Langevin Monte Carlo

Langevin Monte Carlo (LMC) is a Markov Chain Monte Carlo (MCMC) method used to efficiently sample from complex probability distributions, particularly those arising in Bayesian inference and generative modeling. Current research focuses on improving LMC's efficiency and applicability to high-dimensional, non-log-concave, and even nonsmooth distributions, often employing techniques like annealed LMC, midpoint methods, and kinetic Langevin dynamics, sometimes in conjunction with normalizing flows or other neural network architectures. These advancements are significant because they enable more accurate and scalable Bayesian inference and improved performance in applications such as diffusion models for image generation, protein design, and reinforcement learning.