Diffusion Model Sampling

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5 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Latest papers 58

May 23, 2026cs.CV

Self-supervised Dynamic Heterogeneous Degradation Modeling for Unified Zero-Shot Image Restoration

Zero-shot image restoration provides a flexible way to handle diverse degradations without task-specific training. However, existing methods typically rely on stacked layers or pre-trained features to enhance degradation expression, while overlooking physically consistent priors. The insufficient degradation prompts impose the heavy training burden and high sampling costs during zero-shot diffusion. Moreover, the fixed inference trajectory often collapses to suboptimal solutions under complex corruptions. We observe that heterogeneous degradations can be reparameterized into a minimal set of physically coherent parameters for compact representation. Based on this insight, we first propose a unified physical zero-shot image restoration (UP-ZeroIR) framework that explicitly models heterogeneous degradations into a homogeneous all-in-one distribution. The distribution can be optimized directly in the latent space, enabling principled solution exploration and effective prompt adaptation. Besides, we introduce a dynamic quality-refinement strategy that adaptively adjusts the diffusion trajectory for robust globally optimal convergence. Extensive experiments demonstrate that our method achieves state-of-the-art performance across both single and mixed degradations. Our code is available at https://github.com/yangjinglyy/UP-ZeroIR

XiaoWan Hu, Jing Yang, HeNan Liu +2

Beihang University · Tsinghua University

Diffusion Models for Image Restoration Diffusion Model Sampling All-in-One Image Restoration Image Restoration

May 21, 2026cs.LG

Uniform Diffusion Models Revisited: Leave-One-Out Denoiser and Absorbing State Reformulation

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.

Samson Gourevitch, Yazid Janati, Dario Shariatian +4

CMAP, Ecole polytechnique · Institute of Foundation Models · Inria, PSL Research University +2

Diffusion Model Sampling Diffusion Language Models Diffusion Models

May 21, 2026cs.LG

The Value of Covariance Matching in Gaussian DDPMs and the Lanczos Sampler

A central error measure in Gaussian DDPMs is the path-space KL divergence between the exact reverse chain and the learned Gaussian reverse process. This quantity is especially relevant for procedures such as classifier guidance, which perturb the entire reverse trajectory rather than only the terminal sample. Prior analyses show that standard isotropic reverse covariances suffer an unavoidable

Ω(1/T)

path-KL error as the number of denoising steps

T

grows. We show that matching the full posterior covariance breaks this barrier, yielding an order-wise improvement that reduces the path KL to

O(1/T^2)

. To make full covariance matching practical, we introduce the Lanczos Gaussian sampler (LGS), a training-free, matrix-free method for sampling from the optimal reverse covariance using only covariance-vector products, which are available through Jacobian-vector products of the posterior mean. LGS avoids dense covariance storage and auxiliary covariance models. We prove that LGS approximation error decays exponentially in the number of Lanczos steps, where each Lanczos step requires a single Jacobian-vector product. Empirically, using only just three such steps improves sample quality over strong diagonal-covariance baselines, including OCM-DDPM, across standard image benchmarks. This identifies full covariance matching as both theoretically valuable and practically accessible for fast DDPM sampling.

Md Sahil Akhtar, Aymane El Gadarri, Vivek F. Farias +1

Electrical Engineering and Computer Science · Massachusetts Institute of Technology · Operations Research Center +1

Diffusion Model Sampling Distribution Matching Diffusion Models

May 21, 2026cs.LG

A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models

Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential equations, and numerical sampling methods. We write this tutorial to provide a unified and self-contained account of these viewpoints from the perspective of differential equations. Starting from a conditional Gaussian noising process, we derive ordinary differential equation (ODE) and stochastic differential equation (SDE) representations, pass to the corresponding marginal forward dynamics, and then obtain the reverse-time SDE and probability-flow ODE that make generation possible. We show that the central unknown quantity in reverse sampling is the marginal score, explain how score matching becomes the standard denoising objective under a noise-prediction parameterization, and discuss practical reverse-time sampling and guidance. We further place DDPM, DDIM, flow matching, and score-based SDEs in a common framework, and conclude with diffusion language models in continuous embedding space together with a brief discussion of discrete masked-token diffusion. The tutorial is intended as a bridge between the analytical foundations of diffusion processes and the modern generative algorithms built upon them.

Jiayi Fu, Yuxia Wang

INSAIT, Sofia University “St. Kliment Ohridski”, Bulgaria

Diffusion Model Sampling Score-Based Generative Modeling Diffusion Models

May 20, 2026cs.CV

Semantic Granularity Navigation in Image Editing

Despite the generative capabilities of diffusion and flow models, real-image editing remains constrained by a persistent trade-off between semantic editability and structural fidelity. We trace a primary cause of this limitation to the implicit coupling of edit progress with model scale in existing paradigms. Under this coupling, stronger edits typically require visiting noisier states, which spends computation on destabilizing layout before the semantic change is well localized. We introduce NaviEdit, a training-free inference-time controller that decouples edit progress from model scale traversal through a strict self-consistency contract. NaviEdit operates at the rollout level and leaves the underlying pretrained model unchanged. It treats scale as a control input and reallocates a fixed step budget toward semantically responsive intermediate scales instead of destructive high-noise regimes. Experiments show positive average gains across compatible editors and flow backbones, supporting decoupling as a portable inference-time control principle.

Liangsi Lu, Minzhe Guo, Xuhang Chen +1

Guangdong University of Technology, Guangzhou, China · Huizhou University, Huizhou, China.

Diffusion Model Sampling Diffusion Timestep Scheduling Diffusion-Based Image Editing Diffusion Models

May 18, 2026cs.LG

Generative Pseudo-Force Fields for Molecular Generation

Generating stable molecular conformations typically forces a tradeoff between the physical realism of energy-based relaxation and the sampling efficiency of data-driven generative models. While machine learning force fields (MLFFs) can sample stable conformations by relaxing molecular geometries according to physical forces, they require costly ab-initio training data. Conversely, diffusion models (DMs) learn from equilibrium data alone but are dependent on noise schedules and time-step conditioning. In this work, we propose generative pseudo-force fields (GPFFs) to bridge these paradigms by training an MLFF on a quadratic pseudo-potential energy surface relative to reference equilibrium structures. Because no ab-initio calculations are required for the perturbed geometries, non-equilibrium training data can be generated on the fly by perturbing the equilibria with Gaussian noise. We show that GPFFs constitute a time-step-agnostic variant of variance exploding DMs: the score comes from the predicted pseudo-forces but because force magnitudes implicitly encode the noise level, no time-step conditioning is needed. Our GPFF can hence be used as a drop-in replacement in standard diffusion sampling (ancestral, Heun) but also facilitates more efficient, adaptive variants and an MLFF inspired direct denoising scheme. Our proposed sampling algorithms support arbitrary structural priors and geometric constraints. On QM9, GPFF has 100 % validity at 256 neural function evaluations (NFE) and over 50 % at just 6 NFE, outperforming diffusion baselines across all samplers. Combined with custom priors, we showcase the fast and accurate generation process of our method in a molecular editor for a drug design setting, where a molecule is generated in real time.

Stefaan Simon Pierre Hessmann, Khaled Kahouli, Stefan Gugler +4

Machine Learning Group, Technische Universität Berlin, Berlin, Germany · BIFOLD – Berlin Institute for the Foundations of Learning and Data, Berlin, Germany · Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany +6

Machine Learning Interatomic Potentials Diffusion Model Sampling Few-Step Diffusion Sampling 3D Molecular Generation Molecular Generation

May 13, 2026cs.LG

Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training

Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is intuitive: if the data are heavy-tailed, HT noise may appear better matched than light-tailed (LT) Gaussian noise. However, replacing Gaussian noise by HT noise also changes the underlying estimation problem. In this paper, we revisit this paradigm through a combined theoretical and empirical study, establishing sampling-error bounds for two representative diffusion models driven by HT and LT noise. We show that HT noise makes the statistical estimation problem harder, leading to less favorable sampling-error bounds. We support these findings with experiments on synthetic and real-world datasets, empirically recovering the predicted error trade-off. Our results call into question a growing design trend in generative modeling and challenge the use of HT noise to improve rare-region exploration.

Hamza Cherkaoui, Hélène Halconruy, Antonio Ocello

SAMOVAR, Télécom SudParis, Institut Polytechnique de Paris, Palaiseau, France · Modal’X, Université Paris Nanterre, Nanterre, France · CREST, ENSAE Paris, Institut Polytechnique de Paris, Palaiseau, France

Diffusion Model Sampling Heavy-Tailed Noise Heavy-Tailed Distributions Diffusion Models

May 13, 2026stat.ML

Covariance-aware sampling for Diffusion Models

We present a covariance-aware sampler that improves the quality of pixel-space Diffusion Model (DM) sampling in the few-step regime. We hypothesize that in the few-step regime samplers fail because they rely solely on the predicted mean of the reverse distribution, while our solution explicitly models the reverse-process covariance. Our method combines Tweedie's formula to estimate the covariance with an efficient, structured Fourier-space decomposition of the covariance matrix. Implemented as an extension of DDIM, our method requires only a minimal overhead: one extra Jacobian-Vector Product (JVP) per step. We demonstrate that for pixel-based DMs, our method consistently produces superior samples compared to state-of-the-art second order samplers (Heun, DPM-Solver++) and the recent aDDIM sampler, at an identical number of function evaluations (NFE).

Andrea Schioppa, Tim Salimans

GDM - Amsterdam · work done at GDM - Amsterdam

Diffusion Model Sampling Diffusion Sampling Pixel-Space Diffusion Models Few-Step Diffusion Sampling Covariance Estimation

May 12, 2026cs.GR

Generative Motion In-betweening by Diffusion over Continuous Implicit Representations

Recent advances in generative models have yielded impressive progress on motion in-betweening, allowing for more complex, varied, and realistic motion transitions. However, recent methods still exhibit noticeable limitations in preserving keyframe information and ensuring motion continuity. In this paper, we propose a novel pipeline and sampling optimization strategy for latent diffusion models (LDM) based on motion implicit neural representations (INR). By establishing a mapping between INR and sparse spatial or temporal information within latent diffusion, our model can sample the INR parameters from extremely sparse and ambiguous keyframe data and reconstruct plausible and smooth motions from the manifold. Our experiments demonstrate the superior performance of our model, which significantly improves motion generation quality in scenarios with few keyframes while ensuring both keyframe accuracy and diversity of in-between motions.

Shiyu Fan, Paul Henderson, Edmond S. L. Ho

School of Computing Science, University of Glasgow, United Kingdom.

Implicit Neural Representations Latent Diffusion Models Diffusion Model Sampling Diffusion Models for Motion Generation Conditional Diffusion Models

May 12, 2026cs.CV

MoCam: Unified Novel View Synthesis via Structured Denoising Dynamics

Generative novel view synthesis faces a fundamental dilemma: geometric priors provide spatial alignment but become sparse and inaccurate under view changes, while appearance priors offer visual fidelity but lack geometric correspondence. Existing methods either propagate geometric errors throughout generation or suffer from signal conflicts when fusing both statically. We introduce MoCam, which employs structured denoising dynamics to orchestrate a coordinated progression from geometry to appearance within the diffusion process. MoCam first leverages geometric priors in early stages to anchor coarse structures and tolerate their incompleteness, then switches to appearance priors in later stages to actively correct geometric errors and refine details. This design naturally unifies static and dynamic view synthesis by temporally decoupling geometric alignment and appearance refinement within the diffusion process. Experiments demonstrate that MoCam significantly outperforms prior methods, particularly when point clouds contain severe holes or distortions, achieving robust geometry-appearance disentanglement.

Haofeng Liu, Yang Zhou, Ziheng Wang +6

Diffusion Model Sampling Dynamic Novel View Synthesis Novel View Synthesis

May 5, 2026stat.ML

Tempered Guided Diffusion

Training-free conditional diffusion provides a flexible alternative to task-specific conditional model training, but existing samplers often allocate computation inefficiently: independent guided trajectories can vary widely in quality, and additional function evaluations along a single trajectory may not recover from poor early decisions. We propose Tempered Guided Diffusion (TGD), an annealed sequential Monte Carlo framework for training-free conditional sampling with diffusion priors. TGD targets tempered posterior distributions over the clean signal, using noisy diffusion states only as auxiliary variables for proposing reconstructions and propagating particles. Particles are reweighted by incremental likelihood ratios, resampled, and propagated across noise levels, concentrating computation on trajectories plausible under both the prior and observation. Under idealized exact-reconstruction assumptions, full TGD yields a consistent particle approximation to the posterior as the number of particles grows. For expensive reconstruction tasks, Accelerated TGD (A-TGD) retains early particle exploration but prunes to a single high-likelihood trajectory partway through sampling. Experiments on a controlled two-dimensional inverse problem and image inverse problems show improved posterior approximation and favorable wall-clock speed-quality tradeoffs over independent multi-trajectory baselines.

Andreas Makris, Paul Fearnhead, Chris Nemeth

Department of Mathematics and Statistics Lancaster University, UK · Department of Mathematics and Statistics2026 Lancaster University, UK

Diffusion Model Sampling Diffusion-Based Inverse Problems Diffusion Posterior Sampling Diffusion Model Inference Acceleration Inverse Problems

Apr 29, 2026cs.CV

Delta Score Matters! Spatial Adaptive Multi Guidance in Diffusion Models

Diffusion models have achieved remarkable success in synthesizing complex static and temporal visuals, a breakthrough largely driven by Classifier-Free Guidance (CFG). However, despite its pivotal role in aligning generated content with textual prompts, standard CFG relies on a globally uniform scalar. This homogeneous amplification traps models in a well-documented "detail-artifact dilemma": low guidance scales fail to inject intricate semantics, while high scales inevitably cause structural degradation, color over-saturation, and temporal inconsistencies in videos. In this paper, we expose the physical root of this flaw through the lens of differential geometry. By analyzing Tweedie's Formula, we reveal that CFG intrinsically performs a tangential linear extrapolation. Because the natural data manifold is highly curved, this uniform linear step introduces a severe orthogonal deviation. To keep the generation trajectory safely bounded, we formulate a theoretical upper bound for spatial and adaptive guidance. Based on these geometric insights, we propose Spatial Adaptive Multi Guidance (SAMG), a training-free and virtually zero-cost sampling algorithm. SAMG dynamically computes point-wise conditional guidance energy, applying a conservative minimum scale to high-energy boundary regions to preserve delicate micro-textures, while deploying an aggressive maximum scale in low-energy regions to maximize semantic injection. Extensive experiments across diverse image (SD 1.5, SDXL, SD3.5 Medium) and video (CogVideoX, ModelScope) architectures demonstrate that SAMG effectively resolves the detail-artifact dilemma, achieving superior semantic alignment, structural integrity, and temporal smoothness without any computational overhead.

Haosen Li, Wenshuo Chen, Lei Wang +4

1The Hong Kong University of Science and Technology (Guangzhou) · 2Griffith University & Data61/CSIRO

Diffusion Model Guidance Classifier-Free Guidance Diffusion Model Sampling

Apr 28, 2026cs.LG

Exploring Time Conditioning in Diffusion Generative Models from Disjoint Noisy Data Manifolds

Practically, training diffusion models typically requires explicit time conditioning to guide the network through the denoising sampling process. Especially in deterministic methods like DDIM, the absence of time conditioning leads to significant performance degradation. However, other deterministic sampling approaches, such as flow matching, can generate high-quality content without this conditioning, raising the question of its necessity. In this work, we revisit the role of time conditioning from a geometric perspective. We analyze the evolution of noisy data distributions under the forward diffusion process and demonstrate that, in high-dimensional spaces, these distributions concentrate on low-dimensional hyper-cylinder-like manifolds embedded within the input space. Successful generation, we argue, stems from the disentanglement of these manifolds in high-dimensional space. Based on this insight, we modify the forward process of DDIM to align the noisy data manifold with the flow-matching approach, proving that DDIM can generate high-quality content without time conditioning, provided the noisy manifold evolves according to the flow-matching method. Additionally, we extend our framework to class-conditioned generation by decoupling classes into distinct time spaces, enabling class-conditioned synthesis with a class-unconditional denoising model. Extensive experiments validate our theoretical analysis and show that high-quality generation is achievable without explicit conditional embeddings.

Liuzhuozheng Li, Zhiyuan Zhan, Shuhong Liu +5

SGIT AI Lab · UTokyo · RIKEN AIP +4

Diffusion Model Sampling Conditional Diffusion Models

Apr 21, 2026cs.CV

Denoising, Fast and Slow: Difficulty-Aware Adaptive Sampling for Image Generation

Diffusion- and flow-based models usually allocate compute uniformly across space, updating all patches with the same timestep and number of function evaluations. While convenient, this ignores the heterogeneity of natural images: some regions are easy to denoise, whereas others benefit from more refinement or additional context. Motivated by this, we explore patch-level noise scales for image synthesis. We find that naively varying timesteps across image tokens performs poorly, as it exposes the model to overly informative training states that do not occur at inference. We therefore introduce a timestep sampler that explicitly controls the maximum patch-level information available during training, and show that moving from global to patch-level timesteps already improves image generation over standard baselines. By further augmenting the model with a lightweight per-patch difficulty head, we enable adaptive samplers that allocate compute dynamically where it is most needed. Combined with noise levels varying over both space and diffusion time, this yields Patch Forcing (PF), a framework that advances easier regions earlier so they can provide context for harder ones. PF achieves superior results on class-conditional ImageNet, remains orthogonal to representation alignment and guidance methods, and scales to text-to-image synthesis. Our results suggest that patch-level denoising schedules provide a promising foundation for adaptive image generation.

Johannes Schusterbauer, Ming Gui, Yusong Li +3

Diffusion Model Sampling Diffusion Sampling Diffusion-Based Image Generation Diffusion Timestep Scheduling Diffusion Model Inference Acceleration

Apr 20, 2026cs.LG

Efficient Diffusion Models under Nonconvex Equality and Inequality constraints via Landing

Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for constrained diffusion models on generic nonconvex feasible sets

Σ

that simultaneously enforces equality and inequality constraints throughout the diffusion process. Our framework incorporates both overdamped and underdamped dynamics for forward and backward sampling. A key algorithmic innovation is a computationally efficient landing mechanism that replaces costly and often ill-defined projections onto

Σ

, ensuring feasibility without iterative Newton solves or projection failures. By leveraging underdamped dynamics, we accelerate mixing toward the prior distribution, effectively alleviating the high simulation costs typically associated with constrained diffusion. Empirically, this approach reduces function evaluations and memory usage during both training and inference while preserving sample quality. On benchmarks featuring equality and mixed constraints, our method achieves comparable sample quality to state-of-the-art baselines while significantly reducing computational cost, providing a practical and scalable solution for diffusion on nonconvex feasible sets.

Kijung Jeon, Michael Muehlebach, Molei Tao

Georgia Institute of Technology · Max Planck Institute for Int. Sys.

Constrained Generative Modeling Langevin Dynamics Diffusion Model Sampling Diffusion Model Inference Acceleration Diffusion Models

Apr 19, 2026cs.LG

Interpolating Discrete Diffusion Models with Controllable Resampling

Discrete diffusion models form a powerful class of generative models across diverse domains, including text and graphs. However, existing approaches face fundamental limitations. Masked diffusion models suffer from irreversible errors due to early unmasking, while uniform diffusion models, despite enabling self-correction, often yield low-quality samples due to their strong reliance on intermediate latent states. We introduce IDDM, an Interpolating Discrete Diffusion Model, that improves diffusion by reducing dependence on intermediate latent states. Central to IDDM is a controllable resampling mechanism that partially resets probability mass to the marginal distribution, mitigating error accumulation and enabling more effective token corrections. IDDM specifies a generative process whose transitions interpolate between staying at the current state, resampling from a prior, and flipping toward the target state, while enforcing marginal consistency and fully decoupling training from inference. We benchmark our model against state-of-the-art discrete diffusion models across molecular graph generation as well as text generation tasks, demonstrating competitive performance.

Marcel Kollovieh, Sirine Ayadi, Stephan Günnemann

School of Computation, Information and Technology, Technical University of Munich

Diffusion Model Sampling Molecular Graph Generation Text Generation Diffusion Models

Apr 17, 2026cs.CV

Elucidating the SNR-t Bias of Diffusion Probabilistic Models

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.

Meng Yu, Lei Sun, Jianhao Zeng +2

Lanzhou University · AMAP Alibaba Group

Diffusion Model Sampling Diffusion Sampling Diffusion-Based Image Generation Diffusion Models

Mar 18, 2026cs.CV

Q-Drift: Quantization-Aware Drift Correction for Diffusion Model Sampling

Post-training quantization (PTQ) is a practical path to deploy large diffusion models, but quantization noise can accumulate over the denoising trajectory and degrade generation quality. We propose Q-Drift, a sampler-side correction that aims to preserve the intended sampling marginals through a deterministic drift adjustment motivated by generalized marginal-preserving SDEs. Q-Drift uses the calibrated conditional residual variance of quantization error to determine a correction factor at each step. Our SDXL study shows that calibration with as few as 10 paired full-precision/quantized runs remains effective. The resulting sampler correction is plug-and-play with common samplers, diffusion models, and PTQ methods, while incurring negligible overhead at inference. Across six diverse text-to-image models (spanning DiT and U-Net), three samplers (Euler, flow-matching, DPM-Solver++), and two PTQ methods (SVDQuant, MixDQ), Q-Drift improves FID over the corresponding quantized baseline in all seven settings of our main evaluation, with up to 4.79 FID reduction on PixArt-Sigma (SVDQuant W3A4), while preserving CLIP scores. Code is available at https://github.com/sooyoung-ryu/Q-Drift.

Sooyoung Ryu, Mathieu Salzmann, Saqib Javed

Department of Computer Science and Engineering, Seoul National University, Seoul, South Korea · School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland · Meta Reality Labs, Redmond, USA

Diffusion Model Quantization Diffusion Model Sampling Post-Training Quantization Neural Network Quantization T2I Diffusion Models

Mar 15, 2026cs.LG

Trust-Region Noise Search for Black-Box Alignment of Diffusion and Flow Models

Optimizing the noise samples of diffusion and flow models is an increasingly popular approach to align these models to target rewards at inference time. However, we observe that these approaches are usually restricted to differentiable or cheap reward models, the formulation of the underlying pretrained generative model, or are memory/compute inefficient. We instead propose a simple trust-region based search algorithm (TRS) which treats the pre-trained generative and reward models as a black-box and only optimizes the source noise. Our approach achieves a good balance between global exploration and local exploitation, and is versatile and easily adaptable to various generative settings and reward models with minimal hyperparameter tuning. We evaluate TRS across text-to-image, molecule and protein design tasks, and obtain significantly improved output samples over the base generative models and other inference-time alignment approaches which optimize the source noise sample, or even the entire reverse-time sampling noise trajectories in the case of diffusion models. Our source code is publicly available.

Niklas Schweiger, Daniel Cremers, Karnik Ram

Technical University of Munich, Germany · Munich Center for Machine Learning, Germany

Diffusion Model Alignment Black-Box Optimization Diffusion Model Sampling Protein Design T2I Diffusion Models

Feb 17, 2026cs.CV

Efficient Generative Modeling beyond Memoryless Diffusion via Adjoint Schrödinger Bridge Matching

Diffusion models often yield highly curved trajectories and noisy score targets due to an uninformative, memoryless forward process that induces independent data-noise coupling. We propose Adjoint Schrödinger Bridge Matching (ASBM), a generative modeling framework that recovers optimal trajectories in high dimensions via two stages. First, we view the Schrödinger Bridge (SB) forward dynamic as a coupling construction problem and learn it through a data-to-energy sampling perspective that transports data to an energy-defined prior. Then, we learn the backward generative dynamic with a simple matching loss supervised by the induced optimal coupling. By operating in a non-memoryless regime, ASBM produces significantly straighter and more efficient sampling paths. Compared to prior works, ASBM scales to high-dimensional data with notably improved stability and efficiency. Extensive experiments on image generation show that ASBM improves fidelity with fewer sampling steps. We further showcase the effectiveness of our optimal trajectory via distillation to a one-step generator.

Jeongwoo Shin, Jinhwan Sul, Joonseok Lee +2

Seoul National University, Seoul, Korea · Georgia Institute of Technology, Atlanta, GA, USA · Sungkyunkwan University, Seoul, Korea

Diffusion Model Sampling Schrödinger Bridges Few-Step Diffusion Sampling Diffusion Models

Feb 16, 2026cs.LG

Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees

Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a continuous-time Markov chain (CTMC) formulation, with a focus on

τ

-leaping-based samplers. We establish sharp convergence guarantees for attaining

\varepsilon

accuracy in Kullback-Leibler (KL) divergence for both uniform and masking noising processes. For uniform discrete diffusion, we show that the

τ

-leaping algorithm achieves an iteration complexity of order

\tilde O(d/\varepsilon)

, with

d

the ambient dimension of the target distribution, eliminating linear dependence on the vocabulary size

S

and improving existing bounds by a factor of

d

; moreover, we establish a matching algorithmic lower bound showing that linear dependence on the ambient dimension is unavoidable in general. For masking discrete diffusion, we introduce a modified

τ

-leaping sampler whose convergence rate is governed by an intrinsic information-theoretic quantity, termed the effective total correlation, which is bounded by

d \log S

but can be sublinear or even constant for structured data. As a consequence, the sampler provably adapts to low-dimensional structure without prior knowledge or algorithmic modification, yielding sublinear convergence rates for various practical examples (such as hidden Markov models, image data, and random graphs). Our analysis requires no boundedness or smoothness assumptions on the score estimator beyond control of the score entropy loss.

Daniil Dmitriev, Zhihan Huang, Yuting Wei

Department of Statistics and Data Science, the Wharton School, University of Pennsylvania

Sample Complexity Diffusion Model Sampling Diffusion Sampling Diffusion Models

Feb 13, 2026cs.LG

Formalizing the Sampling Design Space of Diffusion-Based Generative Models via Adaptive Solvers and Wasserstein-Bounded Timesteps

Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by high sampling costs. While prior work focuses on training objectives or individual solvers, the broader sampling design problem, specifically solver selection and scheduling, remains largely governed by static heuristics. We propose SDM, a principled, training-free sampling framework that adapts both the numerical solver and the timestep schedule to the intrinsic properties of the diffusion trajectory. By analyzing the PF-ODE dynamics, we show that velocity variation is small in high-noise stages and increases near the data manifold, identifying intervals where solver order is most consequential. In parallel, we introduce an offline-calibrated adaptive scheduling method that explicitly controls the local Wasserstein discretization error and projects the calibrated trajectory to a prescribed NFE budget. We further extend the formulation to a mixed-transition Wasserstein error bound, providing a unified error-propagation view of adaptive scheduling and solver selection within the overall SDM framework. Across standard benchmarks, with extensions to modern ODE samplers, high-resolution synthesis, and text-to-image generation, SDM achieves improved sample quality compared to baseline methods, attaining an FID of 1.93 on CIFAR-10, 2.41 on FFHQ, and 1.98 on AFHQv2, with a reduced number of function evaluations compared to existing samplers. Our code is available at https://github.com/aiimaginglab/sdm.

Sangwoo Jo, Sungjoon Choi

Department of Artificial Intelligence, Korea University, Seoul, South Korea.

Diffusion Model Sampling Diffusion Sampling Adaptive Sampling Diffusion Timestep Scheduling Diffusion Model Acceleration

Feb 2, 2026cs.LG

A Random Matrix Theory Perspective on the Consistency of Diffusion Models

Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across splits already predict much of the generated images. To formalize this, we develop a random matrix theory (RMT) framework that quantifies how finite datasets shape the expectation and variance of the learned denoiser and sampling map in the linear setting. For expectations, sampling variability acts as a renormalization of the noise level through a self-consistent relation

σ^2 \mapsto κ(σ^2)

, explaining why limited data overshrink low-variance directions and pull samples toward the dataset mean. For fluctuations, our variance formulas reveal three key factors behind cross-split disagreement: \textit{anisotropy} across eigenmodes, \textit{inhomogeneity} across inputs, and overall scaling with dataset size. Extending deterministic-equivalence tools to fractional matrix powers further allows us to analyze entire sampling trajectories. The theory sharply predicts the behavior of linear diffusion models, and we validate its predictions on UNet and DiT architectures in their non-memorization regime, identifying where and how samples deviates across training data split. This provides a principled baseline for reproducibility in diffusion training, linking spectral properties of data to the stability of generative outputs.

Binxu Wang, Jacob Zavatone-Veth, Cengiz Pehlevan

Kempner Institute, Harvard University, Boston, MA, USA · Center for Brain Science, Harvard University, Cambridge, MA, USA · Society of Fellows, Harvard University, Cambridge, MA, USA +1

Diffusion Model Sampling ML Reproducibility Diffusion Models

Dec 23, 2025cs.LG

Control Variate Score Matching for Diffusion Models

Sampling from unnormalized probability densities is a pervasive challenge across the computational and physical sciences. Diffusion models provide a powerful generative framework for this task, but their success relies on accurately estimating the score of the perturbed target distribution. Current approaches face a dichotomy between two standard estimation methods: the Denoising Score Identity (DSI) requires data samples and exhibits high variance at low noise levels, whereas the Target Score Identity (TSI) relies on the energy function and suffers from diverging variance at high noise levels. In this work, we reconcile both approaches by introducing the Control Variate Score Identity (CVSI), an unbiased estimator with an analytically optimal, state- and time-dependent control coefficient that theoretically minimizes variance over the entire diffusion process. CVSI serves as a robust plug-in estimator that significantly enhances performance and efficiency in data-free sampler learning and training-free diffusion sampling. These gains scale to complex, high-dimensional energy-based models.

Khaled Kahouli, Romuald Elie, Klaus-Robert Müller +3

1Google DeepMind · 2BIFOLD – Berlin Institute for the Foundations of Learning and Data · 3Machine Learning Group, Technische Universität Berlin +2

Score Matching Diffusion Model Sampling Score-Based Generative Modeling Variance Reduction

Oct 6, 2025cs.LG

Demystifying MaskGIT Sampler and Beyond: Adaptive Order Selection in Masked Diffusion

Masked diffusion models have shown promising performance in generating high-quality samples in a wide range of domains, but accelerating their sampling process remains relatively underexplored. To investigate efficient samplers for masked diffusion, this paper theoretically analyzes the MaskGIT sampler for image modeling, revealing its implicit temperature sampling mechanism. Through this analysis, we show that MaskGIT is asymptotically equivalent to a choose-then-sample (CTS) formulation, instantiated as the "moment sampler," which explicitly separates index selection from token sampling. This CTS reformulation is essential: it yields unbiased token sampling and exposes an algorithmic design space for index selection, both of which are inaccessible in MaskGIT's original formulation. Regarding token sampling, we reveal that MaskGIT implicitly adopts a low-temperature sampler, which explains why MaskGIT often degrades with more sampling steps. The CTS reformulation of MaskGIT allows us to fix the temperature sampling to ensure unbiasedness. We also improve the index selection in CTS through two key innovations: a partial caching technique for transformers that approximates longer sampling trajectories without proportional computational cost, and a hybrid approach formalizing the exploration-exploitation trade-off in adaptive unmasking. Experiments in image and text domains demonstrate our theory as well as the efficiency of our proposed methods, advancing both theoretical understanding and practical implementation of masked diffusion samplers.

Satoshi Hayakawa, Yuhta Takida, Masaaki Imaizumi +2

Sony Group Corporation · Sony AI · The University of Tokyo

Diffusion Model Sampling Diffusion Sampling Diffusion Language Models

Oct 2, 2025eess.IV

MACS: Measurement-Aware Consistency Sampling for Inverse Problems

Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency Models (CMs) address this limitation by enabling high-quality generation in only one or a few steps, their direct application to inverse problems has remained largely unexplored. This paper introduces a modified consistency sampling framework specifically designed for inverse problems. The proposed approach regulates the sampler's stochasticity through a measurement-consistency mechanism that leverages the degradation operator, thereby enforcing fidelity to the observed data while preserving the computational efficiency of consistency-based generation. Comprehensive experiments on the Fashion-MNIST and LSUN Bedroom datasets demonstrate consistent improvements across both perceptual and pixel-level metrics, including the Fréchet Inception Distance (FID), Kernel Inception Distance (KID), peak signal-to-noise ratio (PSNR), and structural similarity index measure (SSIM), compared with baseline consistency and diffusion-based sampling methods. The proposed method achieves competitive or superior reconstruction quality with only a small number of sampling steps.

Amirreza Tanevardi, Pooria Abbas Rad Moghadam, Seyed Mohammad Eshtehardian +2

Department of Electrical Engineering Sharif University of Technology Tehran, Iran · Electronics Research Institute Sharif University of Technology Tehran, Iran

Diffusion Model Sampling Inverse Problems Consistency Models Image Inverse Problems

Date pendingcs.LG

Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models

Diffusion probabilistic models generate samples by learning to reverse a noise-injection process that transforms data into noise. A key development is the reformulation of the reverse sampling process as a deterministic probability flow ordinary differential equation (ODE), which allows for efficient sampling using high-order numerical solvers. Unlike traditional time integrator analysis, the accuracy of this sampling procedure depends not only on numerical integration errors but also on the approximation quality and regularity of the learned score function, as well as their interaction. In this work, we present a rigorous convergence analysis of deterministic samplers derived from probability flow ODEs for general forward processes with arbitrary variance schedules. Specifically, we develop and analyze

p

-th order (exponential) Runge-Kutta schemes, under the practical assumption that the first and second derivatives of the learned score function are bounded. We prove that the total variation distance between the generated and target distributions can be bounded as \begin{align*} O\bigl(d^{\frac{7}{4}}\varepsilon_{\text{score}}^{\frac{1}{2}} +d(dH_{\max})^p\bigr), \end{align*} where

\varepsilon^2_{\text{score}}

denotes the

L^2

error in the score function approximation,

d

is the data dimension, and

H_{\max}

represents the maximum solver step size. Numerical experiments on benchmark datasets further confirm that the derivatives of the learned score function are bounded in practice.

Daniel Zhengyu Huang, Jiaoyang Huang, Zhengjiang Lin

Beijing International Center for Mathematical Research, Center for Machine Learning Research, Peking University, Beijing, China · Department of Statistics and Data Science, University of Pennsylvania, Philadelphia, PA, USA · Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, 02139 Cambridge MA, USA

Diffusion Model Sampling Diffusion Sampling

Date pendingcs.CV

Anomaly-Preference Image Generation

Synthesizing realistic and diverse anomalous samples from limited data is vital for robust model generalization. However, existing methods struggle to reconcile fidelity and diversity, often hampered by distribution misalignment and overfitting, respectively.To mitigate this, we introduce Anomaly Preference Optimization,a novel paradigm that reformulates anomaly generation as a preference learning problem.Central to our approach is an implicit preference alignment mechanism that leverages real anomalies as positive references, deriving optimization signals directly from denoising trajectory deviations without requiring costly human annotation. Furthermore, we propose a Time-Aware Capacity Allocation module that dynamically distributes model capacity along the diffusion timeline,prioritizing structural diversity during highnoise phases while enhancing fine-grained fidelity in low-noise stages. During inference, a hierarchical sampling strategy modulates the coherencealignment trade-off, enabling precise control over generation. Extensive experiments demonstrate that significantly outperforms existing baselines,achieving state-of-the-art performance in both realism and diversity.

Fuyun Wang, Yuanzhi Wang, Xu Guo +6

Nanjing University of Science and Technology, Nanjing, China · Beijing Normal University, Beijing, China · China Academy of Space Technology, Beijing, China +1

Diffusion Model Alignment Diffusion Model Sampling Synthetic Anomaly Generation Preference Learning