BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matching

RuiKang OuYang, Bo Qiang, José Miguel Hernández-Lobato

Keywords: neural sampler, Boltzmann distribution, diffusion model

TL;DR: We propose an energy based model to target energies of noised data which can enable independent samples generation through a denoising diffusion approach, with state-of-the-art performance.

Abstract:

Generating independent samples from a Boltzmann distribution is a highly relevant problem in scientific research, e.g. in molecular dynamics, where one has initial access to the underlying energy function but not to samples from the Boltzmann distribution. We address this problem by learning the energies of the convolution of the Boltzmann distribution with Gaussian noise. These energies are then used to generate independent samples through a denoising diffusion approach. The resulting method, Noised Energy Matching (NEM), has lower variance and only slightly higher cost than previous related works. We also improve NEM through a novel bootstrapping technique called Bootstrap NEM (BNEM) that further reduces variance while only slightly increasing bias. Experiments on a collection of problems demonstrate that NEM can outperform previous methods while being more robust and that BNEM further improves on NEM.

Primary Area: generative models

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Submission Number: 6287