Sampling from Gibbs measures and Bayes posteriors via diffusion processes

Sampling from high-dimensional distributions is a notoriously difficult problem, especially when the distribution isn't log-concave or has multiple modes. While Markov chain Monte Carlo is a powerful approach, new tools are much needed. I will present a different class of algorithms which is closely related to the denoising diffusions method in machine learning, and to the stochastic localization technique in probability theory. I will use this approach to establish new sampling guarantees in a problem in Bayesian estimation (rank-one matrix estimation) and a class of problems in statistical physics (mean field spin glasses).

This is based on joint papers with Ahmed El Alaoui, Mark Sellke, and with Yuchen Wu.