Document Type


Publication Date




Publication Title

Computer Physics Communications




109059 (1-9)


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


© 2023 The Authors.

This is an open access article under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.

Data Availability

Article states: "A link to the GitHub repo containing the code can be found in the abstract, or at"

Original Publication Citation

Hunt-Smith, N. T., Melnitchouk, W., Ringer, F., Sato, N., Thomas, A. W., & White, M. J. (2024). Accelerating Markov chain Monte Carlo sampling with diffusion models. Computer Physics Communications, 296, 1-9, Article 109059.


0000-0002-5939-3510 (Ringer)