Boltzmann Generators for Condensed Matter via Riemannian Flow Matching

arXiv stat.ML / 3/31/2026

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Key Points

The paper proposes a framework that extends flow matching to sample equilibrium distributions in condensed-matter systems by enforcing the systems’ periodicity via Riemannian flow matching in continuous normalizing flows.
It reduces the high computational cost of exact density estimation by using Hutchinson’s trace estimator, combined with a bias-correction step based on cumulant expansion to support thermodynamic reweighting.
The method is tested on monatomic ice, where the authors report training on significantly larger system sizes than previously feasible.
Results indicate that the approach yields highly accurate free energy estimates without relying on conventional multistage estimators, aiming to streamline equilibrium free-energy calculations.

Abstract

Sampling equilibrium distributions is fundamental to statistical mechanics. While flow matching has emerged as scalable state-of-the-art paradigm for generative modeling, its potential for equilibrium sampling in condensed-phase systems remains largely unexplored. We address this by incorporating the periodicity inherent to these systems into continuous normalizing flows using Riemannian flow matching. The high computational cost of exact density estimation intrinsic to continuous normalizing flows is mitigated by using Hutchinson's trace estimator, utilizing a crucial bias-correction step based on cumulant expansion to render the stochastic estimates suitable for rigorous thermodynamic reweighting. Our approach is validated on monatomic ice, demonstrating the ability to train on systems of unprecedented size and obtain highly accurate free energy estimates without the need for traditional multistage estimators.