Leveraging generative models to assist Monte Carlo sampling
Marylou Gabrié
stat.ML, cond-mat.dis-nn, cond-mat.stat-mech, cs.LG, physics.comp-ph
Submitted: 2026-08-07
Updated: 2026-08-11
License: http://creativecommons.org/licenses/by/4.0/
The gist: Sampling high-dimensional probability distributions is a central task in scientific computing, with applications ranging from Bayesian inference to statistical physics and molecular simulation.
Terminology
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.
Sources
- Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
- Variational Inference: A Review for Statisticians
- Demonstrating Real Advantage of Machine-Learning-Enhanced Monte Carlo for Combinatorial Optimization
- Markov Chain Monte Carlo with Diffusion Paths
- Efficient Modelling of Trivializing Maps for Lattice $\phi^4$ Theory Using Normalizing Flows: A First Look at Scalability
- Transferable Generative Models Bridge Femtosecond to Nanosecond Time-Step Molecular Dynamics
- Annealing in variational inference mitigates mode collapse: A theoretical study on Gaussian mixtures
- Boltzmann generators for amorphous particle systems
- Adaptive Monte Carlo augmented with normalizing flows
- e3nn: Euclidean Neural Networks
- Flow-based sampling for multimodal and extended-mode distributions in lattice field theory
- Denoising Diffusion Probabilistic Models
- NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport
- Accelerating astronomical and cosmological inference with Preconditioned Monte Carlo
- Natural Variational Annealing for Multimodal Optimization
- Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
- Sampling, Diffusions, and Stochastic Localization
- Posterior Sampling in High Dimension via Diffusion Processes
- Asymptotically unbiased estimation of physical observables with neural samplers
- Assessing generative modeling approaches for free energy estimates in condensed matter
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