mlsanityData to 13 Oct 2026

Generative Modeling with Denoising Auto-Encoders and Langevin Sampling

arXiv 2002.00107 ↗First posted 31 Jan 2020stat.ML cs.LG math.PRcited by 119

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Cited by 98 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

We study convergence of a generative modeling method that first estimates the score function of the distribution using Denoising Auto-Encoders (DAE) or Denoising Score Matching (DSM) and then employs Langevin diffusion for sampling. We show that both DAE and DSM provide estimates of the score of the Gaussian smoothed population density, allowing us to apply the machinery of Empirical Processes. We overcome the challenge of relying only on L2 bounds on the score estimation error and provide finite-sample bounds in the Wasserstein distance between the law of the population distribution and the law of this sampling scheme. We then apply our results to the homotopy method of arXiv:1907.05600 and provide theoretical justification for its empirical success.

Key facts. Cited by 119 papers in the map (data through 13 Oct 2026). First posted on arXiv 31 Jan 2020.

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Citing papers per year: 2021: 5; 2022: 8; 2023: 26; 2024: 37; 2025: 29; 2026: 14.

119 papers.

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  1. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 598
  2. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 441
  3. 2022Convergence of denoising diffusion models under the manifold hypothesiscited by 240
  4. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localizationcited by 230
  5. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptionscited by 216
  6. 2022Convergence of score-based generative modeling for general data distributionscited by 180
  7. 2022Convergence for score-based generative modeling with polynomial complexitycited by 177
  8. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Datacited by 172
  9. 2023Diffusion Models are Minimax Optimal Distribution Estimatorscited by 160
  10. 2023The probability flow ODE is provably fastcited by 146
  11. 2021Deep Generative Learning via Schr"odinger Bridgecited by 104
  12. 2023Error Bounds for Flow Matching Methodscited by 90
38 more
  1. 2024A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Datacited by 90
  2. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Modelscited by 84
  3. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplerscited by 74
  4. 2024Accelerating Convergence of Score-Based Diffusion Models, Provablycited by 74
  5. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 72
  6. 2022Statistical Efficiency of Score Matching: The View from Isoperimetrycited by 64
  7. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Modelscited by 64
  8. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptionscited by 61
  9. 2024Gradient Guidance for Diffusion Models: An Optimization Perspectivecited by 61
  10. 2024Optimal score estimation via empirical Bayes smoothingcited by 60
  11. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theorycited by 60
  12. 2023Learning Mixtures of Gaussians Using the DDPM Objectivecited by 57
  13. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Modelscited by 57
  14. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distancescited by 56
  15. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Modelscited by 55
  16. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptionscited by 48
  17. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  18. 2024Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Modelscited by 46
  19. 2024Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptionscited by 45
  20. 2024Critical windows: non-asymptotic theory for feature emergence in diffusion modelscited by 45
  21. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  22. 2022Normalizing flow neural networks by JKO schemecited by 39
  23. 2023Analysis of learning a flow-based generative model from limited sample complexitycited by 38
  24. 2024A Good Score Does not Lead to A Good Generative Modelcited by 36
  25. 2024Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Modelscited by 35
  26. 2023Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behaviorcited by 33
  27. 2024Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallelcited by 29
  28. 2024From optimal score matching to optimal samplingcited by 27
  29. 2024Provable Acceleration for Diffusion Models under Minimal Assumptionscited by 27
  30. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distancecited by 27
  31. 2024Towards a mathematical theory for consistency training in diffusion modelscited by 26
  32. 2024An analysis of the noise schedule for score-based generative modelscited by 25
  33. 2024Evaluating the design space of diffusion-based generative modelscited by 25
  34. 2025Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Modelscited by 25
  35. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimatescited by 24
  36. 2024Diffusion Model for Data-Driven Black-Box Optimizationcited by 24
  37. 2025How Compositional Generalization and Creativity Improve as Diffusion Models are Trainedcited by 24
  38. 2023Improved Convergence of Score-Based Diffusion Models via Prediction-Correctioncited by 23

50 most cited of 119 All 119 (JSON)