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.

翻译：从玻尔兹曼分布中生成独立同分布样本的高效采样器开发，是科学研究（例如分子动力学）中的一个关键挑战。在本工作中，我们旨在给定能量函数而非玻尔兹曼分布采样数据的情况下，学习神经采样器。通过学习噪声数据的能量，我们提出了一种基于扩散的采样器——噪声能量匹配，该采样器在理论上与相关工作相比具有更低的方差和更高的复杂度。此外，一种新颖的自举技术被应用于NEM，以在偏差和方差之间取得平衡。我们在一个二维40高斯混合模型和一个4粒子双阱势系统上评估了NEM和BNEM。实验结果表明，BNEM能够实现最先进的性能，同时具有更强的鲁棒性。