Efficient and Unbiased Sampling of Boltzmann Distributions via Consistency Models
This addresses the challenge of slow and biased sampling in Boltzmann Generators for computational physics or chemistry, representing an incremental improvement by integrating existing techniques.
The paper tackles the problem of sampling from Boltzmann distributions efficiently and without bias by combining Consistency Models with importance sampling, achieving unbiased samples with only 6-25 functional evaluations while matching the effective sample size of methods requiring about 100 evaluations.
Diffusion models have shown promising potential for advancing Boltzmann Generators. However, two critical challenges persist: (1) inherent errors in samples due to model imperfections, and (2) the requirement of hundreds of functional evaluations (NFEs) to achieve high-quality samples. While existing solutions like importance sampling and distillation address these issues separately, they are often incompatible, as most distillation models lack the necessary density information for importance sampling. This paper introduces a novel sampling method that effectively combines Consistency Models (CMs) with importance sampling. We evaluate our approach on both synthetic energy functions and equivariant n-body particle systems. Our method produces unbiased samples using only 6-25 NFEs while achieving a comparable Effective Sample Size (ESS) to Denoising Diffusion Probabilistic Models (DDPMs) that require approximately 100 NFEs.