BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matching
This work addresses a crucial problem in scientific fields like molecular dynamics by providing an efficient sampler, though it appears incremental as it builds on existing diffusion-based methods with a bootstrapping technique.
The paper tackles the challenge of generating IID samples from Boltzmann distributions, such as in molecular dynamics, by proposing BNEM, a diffusion-based sampler that learns from energy functions rather than data, achieving state-of-the-art performance with improved robustness.
Developing an efficient sampler capable of generating independent and identically distributed (IID) samples from a Boltzmann distribution is a crucial challenge in scientific research, e.g. molecular dynamics. In this work, we intend to learn neural samplers given energy functions instead of data sampled from the Boltzmann distribution. By learning the energies of the noised data, we propose a diffusion-based sampler, Noised Energy Matching, which theoretically has lower variance and more complexity compared to related works. Furthermore, a novel bootstrapping technique is applied to NEM to balance between bias and variance. We evaluate NEM and BNEM on a 2-dimensional 40 Gaussian Mixture Model (GMM) and a 4-particle double-well potential (DW-4). The experimental results demonstrate that BNEM can achieve state-of-the-art performance while being more robust.