mlsanityData to 7 Oct 2026

Convergence of score-based generative modeling for general data distributions

arXiv 2209.12381 ↗First posted 26 Sep 2022cs.LG math.PR math.STcited by 179

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Score-based generative modeling (SGM) has grown to be a hugely successful method for learning to generate samples from complex data distributions such as that of images and audio. It is based on evolving an SDE that transforms white noise into a sample from the learned distribution, using estimates of the score function, or gradient log-pdf. Previous convergence analyses for these methods have suffered either from strong assumptions on the data distribution or exponential dependencies, and hence fail to give efficient guarantees for the multimodal and non-smooth distributions that arise in practice and for which good empirical performance is observed. We consider a popular kind of SGM -- denoising diffusion models -- and give polynomial convergence guarantees for general data distributions, with no assumptions related to functional inequalities or smoothness. Assuming L2-accurate score estimates, we obtain Wasserstein distance guarantees for any distribution of bounded support or sufficiently decaying tails, as well as TV guarantees for distributions with further smoothness assumptions.

Key facts. Cited by 179 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 18 of its 25 references that are in the map. First posted on arXiv 26 Sep 2022.

Builds on

18 of 25 references.

Closest ancestors · 10

Same direction, newest first

  1. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  2. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  3. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  4. 2022Subspace Diffusion Generative Models3 May
  5. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  6. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  7. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  8. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  9. 2020Denoising Diffusion Probabilistic Models19 Jun
  10. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 8

  1. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  3. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,903
  4. 2019Plug and Play Language Models: A Simple Approach to Controlled Text Generationcited by 793
  5. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  6. 2019Your Classifier is Secretly an Energy Based Model and You Should Treat it Like Onecited by 402
  7. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 118
  8. 2020Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergencecited by 42

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 5; 2023: 39; 2024: 60; 2025: 44; 2026: 31.

179 papers.

Sort:

By area:

  1. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  2. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 707
  3. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localizationcited by 230
  4. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptionscited by 215
  5. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Datacited by 171
  6. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
  7. 2023The probability flow ODE is provably fastcited by 145
  8. 2023Denoising Diffusion Samplerscited by 144
  9. 2023Policy Representation via Diffusion Probability Model for Reinforcement Learningcited by 105
  10. 2023Error Bounds for Flow Matching Methodscited by 88
  11. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Modelscited by 84
  12. 2024Accelerating Convergence of Score-Based Diffusion Models, Provablycited by 74
38 more
  1. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplerscited by 73
  2. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 72
  3. 2024Accelerating Diffusion Sampling with Optimized Time Stepscited by 67
  4. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Modelscited by 64
  5. 2022Statistical Efficiency of Score Matching: The View from Isoperimetrycited by 63
  6. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptionscited by 61
  7. 2023The Blessing of Randomness: SDE Beats ODE in General Diffusion-based Image Editingcited by 61
  8. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorialcited by 60
  9. 2024Optimal score estimation via empirical Bayes smoothingcited by 60
  10. 2024Gradient Guidance for Diffusion Models: An Optimization Perspectivecited by 59
  11. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theorycited by 58
  12. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  13. 2023Learning Mixtures of Gaussians Using the DDPM Objectivecited by 56
  14. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distancescited by 56
  15. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Modelscited by 56
  16. 2024Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributionscited by 53
  17. 2024On the Trajectory Regularity of ODE-based Diffusion Samplingcited by 51
  18. 2023Reward-Directed Conditional Diffusion: Provable Distribution Estimation and Reward Improvementcited by 49
  19. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptionscited by 48
  20. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  21. 2023Closed-Form Diffusion Modelscited by 46
  22. 2024Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Modelscited by 46
  23. 2024Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptionscited by 45
  24. 2024What does guidance do? A fine-grained analysis in a simple settingcited by 45
  25. 2024Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformizationcited by 44
  26. 2024Trajectory Consistency Distillation: Improved Latent Consistency Distillation by Semi-Linear Consistency Function with Trajectory Mappingcited by 44
  27. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionalitycited by 44
  28. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  29. 2023Reverse Diffusion Monte Carlocited by 41
  30. 2024Critical windows: non-asymptotic theory for feature emergence in diffusion modelscited by 41
  31. 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Modelscited by 39
  32. 2024Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalizationcited by 39
  33. 2023Analysis of learning a flow-based generative model from limited sample complexitycited by 38
  34. 2024Understanding Generalizability of Diffusion Models Requires Rethinking the Hidden Gaussian Structurecited by 38
  35. 2023A Theoretical Justification for Image Inpainting using Denoising Diffusion Probabilistic Modelscited by 37
  36. 2023Conditional score-based diffusion models for Bayesian inference in infinite dimensionscited by 37
  37. 2024Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Modelscited by 35
  38. 2025Much Ado About Noising: Dispelling the Myths of Generative Robotic Controlcited by 35

50 most cited of 179 All 179 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models
  2. 2022Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance
  3. 2026Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data
  4. 2026Non-asymptotic Convergence of Stochastic Gradient Descent in Score-based Generative Models
  5. 2024Discrete vs. Continuous Trade-offs for Generative Models
  6. 2024A Good Score Does not Lead to A Good Generative Model
  7. 2024Score-based Generative Models with Adaptive Momentum
  8. 2025DDPM Score Matching and Distribution Learning