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

arXiv: https://arxiv.org/abs/2502.04849 · HTML: https://mlsanity.com/paper/2502.04849/

## Key facts

- Cited by 17 papers in the map (data through 14 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.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2205.15019/) (2022)
- [Accelerating Convergence of Score-Based Diffusion Models, Provably](https://mlsanity.com/paper/2403.03852/) (2024)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models](https://mlsanity.com/paper/2408.02320/) (2024)
- [Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial](https://mlsanity.com/paper/2402.07487/) (2024)
- [Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models](https://mlsanity.com/paper/2311.11003/) (2023)
- [Convergence Analysis of Probability Flow ODE for Score-based Generative Models](https://mlsanity.com/paper/2404.09730/) (2024)
- [Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances](https://mlsanity.com/paper/2401.17958/) (2024)
- [Low-dimensional adaptation of diffusion models: Convergence in total variation](https://mlsanity.com/paper/2501.12982/) (2025)
- [Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Models](https://mlsanity.com/paper/2410.04760/) (2024)
- [Contractive Diffusion Probabilistic Models](https://mlsanity.com/paper/2401.13115/) (2024)
- [Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel](https://mlsanity.com/paper/2406.00924/) (2024)
- [Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance](https://mlsanity.com/paper/2501.02298/) (2025)
- [An analysis of the noise schedule for score-based generative models](https://mlsanity.com/paper/2402.04650/) (2024)
- [Provable Acceleration for Diffusion Models under Minimal Assumptions](https://mlsanity.com/paper/2410.23285/) (2024)
- [On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates](https://mlsanity.com/paper/2311.13584/) (2023)
- [Instance-dependent Convergence Theory for Diffusion Models](https://mlsanity.com/paper/2410.13738/) (2024)
- [Broadening Target Distributions for Accelerated Diffusion Models via a Novel Analysis Approach](https://mlsanity.com/paper/2402.13901/) (2024)
- [Score-based generative models are provably robust: an uncertainty quantification perspective](https://mlsanity.com/paper/2405.15754/) (2024)
- [Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisited](https://mlsanity.com/paper/2306.08494/) (2023)
- [Parallelized Midpoint Randomization for Langevin Monte Carlo](https://mlsanity.com/paper/2402.14434/) (2024)
- [The Poisson Midpoint Method for Langevin Dynamics: Provably Efficient Discretization for Diffusion Models](https://mlsanity.com/paper/2405.17068/) (2024)
- [Randomized Midpoint Method for Log-Concave Sampling under Constraints](https://mlsanity.com/paper/2405.15379/) (2024)

## Built on by (most cited first, 17 of 17)

- [Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance](https://mlsanity.com/paper/2508.03210/) (2025)
- [Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradients](https://mlsanity.com/paper/2505.03432/) (2025)
- [Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds](https://mlsanity.com/paper/2506.09681/) (2025)
- [Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models](https://mlsanity.com/paper/2506.13061/) (2025)
- [Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalities](https://mlsanity.com/paper/2604.06065/) (2026)
- [Sublinear iterations can suffice even for DDPMs](https://mlsanity.com/paper/2511.04844/) (2025)
- [Diffusion Models with Heavy-Tailed Targets: Score Estimation and Sampling Guarantees](https://mlsanity.com/paper/2601.06715/) (2026)
- [On Forgetting and Stability of Score-based Generative models](https://mlsanity.com/paper/2601.21868/) (2026)
- [Dimension-free error estimate for diffusion model and optimal scheduling](https://mlsanity.com/paper/2512.01820/) (2025)
- [Wasserstein bounds for denoising diffusion probabilistic models via the F"ollmer process](https://mlsanity.com/paper/2605.18069/) (2026)
- [Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplers](https://mlsanity.com/paper/2603.19670/) (2026)
- [On the Limits of Latent Reuse in Diffusion Models](https://mlsanity.com/paper/2605.13448/) (2026)
- [Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices](https://mlsanity.com/paper/2606.23627/) (2026)
- [Are First-Order Diffusion Samplers Really Slower? A Fast Forward-Value Approach](https://mlsanity.com/paper/2512.24927/) (2025)
- [Kinetic Langevin Splitting Schemes for Constrained Sampling](https://mlsanity.com/paper/2603.23397/) (2026)
- [Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspective](https://mlsanity.com/paper/2605.06172/) (2026)
- [Recursively Trained Diffusion Models: Limiting Collapse Distribution and Spectral Characterization](https://mlsanity.com/paper/2606.13796/) (2026)

## 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.