mlsanityData to 7 Oct 2026

Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Acceleration

arXiv 2502.04849 ↗First posted 7 Feb 2025stat.ML cs.LG math.PRcited by 17

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models. Specifically, we investigate the impact of various discretization schemes, including Euler discretization, exponential integrators, and midpoint randomization methods. Our analysis provides a quantitative comparison of these discrete approximations, emphasizing their influence on convergence behavior. Furthermore, we explore scenarios where Hessian information is available and propose an accelerated sampler based on the local linearization method. We demonstrate that this Hessian-based approach achieves faster convergence rates of order widetildeOleft(frac1varepsilonright) significantly improving upon the standard rate widetildeOleft(frac1varepsilon2right) of vanilla diffusion models, where varepsilon denotes the target accuracy.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 30 of its 48 references that are in the map. First posted on arXiv 7 Feb 2025.

Builds on

30 of 48 references.

Closest ancestors · 24

Same direction, newest first

  1. 2025Low-dimensional adaptation of diffusion models: Convergence in total variation22 Jan
  2. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance4 Jan
  3. 2024Provable Acceleration for Diffusion Models under Minimal Assumptions30 Oct
  4. 2024Instance-dependent Convergence Theory for Diffusion Models17 Oct
  5. 2024Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Models7 Oct
  6. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models5 Aug
  7. 2024Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel3 Jun
  8. 2024The Poisson Midpoint Method for Langevin Dynamics: Provably Efficient Discretization for Diffusion Models27 May
  9. 2024Score-based generative models are provably robust: an uncertainty quantification perspective24 May
  10. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Models15 Apr
  11. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization11 Apr
  12. 2024Accelerating Convergence of Score-Based Diffusion Models, Provably6 Mar
12 more
  1. 2024Broadening Target Distributions for Accelerated Diffusion Models via a Novel Analysis Approach21 Feb
  2. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial12 Feb
  3. 2024An analysis of the noise schedule for score-based generative models7 Feb
  4. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances31 Jan
  5. 2024Contractive Diffusion Probabilistic Models23 Jan
  6. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates22 Nov
  7. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models18 Nov
  8. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  9. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  10. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  11. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  12. 2020Denoising Diffusion Implicit Models6 Oct

Other references · 6

  1. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  2. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  3. 2022Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Modelscited by 97
  4. 2023Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisitedcited by 10
  5. 2024Parallelized Midpoint Randomization for Langevin Monte Carlocited by 9
  6. 2024Randomized Midpoint Method for Log-Concave Sampling under Constraintscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 7; 2026: 10.

17 papers.

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  1. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distancecited by 20
  2. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradientscited by 15
  3. 2025Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Modelscited by 9
  4. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Boundscited by 8
  5. 2025Sublinear iterations can suffice even for DDPMscited by 7
  6. 2026Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalitiescited by 6
  7. 2026Diffusion Models with Heavy-Tailed Targets: Score Estimation and Sampling Guaranteescited by 4
  8. 2025Dimension-free error estimate for diffusion model and optimal schedulingcited by 3
  9. 2026On Forgetting and Stability of Score-based Generative modelscited by 3
  10. 2026Wasserstein bounds for denoising diffusion probabilistic models via the F"ollmer processcited by 2
  11. 2026Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplerscited by 1
  12. 2026On the Limits of Latent Reuse in Diffusion Modelscited by 1
5 more
  1. 2026Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choicescited by 1
  2. 2025Are First-Order Diffusion Samplers Really Slower? A Fast Forward-Value Approachcited by 0
  3. 2026Kinetic Langevin Splitting Schemes for Constrained Samplingcited by 0
  4. 2026Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspectivecited by 0
  5. 2026Recursively Trained Diffusion Models: Limiting Collapse Distribution and Spectral Characterizationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data
  2. 2026From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models
  3. 2022Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance
  4. 2026Wasserstein Convergence of ODE-Based Samplers in Decentralized Diffusion Model via Velocity Field Decomposition
  5. 2024Wasserstein proximal operators describe score-based generative models and resolve memorization
  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. 2025Non-asymptotic error bounds for probability flow ODEs under weak log-concavity