Leveraging generative models to assist Monte Carlo sampling

2026-08-07

AI Summary

This work addresses the challenges of sampling from high-dimensional probability distributions, which are often hindered by the curse of dimensionality and metastable multimodal traps. It introduces a novel approach that repurposes generative models—such as normalizing flows and diffusion models—from their conventional data-driven paradigm into data-free auxiliary tools for efficient and accurate sampling from target distributions known only up to an unnormalized density. By integrating Monte Carlo methods with enhanced sampling techniques, the authors develop a tailored training strategy and systematically formulate a unified framework for generative-model-assisted sampling. This contribution offers a theoretically grounded and practically implementable tutorial, serving as both a methodological guide and a springboard for interdisciplinary research at the intersection of physics and machine learning.

Abstract

Sampling high-dimensional probability distributions is a central task in scientific computing, with applications ranging from Bayesian inference to statistical physics and molecular simulation. Despite decades of methodological developments, two major challenges remain: scaling to high dimensions and efficiently exploring multimodal distributions characterized by metastable states. Classical approaches such as Markov chain Monte Carlo, tempering methods, or enhanced sampling based on collective variables have achieved major successes, but they also face intrinsic limitations. This tutorial review explores a new paradigm that has recently emerged at the interface of machine learning and computational statistical physics: the use of generative models as tools for sampling. In this context, models such as normalizing flows and diffusion models are not used in their traditional data-driven setting, but rather as flexible probabilistic models that can assist the sampling of distributions known only up to a normalization constant. This manuscript reviews the early development of this rapidly evolving field and discusses several methodological directions, including exact samplers based on generative models and strategies to train such models in the absence of data. While an exhaustive survey of the literature is not attempted, we present a selection of key ideas and methods, along with a discussion of their strengths and limitations. The review is intended to be an accessible tutorial for both physics and machine learning audiences, and it aims to provide a starting point for researchers interested in exploring this exciting area of research.

Problem

• high-dimensional sampling
• multimodal distributions
• Monte Carlo sampling
• metastable states
• probability distributions

Innovation

• generative models
• Monte Carlo sampling
• normalizing flows
• diffusion models
• multimodal distributions