# Accelerating Markov Chain Monte Carlo sampling with diffusion models

arXiv: https://arxiv.org/abs/2309.01454 · HTML: https://mlsanity.com/paper/2309.01454/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 4 Sep 2023.

## Placed in

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

## Builds on (most cited first, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Sampling using SU(N) gauge equivariant flows](https://mlsanity.com/paper/2008.05456/) (2020)
- [Diffusion Normalizing Flow](https://mlsanity.com/paper/2110.07579/) (2021)
- [Introduction to Normalizing Flows for Lattice Field Theory](https://mlsanity.com/paper/2101.08176/) (2021)
- [Local-Global MCMC kernels: the best of both worlds](https://mlsanity.com/paper/2111.02702/) (2021)
- [Efficient Bayesian Sampling Using Normalizing Flows to Assist Markov Chain Monte Carlo Methods](https://mlsanity.com/paper/2107.08001/) (2021)
- [Computing Bayes: Bayesian Computation from 1763 to the 21st Century](https://mlsanity.com/paper/2004.06425/) (2020)

## Built on by (most cited first, 10 of 10)

- [Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flows](https://mlsanity.com/paper/2405.14392/) (2024)
- [Reinforcement Learning for Adaptive MCMC](https://mlsanity.com/paper/2405.13574/) (2024)
- [Discrete generative diffusion models without stochastic differential equations: a tensor network approach](https://mlsanity.com/paper/2407.11133/) (2024)
- [Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models](https://mlsanity.com/paper/2505.22598/) (2025)
- [Demonstrating Real Advantage of Machine-Learning-Enhanced Monte Carlo for Combinatorial Optimization](https://mlsanity.com/paper/2510.19544/) (2025)
- [Harnessing the Power of Reinforcement Learning for Adaptive MCMC](https://mlsanity.com/paper/2507.00671/) (2025)
- [Sampling Data with Chains of Forward-Backward Diffusion Steps](https://mlsanity.com/paper/2605.27006/) (2026)
- [Accelerating Multilevel Markov Chain Monte Carlo Using Machine Learning Models](https://mlsanity.com/paper/2405.11179/) (2024)
- [A comparison of Bayesian sampling algorithms for high-dimensional particle physics and cosmology applications](https://mlsanity.com/paper/2409.18464/) (2024)
- [Discrete Diffusion Models via Evolving Variational Autoregressive Networks](https://mlsanity.com/paper/2609.27306/) (2026)

## Abstract (arXiv)

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global analysis of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalizing flows. A code implementation can be found at https://github.com/NickHunt-Smith/MCMC-diffusion.