UCPH Statistics Seminar: Han Chen

Title: Sampling with Metropolis-adjusted Diffusion Paths

Speaker: Han Chen from Duke University

Abstract: Sampling from complex distributions with isolated regions of probability mass remains a persistent challenge for classical local Markov chain Monte Carlo (MCMC) methods. We introduce the Metropolis-adjusted diffusion path (MAD-Path) sampler, a novel MCMC algorithm that leverages diffusion models to generate structured, nonlocal proposals. By coupling a forward diffusion process with its time-reversed counterpart, guided by an estimated score function, MAD-Path creates global moves that can traverse low-probability barriers. Through a rigorous analysis in the high-dimensional scaling limit, we derive acceptance-rate expansions that quantify the intertwined effects of discretization step size, diffusion time horizon, and score approximation error, thereby identifying optimal tuning trade-offs. Empirically, we evaluate our method on challenging multimodal distributions, demonstrating its practical viability and robustness even under moderate score misspecification. Our work provides a principled framework for integrating modern generative diffusion models into rigorous Bayesian computation.