# Leveraging generative models to assist Monte Carlo sampling

arXiv: https://arxiv.org/abs/2608.07648 · HTML: https://mlsanity.com/paper/2608.07648/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 189 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Accelerated Parallel Tempering via Neural Transports](https://mlsanity.com/paper/2502.10328/) (2025)
- [Efficient Bayesian Sampling Using Normalizing Flows to Assist Markov Chain Monte Carlo Methods](https://mlsanity.com/paper/2107.08001/) (2021)
- [Transferable Generative Models Bridge Femtosecond to Nanosecond Time-Step Molecular Dynamics](https://mlsanity.com/paper/2510.07589/) (2025)
- [Mitigating mode collapse in normalizing flows by annealing with an adaptive schedule: Application to parameter estimation](https://mlsanity.com/paper/2505.03652/) (2025)
- [Boltzmann generators for amorphous particle systems](https://mlsanity.com/paper/2512.16607/) (2025)
- [Demonstrating Real Advantage of Machine-Learning-Enhanced Monte Carlo for Combinatorial Optimization](https://mlsanity.com/paper/2510.19544/) (2025)
- [Markov Chain Monte Carlo with Diffusion Paths](https://mlsanity.com/paper/2607.11631/) (2026)
- [Annealing in variational inference mitigates mode collapse: A theoretical study on Gaussian mixtures](https://mlsanity.com/paper/2602.12923/) (2026)
- [Natural Variational Annealing for Multimodal Optimization](https://mlsanity.com/paper/2501.04667/) (2025)
- [Assessing generative modeling approaches for free energy estimates in condensed matter](https://mlsanity.com/paper/2512.23930/) (2025)

## Built on by (most cited first, 1 of 1)

- [Amortised adaptive importance sampling](https://mlsanity.com/paper/2610.16736/) (2026)

## Abstract (arXiv)

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.