Bridging Stochastic Flow Maps and Boltzmann Generators with Normalizing Flows
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 (NF2M), 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, NF2M 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 NF2M on peptide systems, demonstrating improved sampling efficiency and sample quality.
Related
- Mode Coverage in Normalizing Flow Boltzmann Generators via Log-Ratio Variation
- POD-CNF: reduced order modeling of parametrized stochastic PDEs via normalizing flows and proper orthogonal decomposition
- Recovering Weak Signals with Normalizing Flows
- Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme
- Likelihood-free inference with nuisance parameters through normalizing flows
BibTeX
@misc{grenioux2026bridging,
title = {{Bridging Stochastic Flow Maps and Boltzmann Generators with Normalizing Flows}},
author = {Louis Grenioux and RuiKang OuYang and Luhuan Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31978},
eprint = {2609.31978},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31978},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bridging Stochastic Flow Maps and Boltzmann Generators with Normalizing Flows
AU - Louis Grenioux
AU - RuiKang OuYang
AU - Luhuan Wu
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31978
UR - https://arxiv.org/abs/2609.31978
AB - 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^2M), 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^2M 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^2M on peptide systems, demonstrating improved sampling efficiency and sample quality.
ER -