BoltzNCE: Learning Likelihoods for Boltzmann Generation with Stochastic Interpolants and Noise Contrastive Estimation

Abstract: Efficient sampling from the Boltzmann distribution defined by an energy function is a key challenge in modeling physical systems such as molecules. Boltzmann Generators tackle this by leveraging Continuous Normalizing Flows that transform a simple prior into a distribution that can be reweighted to match the Boltzmann distribution using sample likelihoods. However, obtaining likelihoods requires computing costly Jacobians during integration, making it impractical for large molecular systems. To overcome this, we propose learning the likelihood of the generated distribution via an energy-based model trained with noise contrastive estimation and score matching. By using stochastic interpolants to anneal between the prior and generated distributions, we combine both the objective functions to efficiently learn the density function. On the alanine dipeptide system, we demonstrate that our method yields free energy profiles and energy distributions comparable to those obtained with exact likelihoods. Additionally, we show that free energy differences between metastable states can be estimated accurately with orders-of-magnitude speedup.