  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.
