Bridging Stochastic Flow Maps and Boltzmann Generators with Normalizing Flows

2026-09-25

AI Summary

This study addresses the low efficiency and severe computational redundancy in generating independent equilibrium samples for large-scale molecular systems by proposing the NF²M framework. This method integrates stochastic flow maps with normalizing flows, introducing an innovative reweighting correction mechanism at each denoising step. By replacing conventional terminal corrections with progressive exact likelihood adjustments, it effectively eliminates wasteful trajectory computations. Experiments on peptide systems demonstrate that NF²M substantially improves both sampling efficiency and sample quality, enhancing statistical reliability while significantly reducing computational costs. Overall, this work establishes an efficient new paradigm for molecular simulations based on Boltzmann generators and importance sampling.

Abstract

Generating independent, equilibrium samples of molecular systems at scale remains a central obstacle in computational statistical mechanics. Boltzmann Generators address this by pairing a generative model with importance sampling to obtain consistent samples from the target distribution. We introduce Normalizing Flow Flow Maps (NF$^2$M), which combines the strengths of recent stochastic flow maps with the tractability of classic normalizing flows to build a Boltzmann Generator. Unlike most methods, which correct the generative model only at the end, NF$^2$M reweighs each denoising transition as generation proceeds, avoiding wasted compute on trajectories that are ultimately discarded. At each denoising step, a conditional normalizing flow proposes clean configurations given the current noisy state (a simpler task than sampling directly from the target) and its exact likelihood enables correcting each proposal toward the true denoising transition of the target Boltzmann distribution. This is in contrast to most existing methods, whose likelihoods are approximate or expensive to evaluate, undermining the statistical reliability of the correction. We establish consistency of the corrected transitions and bound how approximation errors propagate through the sampling chain. We evaluate NF$^2$M on peptide systems, demonstrating improved sampling efficiency and sample quality.

Problem

• Boltzmann Generators
• Molecular Sampling
• Normalizing Flows
• Statistical Mechanics
• Equilibrium Samples

Innovation

• Normalizing Flows
• Boltzmann Generators
• Stochastic Flow Maps
• Importance Sampling
• Molecular Dynamics