mlsanityData to 14 Oct 2026

A Stochastic Analysis Perspective on Diffusion Models

arXiv 2610.14133 ↗First posted 9 Oct 2026stat.ML cs.LG math.PRcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Generative modelling involves two complementary tasks: learning a probabilistic approximation of an unknown data distribution from observations, and designing a tractable mechanism for sampling from this approximation. We present a stochastic-analysis perspective on score-based generative models, connecting ideas from classical sampling theory, score estimation, and diffusion time reversal. We first explain how score functions link Langevin sampling with score matching, and how Gaussian smoothing leads to denoising score matching and multiscale sampling methods. We then emphasize the distinction between dynamics preserving a fixed distribution and dynamics transporting a prescribed family of marginals. This motivates a path-space treatment of diffusion time reversal. Finally, we connect the ideal reverse diffusion with practical generative algorithms.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 50 of its 107 references that are in the map. First posted on arXiv 9 Oct 2026.

Builds on

50 of 107 references.

Closest ancestors · 29

Same direction, newest first

  1. 2026Non-Asymptotic Error Bounds for SMC with Biased Proposals: Application to Conditional Diffusion Sampling6 Jul
  2. 2026Non-asymptotic Convergence of Stochastic Gradient Descent in Score-based Generative Models6 Jul
  3. 2026On Forgetting and Stability of Score-based Generative models29 Jan
  4. 2025Convergence Dynamics of Over-Parameterized Score Matching for a Single Gaussian27 Nov
  5. 2025Wasserstein Convergence of Critically Damped Langevin Diffusions4 Nov
  6. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance5 Aug
  7. 2025Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models4 Jun
  8. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance4 Jan
  9. 2024From optimal score matching to optimal sampling11 Sep
  10. 2024Diffusion models for Gaussian distributions: Exact solutions and Wasserstein errors23 May
  11. 2024Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions23 Feb
  12. 2024An analysis of the noise schedule for score-based generative models7 Feb
17 more
  1. 2024Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization28 Jan
  2. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates22 Nov
  3. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models18 Nov
  4. 2023On the Generalization Properties of Diffusion Models3 Nov
  5. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptions23 Aug
  6. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  7. 2023Diffusion Models are Minimax Optimal Distribution Estimators3 Mar
  8. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
  9. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  10. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  11. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  12. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
  13. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  14. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  15. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  16. 2020Denoising Diffusion Probabilistic Models19 Jun
  17. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 21

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  3. 2022Flow Matching for Generative Modelingcited by 5,702
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  5. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  6. 2016Density estimation using Real NVPcited by 2,042
  7. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  8. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,150
  9. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  10. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 384
  11. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 227
  12. 2019Generalized Sliced Wasserstein Distancescited by 208
9 more
  1. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 197
  2. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 146
  3. 2019Max-Sliced Wasserstein Distance and its use for GANscited by 119
  4. 2020Adversarial score matching and improved sampling for image generationcited by 96
  5. 2017Convergence of Langevin MCMC in KL-divergencecited by 88
  6. 2015Sliced Wasserstein Kernels for Probability Distributionscited by 65
  7. 2019Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexitycited by 39
  8. 2025Generalization error bound for denoising score matching under relaxed manifold assumptioncited by 20
  9. 2025Approximation and Generalization Abilities of Score-based Neural Network Generative Models for Sub-Gaussian Distributionscited by 2

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  1. 2026A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models
  2. 2024Discrete vs. Continuous Trade-offs for Generative Models
  3. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models
  4. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
  5. 2023Denoising Diffusion Samplers
  6. 2025From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting
  7. 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models
  8. 2026Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs