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Hauptverfasser: Cao, Wenhan, Yan, Keyu, Zhao, Lin
Format: Preprint
Veröffentlicht: 2026
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Online-Zugang:https://arxiv.org/abs/2603.17579
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author Cao, Wenhan
Yan, Keyu
Zhao, Lin
author_facet Cao, Wenhan
Yan, Keyu
Zhao, Lin
contents We present a drifting-based framework for amortized sampling of Boltzmann distributions defined by energy functions. The method trains a one-step neural generator by projecting samples along a Gaussian-smoothed score field from the current model distribution toward the target Boltzmann distribution. For targets specified only up to an unknown normalization constant, we derive a practical target-side drift from a smoothed energy and use two estimators: a local importance-sampling mean-shift estimator and a second-order curvature-corrected approximation. Combined with a mini-batch Gaussian mean-shift estimate of the sampler-side smoothed score, this yields a simple stop-gradient objective for stable one-step training. On a four-mode Gaussian-mixture Boltzmann target, our sampler achieves mean error $0.0754$, covariance error $0.0425$, and RBF MMD $0.0020$. Additional double-well and banana targets show that the same formulation also handles nonconvex and curved low-energy geometries. Overall, the results support drifting as an effective way to amortize iterative sampling from Boltzmann distributions into a single forward pass at test time.
format Preprint
id arxiv_https___arxiv_org_abs_2603_17579
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle One-Step Sampler for Boltzmann Distributions via Drifting
Cao, Wenhan
Yan, Keyu
Zhao, Lin
Machine Learning
We present a drifting-based framework for amortized sampling of Boltzmann distributions defined by energy functions. The method trains a one-step neural generator by projecting samples along a Gaussian-smoothed score field from the current model distribution toward the target Boltzmann distribution. For targets specified only up to an unknown normalization constant, we derive a practical target-side drift from a smoothed energy and use two estimators: a local importance-sampling mean-shift estimator and a second-order curvature-corrected approximation. Combined with a mini-batch Gaussian mean-shift estimate of the sampler-side smoothed score, this yields a simple stop-gradient objective for stable one-step training. On a four-mode Gaussian-mixture Boltzmann target, our sampler achieves mean error $0.0754$, covariance error $0.0425$, and RBF MMD $0.0020$. Additional double-well and banana targets show that the same formulation also handles nonconvex and curved low-energy geometries. Overall, the results support drifting as an effective way to amortize iterative sampling from Boltzmann distributions into a single forward pass at test time.
title One-Step Sampler for Boltzmann Distributions via Drifting
topic Machine Learning
url https://arxiv.org/abs/2603.17579