# High-accuracy sampling for diffusion models and log-concave distributions

arXiv: https://arxiv.org/abs/2602.01338 · HTML: https://mlsanity.com/paper/2602.01338/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 36 of its 48 references that are in the map.
- First posted on arXiv 1 Feb 2026.

## Placed in

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

## Builds on (most cited first, 30 of 36)

- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022)
- [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023)
- [Structured Logconcave Sampling with a Restricted Gaussian Oracle](https://mlsanity.com/paper/2010.03106/) (2020)
- [Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models](https://mlsanity.com/paper/2306.09251/) (2023)
- [Accelerating Convergence of Score-Based Diffusion Models, Provably](https://mlsanity.com/paper/2403.03852/) (2024)
- [Improved analysis for a proximal algorithm for sampling](https://mlsanity.com/paper/2202.06386/) (2022)
- [A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models](https://mlsanity.com/paper/2408.02320/) (2024)
- [Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions](https://mlsanity.com/paper/2409.18804/) (2024)
- [KL Convergence Guarantees for Score diffusion models under minimal data assumptions](https://mlsanity.com/paper/2308.12240/) (2023)
- [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)
- [Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models](https://mlsanity.com/paper/2405.14861/) (2024)
- [Faster high-accuracy log-concave sampling via algorithmic warm starts](https://mlsanity.com/paper/2302.10249/) (2023)
- [Linear Convergence of Diffusion Models Under the Manifold Hypothesis](https://mlsanity.com/paper/2410.09046/) (2024)
- [Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality](https://mlsanity.com/paper/2410.18784/) (2024)
- [Low-dimensional adaptation of diffusion models: Convergence in total variation](https://mlsanity.com/paper/2501.12982/) (2025)
- [Improved dimension dependence of a proximal algorithm for sampling](https://mlsanity.com/paper/2302.10081/) (2023)
- [Provable Acceleration for Diffusion Models under Minimal Assumptions](https://mlsanity.com/paper/2410.23285/) (2024)
- [Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixtures](https://mlsanity.com/paper/2504.05300/) (2025)
- [Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference](https://mlsanity.com/paper/2405.16387/) (2024)
- [Instance-dependent Convergence Theory for Diffusion Models](https://mlsanity.com/paper/2410.13738/) (2024)
- [Faster Diffusion Models via Higher-Order Approximation](https://mlsanity.com/paper/2506.24042/) (2025)
- [Optimal Convergence Analysis of DDPM for General Distributions](https://mlsanity.com/paper/2510.27562/) (2025)
- [Online Estimation via Offline Estimation: An Information-Theoretic Framework](https://mlsanity.com/paper/2404.10122/) (2024)
- [Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models](https://mlsanity.com/paper/2506.13061/) (2025)
- [Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models](https://mlsanity.com/paper/2501.18863/) (2025)

## Built on by (most cited first, 16 of 16)

- [Blind denoising diffusion models and the blessings of dimensionality](https://mlsanity.com/paper/2602.09639/) (2026)
- [Metropolis-Adjusted Diffusion Models](https://mlsanity.com/paper/2605.09654/) (2026)
- [High-accuracy log-concave sampling with stochastic queries](https://mlsanity.com/paper/2602.14342/) (2026)
- [Query Lower Bounds for Diffusion Sampling](https://mlsanity.com/paper/2604.10857/) (2026)
- [Denoising growth complexity: Data geometry and certified schedules for diffusion sampling](https://mlsanity.com/paper/2607.26285/) (2026)
- [Accelerated High-Accuracy Sampling from a Warm Start via the Proximal Bouncy Particle Sampler](https://mlsanity.com/paper/2609.06905/) (2026)
- [Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplers](https://mlsanity.com/paper/2603.19670/) (2026)
- [A proximal gradient algorithm for composite log-concave sampling](https://mlsanity.com/paper/2605.12461/) (2026)
- [A Mathematical Introduction to Diffusion Models](https://mlsanity.com/paper/2607.01693/) (2026)
- [Windowed thinning and query complexity for the bouncy particle and Zigzag samplers](https://mlsanity.com/paper/2607.28413/) (2026)
- [Generalization Bounds for Flow-matching Generative Models for Intrinsically Low-dimensional Data](https://mlsanity.com/paper/2610.02663/) (2026)
- [Complexity of Non-Log-Concave Sampling in Fisher Information](https://mlsanity.com/paper/2605.15859/) (2026)
- [Smoothed Score Queries and the Complexity of Sampling](https://mlsanity.com/paper/2605.27769/) (2026)
- [Local Geometric Mixing via Dobrushin Contraction with Applications to Diffusion Path Monte Carlo and the Proximal Sampler](https://mlsanity.com/paper/2609.28338/) (2026)
- [Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models](https://mlsanity.com/paper/2610.13851/) (2026)
- [Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling](https://mlsanity.com/paper/2610.16248/) (2026)

## Abstract (arXiv)

We present algorithms for diffusion model sampling which obtain δ-error in polylog(1/δ) steps, given access to widetilde O(δ)-accurate score estimates in L2. This is an exponential improvement over all previous results. Specifically, under minimal data assumptions, the complexity is widetilde O(d_star polylog(1/δ)) where d_star is the intrinsic dimension of the data. Further, under a non-uniform L-Lipschitz condition, the complexity reduces to widetilde O(L polylog(1/δ)). Our approach also yields the first polylog(1/δ) complexity sampler for general log-concave distributions using only gradient evaluations.