabling tailored modeling of individual temporal components. A conditional diffusion model is utilized to estimate the future noise term, while our proposed lightweight denoiser, DEMA (Decomposition MLP with AdaLN), conditions on the historical noise term to enhance denoising performance. Through mathematical analysis and empirical validation, we demonstrate that FALDA effectively reduces epistemic uncertainty, allowing probabilistic learning to primarily focus on aleatoric uncertainty. Experiments on six real-world benchmarks demonstrate that FALDA consistently outperforms existing probabilistic forecasting approaches across most datasets for long-term time series forecasting while achieving enhanced computational efficiency without compromising accuracy. Notably, FALDA also achieves superior overall performance compared to state-of-the-art (SOTA) point forecasting approaches, with improvements of up to 9%.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

Recently, there has been extensive research interest in training deep networks to denoise images without clean reference. However, the representative approaches such as Noise2Noise, Noise2Void, Stein's unbiased risk estimator (SURE), etc. seem to differ from one another and it is difficult to find the coherent mathematical structure. To address this, here we present a novel approach, called Noise2Score, which reveals a missing link in order to unite these seemingly different approaches. Specifically, we show that image denoising problems without clean images can be addressed by finding the mode of the posterior distribution and that the Tweedie's formula offers an explicit solution through the score function (i.e. the gradient of log likelihood). Our method then uses the recent finding that the score function can be stably estimated from the noisy images using the amortized residual denoising autoencoder, the method of which is closely related to Noise2Noise or Nose2Void. Our Noise2Score approach is so universal that the same network training can be used to remove noises from images that are corrupted by any exponential family distributions and noise parameters. Using extensive experiments with Gaussian, Poisson, and Gamma noises, we show that Noise2Score significantly outperforms the state-of-the-art self-supervised denoising methods in the benchmark data set such as (C)BSD68, Set12, and Kodak, etc.

Diffusion models have demonstrated remarkable efficacy in various generative tasks with the predictive prowess of denoising model. Currently, diffusion models employ a uniform denoising model across all timesteps. However, the inherent variations in data distributions at different timesteps lead to conflicts during training, constraining the potential of diffusion models. To address this challenge, we propose a novel two-stage divide-and-conquer training strategy termed TDC Training. It groups timesteps based on task similarity and difficulty, assigning highly customized denoising models to each group, thereby enhancing the performance of diffusion models. While two-stage training avoids the need to train each model separately, the total training cost is even lower than training a single unified denoising model. Additionally, we introduce Proxy-based Pruning to further customize the denoising models. This method transforms the pruning problem of diffusion models into a multi-round decision-making problem, enabling precise pruning of diffusion models. Our experiments validate the effectiveness of TDC Training, demonstrating improvements in FID of 1.5 on ImageNet64 compared to original IDDPM, while saving about 20\% of computational resources.

Enhancing the visibility in extreme low-light environments is a challenging task. Under nearly lightless condition, existing image denoising methods could easily break down due to significantly low SNR. In this paper, we systematically study the noise statistics in the imaging pipeline of CMOS photosensors, and formulate a comprehensive noise model that can accurately characterize the real noise structures. Our novel model considers the noise sources caused by digital camera electronics which are largely overlooked by existing methods yet have significant influence on raw measurement in the dark. It provides a way to decouple the intricate noise structure into different statistical distributions with physical interpretations. Moreover, our noise model can be used to synthesize realistic training data for learning-based low-light denoising algorithms. In this regard, although promising results have been shown recently with deep convolutional neural networks, the success heavily depends on abundant noisy clean image pairs for training, which are tremendously difficult to obtain in practice. Generalizing their trained models to images from new devices is also problematic. Extensive experiments on multiple low-light denoising datasets -- including a newly collected one in this work covering various devices -- show that a deep neural network trained with our proposed noise formation model can reach surprisingly-high accuracy. The results are on par with or sometimes even outperform training with paired real data, opening a new door to real-world extreme low-light photography.

In this work, we tackle the challenging problem of denoising hand-object interactions (HOI). Given an erroneous interaction sequence, the objective is to refine the incorrect hand trajectory to remove interaction artifacts for a perceptually realistic sequence. This challenge involves intricate interaction noise, including unnatural hand poses and incorrect hand-object relations, alongside the necessity for robust generalization to new interactions and diverse noise patterns. We tackle those challenges through a novel approach, GeneOH Diffusion, incorporating two key designs: an innovative contact-centric HOI representation named GeneOH and a new domain-generalizable denoising scheme. The contact-centric representation GeneOH informatively parameterizes the HOI process, facilitating enhanced generalization across various HOI scenarios. The new denoising scheme consists of a canonical denoising model trained to project noisy data samples from a whitened noise space to a clean data manifold and a "denoising via diffusion" strategy which can handle input trajectories with various noise patterns by first diffusing them to align with the whitened noise space and cleaning via the canonical denoiser. Extensive experiments on four benchmarks with significant domain variations demonstrate the superior effectiveness of our method. GeneOH Diffusion also shows promise for various downstream applications. Project website: https://meowuu7.github.io/GeneOH-Diffusion/.

Image denoising is a well-known and well studied problem, commonly targeting a minimization of the mean squared error (MSE) between the outcome and the original image. Unfortunately, especially for severe noise levels, such Minimum MSE (MMSE) solutions may lead to blurry output images. In this work we propose a novel stochastic denoising approach that produces viable and high perceptual quality results, while maintaining a small MSE. Our method employs Langevin dynamics that relies on a repeated application of any given MMSE denoiser, obtaining the reconstructed image by effectively sampling from the posterior distribution. Due to its stochasticity, the proposed algorithm can produce a variety of high-quality outputs for a given noisy input, all shown to be legitimate denoising results. In addition, we present an extension of our algorithm for handling the inpainting problem, recovering missing pixels while removing noise from partially given data.

Image denoising is a representative image restoration task in computer vision. Recent progress of image denoising from only noisy images has attracted much attention. Deep image prior (DIP) demonstrated successful image denoising from only a noisy image by inductive bias of convolutional neural network architectures without any pre-training. The major challenge of DIP based image denoising is that DIP would completely recover the original noisy image unless applying early stopping. For early stopping without a ground-truth clean image, we propose to monitor JPEG file size of the recovered image during optimization as a proxy metric of noise levels in the recovered image. Our experiments show that the compressed image file size works as an effective metric for early stopping.

Given a factorization of an image into a sum of linear components, we present a zero-shot method to control each individual component through diffusion model sampling. For example, we can decompose an image into low and high spatial frequencies and condition these components on different text prompts. This produces hybrid images, which change appearance depending on viewing distance. By decomposing an image into three frequency subbands, we can generate hybrid images with three prompts. We also use a decomposition into grayscale and color components to produce images whose appearance changes when they are viewed in grayscale, a phenomena that naturally occurs under dim lighting. And we explore a decomposition by a motion blur kernel, which produces images that change appearance under motion blurring. Our method works by denoising with a composite noise estimate, built from the components of noise estimates conditioned on different prompts. We also show that for certain decompositions, our method recovers prior approaches to compositional generation and spatial control. Finally, we show that we can extend our approach to generate hybrid images from real images. We do this by holding one component fixed and generating the remaining components, effectively solving an inverse problem.

This article provides a mathematically rigorous introduction to denoising diffusion probabilistic models (DDPMs), sometimes also referred to as diffusion probabilistic models or diffusion models, for generative artificial intelligence. We provide a detailed basic mathematical framework for DDPMs and explain the main ideas behind training and generation procedures. In this overview article we also review selected extensions and improvements of the basic framework from the literature such as improved DDPMs, denoising diffusion implicit models, classifier-free diffusion guidance models, and latent diffusion models.

Diffusion model (DM) has achieved SOTA performance by modeling the image synthesis process into a sequential application of a denoising network. However, different from image synthesis, image restoration (IR) has a strong constraint to generate results in accordance with ground-truth. Thus, for IR, traditional DMs running massive iterations on a large model to estimate whole images or feature maps is inefficient. To address this issue, we propose an efficient DM for IR (DiffIR), which consists of a compact IR prior extraction network (CPEN), dynamic IR transformer (DIRformer), and denoising network. Specifically, DiffIR has two training stages: pretraining and training DM. In pretraining, we input ground-truth images into CPEN_{S1} to capture a compact IR prior representation (IPR) to guide DIRformer. In the second stage, we train the DM to directly estimate the same IRP as pretrained CPEN_{S1} only using LQ images. We observe that since the IPR is only a compact vector, DiffIR can use fewer iterations than traditional DM to obtain accurate estimations and generate more stable and realistic results. Since the iterations are few, our DiffIR can adopt a joint optimization of CPEN_{S2}, DIRformer, and denoising network, which can further reduce the estimation error influence. We conduct extensive experiments on several IR tasks and achieve SOTA performance while consuming less computational costs. Code is available at https://github.com/Zj-BinXia/DiffIR.

Blind face restoration usually synthesizes degraded low-quality data with a pre-defined degradation model for training, while more complex cases could happen in the real world. This gap between the assumed and actual degradation hurts the restoration performance where artifacts are often observed in the output. However, it is expensive and infeasible to include every type of degradation to cover real-world cases in the training data. To tackle this robustness issue, we propose Diffusion-based Robust Degradation Remover (DR2) to first transform the degraded image to a coarse but degradation-invariant prediction, then employ an enhancement module to restore the coarse prediction to a high-quality image. By leveraging a well-performing denoising diffusion probabilistic model, our DR2 diffuses input images to a noisy status where various types of degradation give way to Gaussian noise, and then captures semantic information through iterative denoising steps. As a result, DR2 is robust against common degradation (e.g. blur, resize, noise and compression) and compatible with different designs of enhancement modules. Experiments in various settings show that our framework outperforms state-of-the-art methods on heavily degraded synthetic and real-world datasets.

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the reverse generation process, without modifying the original denoising diffusion process. However, since the degraded images already include low-frequency information, starting from Gaussian white noise will result in increased sampling steps. We propose Resfusion, a general framework that incorporates the residual term into the diffusion forward process, starting the reverse process directly from the noisy degraded images. The form of our inference process is consistent with the DDPM. We introduced a weighted residual noise, named resnoise, as the prediction target and explicitly provide the quantitative relationship between the residual term and the noise term in resnoise. By leveraging a smooth equivalence transformation, Resfusion determine the optimal acceleration step and maintains the integrity of existing noise schedules, unifying the training and inference processes. The experimental results demonstrate that Resfusion exhibits competitive performance on ISTD dataset, LOL dataset and Raindrop dataset with only five sampling steps. Furthermore, Resfusion can be easily applied to image generation and emerges with strong versatility. Our code and model are available at https://github.com/nkicsl/Resfusion.

Discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction of feed-forward denoising convolutional neural networks (DnCNNs) to embrace the progress in very deep architecture, learning algorithm, and regularization method into image denoising. Specifically, residual learning and batch normalization are utilized to speed up the training process as well as boost the denoising performance. Different from the existing discriminative denoising models which usually train a specific model for additive white Gaussian noise (AWGN) at a certain noise level, our DnCNN model is able to handle Gaussian denoising with unknown noise level (i.e., blind Gaussian denoising). With the residual learning strategy, DnCNN implicitly removes the latent clean image in the hidden layers. This property motivates us to train a single DnCNN model to tackle with several general image denoising tasks such as Gaussian denoising, single image super-resolution and JPEG image deblocking. Our extensive experiments demonstrate that our DnCNN model can not only exhibit high effectiveness in several general image denoising tasks, but also be efficiently implemented by benefiting from GPU computing.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

Diffusion Models (DM) have democratized AI image generation through an iterative denoising process. Quantization is a major technique to alleviate the inference cost and reduce the size of DM denoiser networks. However, as denoisers evolve from variants of convolutional U-Nets toward newer Transformer architectures, it is of growing importance to understand the quantization sensitivity of different weight layers, operations and architecture types to performance. In this work, we address this challenge with Qua^2SeDiMo, a mixed-precision Post-Training Quantization framework that generates explainable insights on the cost-effectiveness of various model weight quantization methods for different denoiser operation types and block structures. We leverage these insights to make high-quality mixed-precision quantization decisions for a myriad of diffusion models ranging from foundational U-Nets to state-of-the-art Transformers. As a result, Qua^2SeDiMo can construct 3.4-bit, 3.9-bit, 3.65-bit and 3.7-bit weight quantization on PixArt-{alpha}, PixArt-{Sigma}, Hunyuan-DiT and SDXL, respectively. We further pair our weight-quantization configurations with 6-bit activation quantization and outperform existing approaches in terms of quantitative metrics and generative image quality.

Image denoisers have been shown to be powerful priors for solving inverse problems in imaging. In this work, we introduce a generalization of these methods that allows any image restoration network to be used as an implicit prior. The proposed method uses priors specified by deep neural networks pre-trained as general restoration operators. The method provides a principled approach for adapting state-of-the-art restoration models for other inverse problems. Our theoretical result analyzes its convergence to a stationary point of a global functional associated with the restoration operator. Numerical results show that the method using a super-resolution prior achieves state-of-the-art performance both quantitatively and qualitatively. Overall, this work offers a step forward for solving inverse problems by enabling the use of powerful pre-trained restoration models as priors.

Image denoising is a critical component in a camera's Image Signal Processing (ISP) pipeline. There are two typical ways to inject a denoiser into the ISP pipeline: applying a denoiser directly to captured raw frames (raw domain) or to the ISP's output sRGB images (sRGB domain). However, both approaches have their limitations. Residual noise from raw-domain denoising can be amplified by the subsequent ISP processing, and the sRGB domain struggles to handle spatially varying noise since it only sees noise distorted by the ISP. Consequently, most raw or sRGB domain denoising works only for specific noise distributions and ISP configurations. To address these challenges, we propose DualDn, a novel learning-based dual-domain denoising. Unlike previous single-domain denoising, DualDn consists of two denoising networks: one in the raw domain and one in the sRGB domain. The raw domain denoising adapts to sensor-specific noise as well as spatially varying noise levels, while the sRGB domain denoising adapts to ISP variations and removes residual noise amplified by the ISP. Both denoising networks are connected with a differentiable ISP, which is trained end-to-end and discarded during the inference stage. With this design, DualDn achieves greater generalizability compared to most learning-based denoising methods, as it can adapt to different unseen noises, ISP parameters, and even novel ISP pipelines. Experiments show that DualDn achieves state-of-the-art performance and can adapt to different denoising architectures. Moreover, DualDn can be used as a plug-and-play denoising module with real cameras without retraining, and still demonstrate better performance than commercial on-camera denoising. The project website is available at: https://openimaginglab.github.io/DualDn/

Diffusion Probabilistic Models (DPMs) have achieved great success in image generation but suffer from high inference latency due to their iterative denoising nature. Motivated by the evolving feature dynamics across the denoising trajectory, we propose a novel framework to optimize the computational graph of pre-trained DPMs on a per-timestep basis. By learning timestep-specific masks, our method dynamically determines which blocks to execute or bypass through feature reuse at each inference stage. Unlike global optimization methods that incur prohibitive memory costs via full-chain backpropagation, our method optimizes masks for each timestep independently, ensuring a memory-efficient training process. To guide this process, we introduce a timestep-aware loss scaling mechanism that prioritizes feature fidelity during sensitive denoising phases, complemented by a knowledge-guided mask rectification strategy to prune redundant spatial-temporal dependencies. Our approach is architecture-agnostic and demonstrates significant efficiency gains across a broad spectrum of models, including DDPM, LDM, DiT, and PixArt. Experimental results show that by treating the denoising process as a sequence of optimized computational paths, our method achieves a superior balance between sampling speed and generative quality. Our code will be released.

Diffusion models have recently revolutionized the field of image synthesis due to their ability to generate photorealistic images. However, one of the major drawbacks of diffusion models is that the image generation process is costly. A large image-to-image network has to be applied many times to iteratively refine an image from random noise. While many recent works propose techniques to reduce the number of required steps, they generally treat the underlying denoising network as a black box. In this work, we investigate the behavior of the layers within the network and find that 1) the layers' output changes smoothly over time, 2) the layers show distinct patterns of change, and 3) the change from step to step is often very small. We hypothesize that many layer computations in the denoising network are redundant. Leveraging this, we introduce block caching, in which we reuse outputs from layer blocks of previous steps to speed up inference. Furthermore, we propose a technique to automatically determine caching schedules based on each block's changes over timesteps. In our experiments, we show through FID, human evaluation and qualitative analysis that Block Caching allows to generate images with higher visual quality at the same computational cost. We demonstrate this for different state-of-the-art models (LDM and EMU) and solvers (DDIM and DPM).

We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their denoising error vectors over a range of noise amplitudes. Geometrically, this amounts to comparing the score vector fields of the blurred density around the signals over a range of blur levels. We prove that the IEM is a valid global distance metric and derive a closed-form expression for its local second-order approximation, which yields a Riemannian metric. For Gaussian-distributed signals, the IEM coincides with the Mahalanobis distance. But for more complex distributions, it adapts, both locally and globally, to the geometry of the distribution. In practice, the IEM can be computed using a learned denoiser (analogous to generative diffusion models) and solving a one-dimensional integral. To demonstrate the value of our framework, we learn an IEM on the ImageNet database. Experiments show that this IEM is competitive with or outperforms state-of-the-art supervised image quality metrics in predicting human perceptual judgments.

Mask-based lensless imagers are smaller and lighter than traditional lensed cameras. In these imagers, the sensor does not directly record an image of the scene; rather, a computational algorithm reconstructs it. Typically, mask-based lensless imagers use a model-based reconstruction approach that suffers from long compute times and a heavy reliance on both system calibration and heuristically chosen denoisers. In this work, we address these limitations using a bounded-compute, trainable neural network to reconstruct the image. We leverage our knowledge of the physical system by unrolling a traditional model-based optimization algorithm, whose parameters we optimize using experimentally gathered ground-truth data. Optionally, images produced by the unrolled network are then fed into a jointly-trained denoiser. As compared to traditional methods, our architecture achieves better perceptual image quality and runs 20x faster, enabling interactive previewing of the scene. We explore a spectrum between model-based and deep learning methods, showing the benefits of using an intermediate approach. Finally, we test our network on images taken in the wild with a prototype mask-based camera, demonstrating that our network generalizes to natural images.

In this paper, we present a novel generative task: joint scene graph - image generation. While previous works have explored image generation conditioned on scene graphs or layouts, our task is distinctive and important as it involves generating scene graphs themselves unconditionally from noise, enabling efficient and interpretable control for image generation. Our task is challenging, requiring the generation of plausible scene graphs with heterogeneous attributes for nodes (objects) and edges (relations among objects), including continuous object bounding boxes and discrete object and relation categories. We introduce a novel diffusion model, DiffuseSG, that jointly models the adjacency matrix along with heterogeneous node and edge attributes. We explore various types of encodings for the categorical data, relaxing it into a continuous space. With a graph transformer being the denoiser, DiffuseSG successively denoises the scene graph representation in a continuous space and discretizes the final representation to generate the clean scene graph. Additionally, we introduce an IoU regularization to enhance the empirical performance. Our model significantly outperforms existing methods in scene graph generation on the Visual Genome and COCO-Stuff datasets, both on standard and newly introduced metrics that better capture the problem complexity. Moreover, we demonstrate the additional benefits of our model in two downstream applications: 1) excelling in a series of scene graph completion tasks, and 2) improving scene graph detection models by using extra training samples generated from DiffuseSG.

Transfer learning from natural images is standard in supervised and increasingly adopted in self-supervised medical image analysis, but its role in generative modelling, and in particular diffusion denoisers, remains underexplored. Medical diffusion models typically train the denoiser from scratch, with no systematic evaluation of natural-image transfer. We analyse this across latent and pixel paradigms, model sizes (131M-952M) and two radiology datasets (RadImageNet, BraTS), and ask which aspects of transfer support generation. We find that: i) Natural-image initialisation consistently improves generation, by 21-34% relative gFID in pixel space against 14% in latent space, where the tokeniser supplies much of the prior. gFID gains mirror downstream pathology classification and radiomic-feature FD, both proxies for clinical fidelity. ii) Benefits reflect spatial structure, not semantics: semantic probing does not predict generation quality, whereas a spatial-structure metric adapted to internal denoiser representations tracks gFID at |r|=0.85, positioning spatial organisation as a channel through which pretraining manifests. iii) Mixed-domain denoiser training shows that natural and medical images share similar layer-wise representations up to the late blocks, and mixing natural images into medical training improves fidelity. iv) Transfer benefit is tied to natural image initialisation, outperforming in-domain medical pretraining and several reinitialisation schemes. Overall, natural image denoisers transfer positively to medical ones in our setup. Code is available at https://github.com/CAIROLab-Bern/rad-dit

Image denoising is a fundamental challenge in computer vision, with applications in photography and medical imaging. While deep learning-based methods have shown remarkable success, their reliance on specific noise distributions limits generalization to unseen noise types and levels. Existing approaches attempt to address this with extensive training data and high computational resources but they still suffer from overfitting. To address these issues, we conduct image denoising by utilizing dynamically generated kernels via efficient operations. This approach helps prevent overfitting and improves resilience to unseen noise. Specifically, our method leverages a Feature Extraction Module for robust noise-invariant features, Global Statistics and Local Correlation Modules to capture comprehensive noise characteristics and structural correlations. The Kernel Prediction Module then employs these cues to produce pixel-wise varying kernels adapted to local structures, which are then applied iteratively for denoising. This ensures both efficiency and superior restoration quality. Despite being trained on single-level Gaussian noise, our compact model (~ 0.04 M) excels across diverse noise types and levels, demonstrating the promise of iterative dynamic filtering for practical image denoising.

Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation, consistency training, or adversarial objectives, but sacrifice the likelihood framework in the process. We introduce Normalizing Trajectory Models (NTM), which models each reverse step as an expressive conditional normalizing flow with exact likelihood training. Architecturally, NTM combines shallow invertible blocks within each step with a deep parallel predictor across the trajectory, forming an end-to-end network trainable from scratch or initializable from pretrained flow-matching models. Its exact trajectory likelihood further enables self-distillation: a lightweight denoiser trained on the model's own score produces high-quality samples in four steps. On text-to-image benchmarks, NTM matches or outperforms strong image generation baselines in just four sampling steps while uniquely retaining exact likelihood over the generative trajectory.

Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. However, DDPMs require hundreds to thousands of iterations to produce final samples. Several prior works have successfully accelerated DDPMs through adjusting the variance schedule (e.g., Improved Denoising Diffusion Probabilistic Models) or the denoising equation (e.g., Denoising Diffusion Implicit Models (DDIMs)). However, these acceleration methods cannot maintain the quality of samples and even introduce new noise at a high speedup rate, which limit their practicability. To accelerate the inference process while keeping the sample quality, we provide a fresh perspective that DDPMs should be treated as solving differential equations on manifolds. Under such a perspective, we propose pseudo numerical methods for diffusion models (PNDMs). Specifically, we figure out how to solve differential equations on manifolds and show that DDIMs are simple cases of pseudo numerical methods. We change several classical numerical methods to corresponding pseudo numerical methods and find that the pseudo linear multi-step method is the best in most situations. According to our experiments, by directly using pre-trained models on Cifar10, CelebA and LSUN, PNDMs can generate higher quality synthetic images with only 50 steps compared with 1000-step DDIMs (20x speedup), significantly outperform DDIMs with 250 steps (by around 0.4 in FID) and have good generalization on different variance schedules. Our implementation is available at https://github.com/luping-liu/PNDM.

Distributional Diffusion Models (DDMs) replace the standard mean-prediction denoiser with a distributional denoiser trained via a scoring rule objective, learning a stochastic approximation to p(x_1 mid x_t) rather than its conditional mean. However, scaling DDMs to modern image-generation settings faces two obstacles: (i) multi-particle training incurs overhead that scales with the number of particles, (ii) DDMs use globally fixed scoring rule hyperparameters, forcing a single trade-off across sampling budgets. We mitigate these limitations by deferring particle expansion to late transformer layers, and the hyperparameter trade-off by introducing time-dependent scoring rule schedules informed by the dynamical regimes of~Biroli2024. Combined with a DiT-based latent setup, these changes make DDM training practical on class-conditional ImageNet-256^2, achieving 4.48 FID at 4 steps and 2.38 at 50 steps with DiT-XL/2, from a single model trained from scratch in one stage, without a teacher, self-distillation or JVPs. The result is a stochastic few-step generator whose FID does not degrade as the sampling budget grows from 4 to 50 NFE, and the same recipe transfers to text-to-image generation. Code and pre-trained models available at https://github.com/CompVis/iDDM.

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.

Existing feed-forward image-to-3D methods mainly rely on 2D multi-view diffusion models that cannot guarantee 3D consistency. These methods easily collapse when changing the prompt view direction and mainly handle object-centric prompt images. In this paper, we propose a novel single-stage 3D diffusion model, DiffusionGS, for object and scene generation from a single view. DiffusionGS directly outputs 3D Gaussian point clouds at each timestep to enforce view consistency and allow the model to generate robustly given prompt views of any directions, beyond object-centric inputs. Plus, to improve the capability and generalization ability of DiffusionGS, we scale up 3D training data by developing a scene-object mixed training strategy. Experiments show that our method enjoys better generation quality (2.20 dB higher in PSNR and 23.25 lower in FID) and over 5x faster speed (~6s on an A100 GPU) than SOTA methods. The user study and text-to-3D applications also reveals the practical values of our method. Our Project page at https://caiyuanhao1998.github.io/project/DiffusionGS/ shows the video and interactive generation results.

Visual tokens dominate inference cost in vision-language models (VLMs), yet many carry redundant information. Existing pruning methods alleviate this but typically rely on attention magnitude or similarity scores. We reformulate visual token pruning as capacity constrained communication: given a fixed budget K, the model must allocate limited bandwidth to maximally preserve visual information. We propose AutoSelect, which attaches a lightweight Scorer and Denoiser to a frozen VLM and trains with only the standard next token prediction loss, without auxiliary objectives or extra annotations. During training, a variance preserving noise gate modulates each token's information flow according to its predicted importance so that gradients propagate through all tokens; a diagonal attention Denoiser then recovers the perturbed representations. At inference, only the Scorer and a hard top-K selection remain, adding negligible latency. On ten VLM benchmarks, AutoSelect retains 96.5% of full model accuracy while accelerating LLM prefill by 2.85x with only 0.69 ms overhead, and transfers to different VLM backbones without architecture-specific tuning. Code is available at https://github.com/MedHK23/AutoSelect.

Language generation is almost universally treated as a sequential process: autoregressive models emit one token at a time, while diffusion language models replace token-level seriality with a long trajectory of iterative refinement. In this work, we introduce PlaidQ, a 0.7B continuous diffusion language model for code generation, and show that its trajectory can be aggressively distilled into only a few denoising steps---or even one, enabling efficient code generation. PlaidQ repurposes a pretrained autoregressive model as a bidirectional denoiser over continuous token embeddings. We distill PlaidQ with distribution matching for few-step generation and paired-trajectory supervision for one-step generation. At matched model scale, PlaidQ is competitive with discrete diffusion language models on code generation. Distillation then shifts the quality--compute frontier: a 16-step student reaches 31.78 and 40.49 pass@10 on HumanEval and MBPP+, surpassing the same PlaidQ teacher sampled for 512 steps. At the extreme, paired-trajectory distillation achieves 7.07 pass@1 on HumanEval with a single denoising step, producing functionally correct programs. Together, these results establish continuous diffusion as a viable path to few-step and one-step code generation. Broadly, continuous diffusion is not merely another representation for language: it provides an interface through which language models can inherit the acceleration and distillation machinery of continuous diffusion modeling. Training and inference code and model checkpoints are available at https://github.com/pengzhangzhi/plaidq.

Recently, diffusion-based methods for monocular 3D human pose estimation have achieved state-of-the-art (SOTA) performance by directly regressing the 3D joint coordinates from the 2D pose sequence. Although some methods decompose the task into bone length and bone direction prediction based on the human anatomical skeleton to explicitly incorporate more human body prior constraints, the performance of these methods is significantly lower than that of the SOTA diffusion-based methods. This can be attributed to the tree structure of the human skeleton. Direct application of the disentangled method could amplify the accumulation of hierarchical errors, propagating through each hierarchy. Meanwhile, the hierarchical information has not been fully explored by the previous methods. To address these problems, a Disentangled Diffusion-based 3D Human Pose Estimation method with Hierarchical Spatial and Temporal Denoiser is proposed, termed DDHPose. In our approach: (1) We disentangle the 3D pose and diffuse the bone length and bone direction during the forward process of the diffusion model to effectively model the human pose prior. A disentanglement loss is proposed to supervise diffusion model learning. (2) For the reverse process, we propose Hierarchical Spatial and Temporal Denoiser (HSTDenoiser) to improve the hierarchical modeling of each joint. Our HSTDenoiser comprises two components: the Hierarchical-Related Spatial Transformer (HRST) and the Hierarchical-Related Temporal Transformer (HRTT). HRST exploits joint spatial information and the influence of the parent joint on each joint for spatial modeling, while HRTT utilizes information from both the joint and its hierarchical adjacent joints to explore the hierarchical temporal correlations among joints. Code and models are available at https://github.com/Andyen512/DDHPose

The post-training pipeline for diffusion models currently has two stages: supervised fine-tuning (SFT) on curated data and reinforcement learning (RL) with reward models. A fundamental gap separates them. SFT optimizes the denoiser only on ground-truth states sampled from the forward noising process; once inference deviates from these ideal states, subsequent denoising relies on out-of-distribution generalization rather than learned correction, exhibiting the same exposure bias that afflicts autoregressive models, but accumulated along the denoising trajectory instead of the token sequence. RL can in principle address this mismatch, yet its terminal reward signal is sparse, suffers from credit-assignment difficulty, and risks reward hacking. We propose SOAR (Self-Correction for Optimal Alignment and Refinement), a bias-correction post-training method that fills this gap. Starting from a real sample, SOAR performs a single stop-gradient rollout with the current model, re-noises the resulting off-trajectory state, and supervises the model to steer back toward the original clean target. The method is on-policy, reward-free, and provides dense per-timestep supervision with no credit-assignment problem. On SD3.5-Medium, SOAR improves GenEval from 0.70 to 0.78 and OCR from 0.64 to 0.67 over SFT, while simultaneously raising all model-based preference scores. In controlled reward-specific experiments, SOAR surpasses Flow-GRPO in final metric value on both aesthetic and text-image alignment tasks, despite having no access to a reward model. Since SOAR's base loss subsumes the standard SFT objective, it can directly replace SFT as a stronger first post-training stage after pretraining, while remaining fully compatible with subsequent RL alignment.

Denoising generative models deliver high-fidelity generation but remain bottlenecked by inference latency due to the many iterative denoiser calls required during sampling. Training-free acceleration methods reduce latency by either sparsifying the model architecture or shortening the sampling trajectory. Current training-free acceleration methods are more complex than necessary: higher-order predictors amplify error under aggressive speedups, and architectural modifications hinder deployment. Beyond 2x acceleration, step skipping creates structural scarcity -- at most one fresh evaluation per local window -- leaving the computed output and its backward difference as the only causally grounded information. Based on this, we propose ZEUS, an acceleration method that predicts reduced denoiser evaluations using a second-order predictor, and stabilizes aggressive consecutive skipping with an interleaved scheme that avoids back-to-back extrapolations. ZEUS adds essentially zero overhead, no feature caches, and no architectural modifications, and it is compatible with different backbones, prediction objectives, and solver choices. Across image and video generation, ZEUS consistently improves the speed-fidelity performance over recent training-free baselines, achieving up to 3.2x end-to-end speedup while maintaining perceptual quality. Our code is available at: https://github.com/Ting-Justin-Jiang/ZEUS.

Temperature scaling is typically applied as a post-hoc transformation of model probabilities. In posterior-induced flow language models, this creates two mismatches. First, posterior tempering implicitly changes both the endpoint distribution and the distribution of intermediate noisy states, while the denoiser remains trained on the original states. Second, the tempered posterior weights are combined with transport dynamics derived for the untempered flow. These mismatches are reflected empirically: lowering temperature improves GSM8K performance much less reliably in flow LMs than in discrete diffusion LMs. We introduce Bayes-Consistent Tempering (BCT), which makes temperature explicit in both the distributions and dynamics of the generative flow. Its learned realization trains the denoiser on tempered intermediate states and tempers the endpoint distribution using the corresponding tempered dynamics. We also derive training-free variants for conventionally trained checkpoints. Across hyperspherical flow LMs with two denoiser architectures and a von Mises--Fisher flow LM, BCT improves GSM8K generation across broad temperature ranges and achieves the strongest tempering performance. The gains also extend to Sudoku, demonstrating benefits on tightly constrained generation. At very low temperatures, the learned realization is also markedly more robust than the training-free variants, supporting temperature as a property of the generative flow across training and inference rather than a post-hoc probability adjustment. Code and model weights are available at https://daioba.github.io/bct .

Diffusion-based vision-language-action (VLA) models cascade pretrained vision-language models (VLMs) with diffusion action experts, but typically restrict the VLM to providing static conditioning. This separation limits how much pretrained perception and reasoning can guide action generation, especially in out-of-distribution settings. We introduce JADE, a Joint Action DEnoiser that enables the VLM and action expert to jointly refine actions. Our key insight is that structured action latents allow the VLM to read the current noisy action together with visual observations and language instructions. At every denoising step, the VLM contextualizes the noisy action and guides the action expert through gated cross-attention, so that its guidance evolves with the action being generated. We further supervise the VLM to recover clean action latents from noisy ones, which gives it a direct action-learning signal and couples perception with control. Additionally, joint denoising enables JADE to generate actions with fewer sampling steps, helping offset the additional cost of VLM participation. An adaptive step-size schedule further balances task performance and inference latency. On RoboDojo, JADE achieves an average success rate of 12.67%, the highest among the evaluated π_{0.5}-based methods, and is competitive with recent VLA and WAM foundation models pretrained at scale. It also improves performance on RoboTwin 2.0 and raises the average success rate across four real-world bimanual tasks by 20.8 percentage points compared with π_{0.5}.

Training high-quality diffusion models is computationally expensive, and inference-time guidance often adds further sampling cost. In this work, we introduce Swift, a simple yet effective self-guided training method that uses a frozen weak denoiser to improve a stronger model without adding inference overhead. For each noisy input, Swift extrapolates the clean regression target away from the weak denoiser's prediction, amplifying components that remain underfit. The weak guide can be an early training checkpoint, requires no backpropagation during main-model training, and is discarded afterward. The resulting model retains the original sampler and supports both conditional and unconditional generation without label dropout or an unconditional branch. We explain this mechanism through a spectral analysis of finite-time population gradient flow in an RKHS. With an early-stopped weak guide, we prove that a nonempty range of extrapolation strengths yields strictly lower posterior-mean error than matched standard training, despite shifting the regression target away from the posterior mean. Experiments on CIFAR-10 and ImageNet-256 demonstrate improvements across model scales and representations. In one ImageNet-256 configuration, Swift surpasses the baseline's best FID using roughly half the total training compute, including guide preparation and training overhead. On RAEv2, it achieves FID 1.15 without inference-time guidance and 0.99 with guidance. These results establish target extrapolation as an effective approach to weak-to-strong diffusion training with efficient single-model inference.

Diffusion models have achieved remarkable success in generative modeling. However, this study confirms the existence of overfitting in diffusion model training, particularly in data-limited regimes. To address this challenge, we propose Score Augmentation (ScoreAug), a novel data augmentation framework specifically designed for diffusion models. Unlike conventional augmentation approaches that operate on clean data, ScoreAug applies transformations to noisy data, aligning with the inherent denoising mechanism of diffusion. Crucially, ScoreAug further requires the denoiser to predict the augmentation of the original target. This design establishes an equivariant learning objective, enabling the denoiser to learn scores across varied denoising spaces, thereby realizing what we term score augmentation. We also theoretically analyze the relationship between scores in different spaces under general transformations. In experiments, we extensively validate ScoreAug on multiple benchmarks including CIFAR-10, FFHQ, AFHQv2, and ImageNet, with results demonstrating significant performance improvements over baselines. Notably, ScoreAug effectively mitigates overfitting across diverse scenarios, such as varying data scales and model capacities, while exhibiting stable convergence properties. Another advantage of ScoreAug over standard data augmentation lies in its ability to circumvent data leakage issues under certain conditions. Furthermore, we show that ScoreAug can be synergistically combined with traditional data augmentation techniques to achieve additional performance gains.

Recently proposed pyramidal models decompose the conventional forward and backward diffusion processes into multiple stages operating at varying resolutions. These models handle inputs with higher noise levels at lower resolutions, while less noisy inputs are processed at higher resolutions. This hierarchical approach significantly reduces the computational cost of inference in multi-step denoising models. However, existing open-source pyramidal video models have been trained from scratch and tend to underperform compared to state-of-the-art systems in terms of visual plausibility. In this work, we present a pipeline that converts a pretrained diffusion model into a pyramidal one through low-cost finetuning, achieving this transformation without degradation in quality of output videos. Furthermore, we investigate and compare various strategies for step distillation within pyramidal models, aiming to further enhance the inference efficiency. Our results are available at https://qualcomm-ai-research.github.io/PyramidalWan.

The 3D Human Pose Estimation (3D HPE) task uses 2D images or videos to predict human joint coordinates in 3D space. Despite recent advancements in deep learning-based methods, they mostly ignore the capability of coupling accessible texts and naturally feasible knowledge of humans, missing out on valuable implicit supervision to guide the 3D HPE task. Moreover, previous efforts often study this task from the perspective of the whole human body, neglecting fine-grained guidance hidden in different body parts. To this end, we present a new Fine-Grained Prompt-Driven Denoiser based on a diffusion model for 3D HPE, named FinePOSE. It consists of three core blocks enhancing the reverse process of the diffusion model: (1) Fine-grained Part-aware Prompt learning (FPP) block constructs fine-grained part-aware prompts via coupling accessible texts and naturally feasible knowledge of body parts with learnable prompts to model implicit guidance. (2) Fine-grained Prompt-pose Communication (FPC) block establishes fine-grained communications between learned part-aware prompts and poses to improve the denoising quality. (3) Prompt-driven Timestamp Stylization (PTS) block integrates learned prompt embedding and temporal information related to the noise level to enable adaptive adjustment at each denoising step. Extensive experiments on public single-human pose estimation datasets show that FinePOSE outperforms state-of-the-art methods. We further extend FinePOSE to multi-human pose estimation. Achieving 34.3mm average MPJPE on the EgoHumans dataset demonstrates the potential of FinePOSE to deal with complex multi-human scenarios. Code is available at https://github.com/PKU-ICST-MIPL/FinePOSE_CVPR2024.

Automatic layout generation that can synthesize high-quality layouts is an important tool for graphic design in many applications. Though existing methods based on generative models such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) have progressed, they still leave much room for improving the quality and diversity of the results. Inspired by the recent success of diffusion models in generating high-quality images, this paper explores their potential for conditional layout generation and proposes Transformer-based Layout Diffusion Model (LayoutDM) by instantiating the conditional denoising diffusion probabilistic model (DDPM) with a purely transformer-based architecture. Instead of using convolutional neural networks, a transformer-based conditional Layout Denoiser is proposed to learn the reverse diffusion process to generate samples from noised layout data. Benefitting from both transformer and DDPM, our LayoutDM is of desired properties such as high-quality generation, strong sample diversity, faithful distribution coverage, and stationary training in comparison to GANs and VAEs. Quantitative and qualitative experimental results show that our method outperforms state-of-the-art generative models in terms of quality and diversity.

What does a discrete diffusion model actually learn? The literature trains denoisers, bridge plug-ins, and concrete scores, each deriving its own ELBO objective under different conventions. This fragmentation makes the object being learned unclear and ELBO values difficult to interpret and compare. All three methods learn the same object in different coordinates: the exact time-reversal of the noising process. We first prove the Oracle Distance identity: for any noising process, the negative ELBO is not just a bound on the likelihood; it equals the data entropy plus the path KL divergence from the reversed noising process to the learned one. Next, for token-factorizing noise, we show that denoiser, bridge plug-in, and concrete score are three coordinates of this reverse process, derive exact conversions between them, and identify the probability distribution learned by each. In particular, contrary to its standard interpretation, the bridge plug-in learns not a denoiser but the cavity distribution: the clean token given the noisy sequence excluding its own position. We confirm the theory by training all three coordinates with masked, uniform, and GIDD kernels on OpenWebText under a shared recipe, and by training uniform-diffusion solvers on four logic tasks. The learned coordinates agree after conversion, while confusing the cavity with the denoiser can severely degrade sampling quality. Together with exact boundary-term formulas, closed-form NELBO calibrations at initialization, and a clock interpretation of time schedules, these results provide a conceptual framework and a mechanical recipe for deriving, implementing, and comparing discrete diffusion processes.

Masked Generative Models (MGMs) enable parallel decoding and achieve strong performance across modalities, but require full-sequence bidirectional transformers at every step, making training costly and degrading quality under low sampling budgets. Existing work improves efficiency via better samplers or cheaper fixed-depth denoisers, but they still allocate a fixed amount of denoiser computation to each refinement step. We introduce Fixed-Point Masked Generative Models (FP-MGMs), which replace part of the denoiser with a fixed-point solver over shared attention layers to enable adaptive depth with fewer parameters. To make it more effective for masked generation, we first introduce a cross-step consistency loss, which aligns hidden representations at neighboring denoising steps and, second, three-state reuse (3SR) which warm-starts the solver using the previous solution by treating differently unchanged, still-masked, and newly revealed tokens respectively. Together, these components define our complete training-to-inference framework for fixed-point masked generation, CoFRe. We also show that pre-trained MGMs can be converted into FP-MGMs with short fine-tuning, avoiding full retraining. Across modalities, CoFRe improves the quality and cost trade-off. On OpenWebText, CoFRe reduces parameters by 38.8\%, training time by 11.5\%, and VRAM by 16.9\%, while improving generative perplexity from 830.8 to 101.8 at a budget of 96 transformer-block forward passes, compared to MDLM. In ImageNette, CoFRe reduces training time by 48.6\% and VRAM by 50.7\%, while improving FID in all sample budgets tested. Overall, CoFRe offers a practical framework for cheaper training and stronger low-budget masked generation.

Self-conditioning is a core technique that enhances continuous flow-based language models, where the model learns to denoise generated text by conditioning on its own denoising estimate. While empirically successful, its performance improvements are poorly understood. Moreover, there is growing interest in the use of few-step generators based on flow maps, for which how to leverage self-conditioning is unclear. Here, we show that flow language models with self-conditioning solve a fixed-point iteration that bootstraps the performance of the learned denoiser. We use this viewpoint to formulate fixed-point flows, a two-dimensional class of self-conditioned flows, where the first dimension represents the flow process and the second represents the fixed-point iteration. We show that fixed-point flows define valid flow maps, and show that they can be distilled from self-conditioned flow models by compressing both fixed-point iterations and the flow process, the former with fixed-point distillation and the latter with flow map distillation. Our resulting flow map language model, FMLM^star, outperforms state-of-the-art self-conditioned models and few-step models in one- and few-step generation on OpenWebText. Code is available at https://github.com/Ugness/self-conditioned-fmlm.

Discrete diffusion language models offer a compelling alternative to autoregressive generation for tasks demanding bidirectional reasoning and global constraint satisfaction. Yet they share a structural bottleneck: when decoding in parallel, each token is sampled independently from its marginal, severing the statistical dependencies among the tokens decoded together. Continuous diffusion language models avoid this by denoising a shared continuous state, but their denoiser sees only that state, so nothing ties it to a valid token configuration until it is finally decoded. To address this, we propose Hierarchical Continuous Diffusion Language Models (HC-DLM), which couple discrete token generation with a continuous latent trajectory in a single, principled denoising process, whose training objective is derived from a variational bound on the token likelihood. In contrast to recent methods that attach continuous context to a self-contained discrete chain, HC-DLM makes the latent the only persistent generative state: tokens are read out from it at every step and feed back as a scaffold for the next latent update. On structured reasoning (Sudoku), mathematical planning (Countdown) and language modeling (LM1B), HC-DLM improves over discrete and continuous diffusion baselines at matched model size, in puzzle accuracy on Sudoku and Countdown and in generative perplexity on LM1B. Project page: https://hc-dlm.github.io/.

Since convolutional neural networks (CNNs) perform well at learning generalizable image priors from large-scale data, these models have been extensively applied to image restoration and related tasks. Recently, another class of neural architectures, Transformers, have shown significant performance gains on natural language and high-level vision tasks. While the Transformer model mitigates the shortcomings of CNNs (i.e., limited receptive field and inadaptability to input content), its computational complexity grows quadratically with the spatial resolution, therefore making it infeasible to apply to most image restoration tasks involving high-resolution images. In this work, we propose an efficient Transformer model by making several key designs in the building blocks (multi-head attention and feed-forward network) such that it can capture long-range pixel interactions, while still remaining applicable to large images. Our model, named Restoration Transformer (Restormer), achieves state-of-the-art results on several image restoration tasks, including image deraining, single-image motion deblurring, defocus deblurring (single-image and dual-pixel data), and image denoising (Gaussian grayscale/color denoising, and real image denoising). The source code and pre-trained models are available at https://github.com/swz30/Restormer.

Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps. In continuous domains, consistency training along the probability-flow ODE is a popular recipe to accelerate diffusion. For discrete diffusion, no analogous sample-space ODE exists, making direct adaptation ill-defined. We argue that the natural discrete substitute is not a deterministic trajectory but its stochastic counterpart: the exact posterior bridge, available in closed form for broad corruption families including masked and uniform diffusion. Building on this observation, we introduce Multi-Path Discrete Consistency (MPDC), a new principle that trains a denoiser to be path-invariant in expectation across these stochastic bridges, and instantiate it as the Consistent Diffusion Language Model (CDLM), a single-stage, teacher-free training framework. A single CDLM objective unifies masked diffusion, continuous consistency models, and progressive/discrete distillation as analytic limits or empirical approximations of one common view. Empirically, CDLM establishes a new state of the art on both conditional and unconditional text-generation, consistently outperforming strong base discrete diffusion models and often even multi-stage distilled baselines across sampling budgets, with the largest gains in the few-step regime. Together, these results position CDLM as a principled and scalable foundation for the next generation of fast, high-fidelity discrete generative modeling.

Diffusion language models offer a promising alternative to autoregressive models due to their potential for parallel and iterative generation. However, existing approaches use a single network for both context representation and iterative denoising, forcing one model to serve both roles and limiting its capacity for either role. We propose TwoTower, a block-wise autoregressive diffusion model that decouples these roles into two towers: a frozen AR context tower that causally processes clean tokens, and a trainable diffusion denoiser tower with bidirectional block attention that refines noisy blocks via cross-attention to the context. Built on Nemotron-3-Nano-30B-A3B, an open-weight 30B hybrid Mamba-Transformer MoE model, and trained on approximately 2.1T tokens, Nemotron-TwoTower retains 98.7% of the autoregressive baseline's quality while offering 2.42X higher wall-clock generation throughput. We release the code and model weights at https://huggingface.co/collections/nvidia/nemotron-twotower.

Dynamic imaging addresses the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in the case of dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. In this work, we propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem. The first, are partially separable models, which have been used to efficiently introduce a low-rank prior for the spatio-temporal object. The second is the recent Regularization by Denoising (RED), which provides a flexible framework to exploit the impressive performance of state-of-the-art image denoising algorithms, for various inverse problems. We propose a partially separable objective with RED and a computationally efficient and scalable optimization scheme with variable splitting and ADMM. Theoretical analysis proves the convergence of our objective to a value corresponding to a stationary point satisfying the first-order optimality conditions. Convergence is accelerated by a particular projection-domain-based initialization. We demonstrate the performance and computational improvements of our proposed RED-PSM with a learned image denoiser by comparing it to a recent deep-prior-based method known as TD-DIP. Although the main focus is on dynamic tomography, we also show the performance advantages of RED-PSM in a cardiac dynamic MRI setting.

Denoising Diffusion Models (DDMs) have emerged as a strong competitor to Generative Adversarial Networks (GANs). However, despite their widespread use in image synthesis and editing applications, their latent space is still not as well understood. Recently, a semantic latent space for DDMs, coined `h-space', was shown to facilitate semantic image editing in a way reminiscent of GANs. The h-space is comprised of the bottleneck activations in the DDM's denoiser across all timesteps of the diffusion process. In this paper, we explore the properties of h-space and propose several novel methods for finding meaningful semantic directions within it. We start by studying unsupervised methods for revealing interpretable semantic directions in pretrained DDMs. Specifically, we show that global latent directions emerge as the principal components in the latent space. Additionally, we provide a novel method for discovering image-specific semantic directions by spectral analysis of the Jacobian of the denoiser w.r.t. the latent code. Next, we extend the analysis by finding directions in a supervised fashion in unconditional DDMs. We demonstrate how such directions can be found by relying on either a labeled data set of real images or by annotating generated samples with a domain-specific attribute classifier. We further show how to semantically disentangle the found direction by simple linear projection. Our approaches are applicable without requiring any architectural modifications, text-based guidance, CLIP-based optimization, or model fine-tuning.