A Generative Sampler for distributions with possible discrete parameter based on Reversibility

TL;DR

This paper introduces a reversible, target-gradient-free generative sampling method that effectively handles complex distributions, including discrete and hybrid systems, by leveraging detailed balance and energy evaluations without requiring score functions.

Contribution

It presents a unified framework based on detailed balance and MMD minimization that works across diverse state spaces without target score functions or relaxations.

Findings

Accurately reproduces thermodynamic observables.

Captures mode-switching behavior in complex systems.

Demonstrates versatility on continuous, discrete, and hybrid benchmarks.

Abstract

Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to discrete or mixed-variable systems remains difficult due to ill-defined gradients or high variance in estimators. We propose a unified, target-gradient-free generative sampling framework applicable across diverse state spaces. Building on the fact that detailed balance implies the time-reversibility of the equilibrium stochastic process, we enforce this symmetry as a statistical constraint. Specifically, using a prescribed physical transition kernel (such as Metropolis-Hastings), we minimize the Maximum Mean Discrepancy (MMD) between the joint distributions of forward and backward Markov trajectories. Crucially, this training procedure relies solely on energy evaluations via acceptance ratios, circumventing the need for target score functions or continuous relaxations. We demonstrate the versatility of our method on three distinct benchmarks: (1) a continuous multi-modal Gaussian mixture, (2) the discrete high-dimensional Ising model, and (3) a challenging hybrid system coupling discrete indices with continuous dynamics. Experiments show that our framework accurately reproduces thermodynamic observables and captures mode-switching behavior across all regimes, offering a physically grounded and universally applicable alternative for equilibrium sampling.