mlsanityData to 14 Oct 2026

Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models

arXiv 2311.11003 ↗First posted 18 Nov 2023cs.LG math.PR stat.MLcited by 58

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Score-based generative models (SGMs) is a recent class of deep generative models with state-of-the-art performance in many applications. In this paper, we establish convergence guarantees for a general class of SGMs in 2-Wasserstein distance, assuming accurate score estimates and smooth log-concave data distribution. We specialize our result to several concrete SGMs with specific choices of forward processes modelled by stochastic differential equations, and obtain an upper bound on the iteration complexity for each model, which demonstrates the impacts of different choices of the forward processes. We also provide a lower bound when the data distribution is Gaussian. Numerically, we experiment SGMs with different forward processes, some of which are newly proposed in this paper, for unconditional image generation on CIFAR-10. We find that the experimental results are in good agreement with our theoretical predictions on the iteration complexity, and the models with our newly proposed forward processes can outperform existing models.

Key facts. Cited by 58 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 2 of its 43 references that are in the map. First posted on arXiv 18 Nov 2023.

Builds on

2 of 43 references.

References · 2

  1. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  2. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 119

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 15; 2025: 19; 2026: 23.

58 papers.

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  1. 2024Accelerating Convergence of Score-Based Diffusion Models, Provablycited by 76
  2. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorialcited by 60
  3. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distancescited by 56
  4. 2024Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalizationcited by 42
  5. 2024Contractive Diffusion Probabilistic Modelscited by 29
  6. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distancecited by 29
  7. 2024PaGoDA: Progressive Growing of a One-Step Generator from a Low-Resolution Diffusion Teachercited by 27
  8. 2024Convergence of Continuous Normalizing Flows for Learning Probability Distributionscited by 26
  9. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimatescited by 25
  10. 2024Instance-dependent Convergence Theory for Diffusion Modelscited by 21
  11. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distancecited by 21
  12. 2025Discrete Diffusion Models: Novel Analysis and New Sampler Guaranteescited by 20
38 more
  1. 2024Broadening Target Distributions for Accelerated Diffusion Models via a Novel Analysis Approachcited by 19
  2. 2025Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Accelerationcited by 17
  3. 2025Optimal Convergence Analysis of DDPM for General Distributionscited by 16
  4. 2026High-accuracy sampling for diffusion models and log-concave distributionscited by 16
  5. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradientscited by 15
  6. 2026Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approachcited by 11
  7. 2024Latent Schr"odinger Bridge Diffusion Model for Generative Learningcited by 10
  8. 2024Wasserstein Bounds for generative diffusion models with Gaussian tail targetscited by 10
  9. 2024Slight Corruption in Pre-training Data Makes Better Diffusion Modelscited by 9
  10. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Boundscited by 9
  11. 2026Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalitiescited by 8
  12. 2024Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplerscited by 7
  13. 2025Understanding Sampler Stochasticity in Training Diffusion Models for RLHFcited by 7
  14. 2025Non-asymptotic error bounds for probability flow ODEs under weak log-concavitycited by 7
  15. 2025Sublinear iterations can suffice even for DDPMscited by 7
  16. 2025Score-Based Diffusion Policy Compatible with Reinforcement Learning via Optimal Transportcited by 6
  17. 2025Distribution estimation via Flow Matching with Lipschitz guaranteescited by 6
  18. 2025Wasserstein Convergence of Critically Damped Langevin Diffusionscited by 6
  19. 2024Denoising Diffusions with Optimal Transport: Localization, Curvature, and Multi-Scale Complexitycited by 5
  20. 2026On Forgetting and Stability of Score-based Generative modelscited by 5
  21. 2025Pathway to O(√d) Complexity bound under Wasserstein metric of flow-based modelscited by 4
  22. 2024Model Free Prediction with Uncertainty Assessmentcited by 3
  23. 2025Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Financecited by 3
  24. 2025Dimension-free error estimate for diffusion model and optimal schedulingcited by 3
  25. 2026Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Trainingcited by 3
  26. 2025Understanding Generalization in Diffusion Distillation via Probability Flow Distancecited by 2
  27. 2026Query Lower Bounds for Diffusion Samplingcited by 2
  28. 2026Wasserstein bounds for denoising diffusion probabilistic models via the F"ollmer processcited by 2
  29. 2025Error analysis of a compositional score-based algorithm for simulation-based inferencecited by 1
  30. 2026Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplerscited by 1
  31. 2026Cold-Start Forecasting of New Product Life-Cycles via Conditional Diffusion Modelscited by 1
  32. 2026Non-asymptotic Convergence of Stochastic Gradient Descent in Score-based Generative Modelscited by 1
  33. 2026Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Samplingcited by 1
  34. 2025Factor-Based Conditional Diffusion Model for Contextual Portfolio Optimizationcited by 0
  35. 2026Deep Neural Networks as Iterated Function Systems and a Generalization Boundcited by 0
  36. 2026Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization taskscited by 0
  37. 2026Generating DDPM-based Samples from Tilted Distributionscited by 0
  38. 2026Finite Sample Bounds for Learning with Score Matchingcited by 0

50 most cited of 58 All 58 (JSON)

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  1. 2022Convergence of score-based generative modeling for general data distributions
  2. 2022Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance
  3. 2024An analysis of the noise schedule for score-based generative models
  4. 2022Convergence for score-based generative modeling with polynomial complexity
  5. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions
  6. 2026Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds
  7. 2024Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian probability distributions
  8. 2023Improved Convergence of Score-Based Diffusion Models via Prediction-Correction