mlsanityData to 7 Oct 2026

Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance

arXiv 2508.03210 ↗First posted 5 Aug 2025cs.LG stat.MLcited by 20

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze discretization, initialization, and score estimation errors. Notably, we derive the first Wasserstein convergence bound for the Heun sampler and improve existing results for the Euler sampler of the probability flow ODE. Our analysis emphasizes the importance of spatial regularity of the learned score function and argues for controlling the score error with respect to the true reverse process, in line with denoising score matching. We also incorporate recent results on smoothed Wasserstein distances to sharpen initialization error bounds.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 39 of its 53 references that are in the map. First posted on arXiv 5 Aug 2025.

Builds on

39 of 53 references.

Closest ancestors · 36

Same direction, newest first

  1. 2025Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models16 Jun
  2. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradients6 May
  3. 2025Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Acceleration7 Feb
  4. 2025Information-Theoretic Proofs for Diffusion Sampling4 Feb
  5. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance4 Jan
  6. 2024Wasserstein Bounds for generative diffusion models with Gaussian tail targets15 Dec
  7. 2024Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions27 Sep
  8. 2024Score-based generative models are provably robust: an uncertainty quantification perspective24 May
  9. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Models15 Apr
  10. 2024Accelerating Convergence of Score-Based Diffusion Models, Provably6 Mar
  11. 2024An analysis of the noise schedule for score-based generative models7 Feb
  12. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances31 Jan
24 more
  1. 2024Contractive Diffusion Probabilistic Models23 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. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptions23 Aug
  5. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  6. 2023Error Bounds for Flow Matching Methods26 May
  7. 2023The probability flow ODE is provably fast19 May
  8. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers6 Mar
  9. 2023Diffusion Models are Minimax Optimal Distribution Estimators3 Mar
  10. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
  11. 2022Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance13 Dec
  12. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  13. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  14. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  15. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  16. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  17. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  18. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  19. 2021Diffusion Normalizing Flow14 Oct
  20. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matching5 Jun
  21. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  22. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  23. 2020Denoising Diffusion Implicit Models6 Oct
  24. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 3

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  3. 2023Chain of Log-Concave Markov Chainscited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 16.

20 papers.

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  1. 2025Non-asymptotic error bounds for probability flow ODEs under weak log-concavitycited by 7
  2. 2026Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalitiescited by 6
  3. 2025Parallel Sampling via Autospeculationcited by 5
  4. 2026Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Datacited by 4
  5. 2026On Forgetting and Stability of Score-based Generative modelscited by 3
  6. 2026Geometry-Aware Discretization Error of Diffusion Modelscited by 3
  7. 2026Polynomial Convergence of Riemannian Diffusion Modelscited by 2
  8. 2026Inference-Time Alignment for Diffusion Models via Variationally Stable Doob's Matchingcited by 2
  9. 2026Understanding diffusion models requires rethinking (again) generalizationcited by 2
  10. 2026Wasserstein bounds for denoising diffusion probabilistic models via the F"ollmer processcited by 2
  11. 2025Learning Paths for Dynamic Measure Transport: A Control Perspectivecited by 1
  12. 2026Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplerscited by 1
8 more
  1. 2026Why DDIM Hallucinates More Than DDPM: A Theoretical Analysis of Reverse Dynamicscited by 1
  2. 2025Factor-Based Conditional Diffusion Model for Contextual Portfolio Optimizationcited by 0
  3. 2026Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEscited by 0
  4. 2026Convergence of empirical subgradients for optimal transport-based objectivescited by 0
  5. 2026Tightening the Score Matching Gap for Diffusion Modelscited by 0
  6. 2026Robustness of Diffusion Models under Distribution Shiftcited by 0
  7. 2026Universal Local Error and Realized Amplification for the First-Order EDM Predictorcited by 0
  8. 2026Diffusion Removes Langevin's Conditioning Dependence: A Sharp Gaussian Analysiscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
  2. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models
  3. 2023A Note on the Convergence of Denoising Diffusion Probabilistic Models
  4. 2026Wasserstein Convergence of ODE-Based Samplers in Decentralized Diffusion Model via Velocity Field Decomposition
  5. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models
  6. 2025Minimax Optimality of the Probability Flow ODE for Diffusion Models
  7. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions
  8. 2026Formalizing the Sampling Design Space of Diffusion-Based Generative Models via Adaptive Solvers and Wasserstein-Bounded Timesteps