Verlet Flows: Exact-Likelihood Integrators for Flow-Based Generative Models
This work addresses the need for exact-likelihood generative models in importance sampling for Boltzmann distributions, representing an incremental improvement over existing flow-based methods.
The authors tackled the problem of approximating model likelihoods in continuous normalizing flows (CNFs) for importance sampling of Boltzmann distributions by introducing Verlet flows, a class of CNFs on an augmented state-space inspired by symplectic integrators, which provide exact-likelihood generative models. They demonstrated that Verlet flows perform comparably to full autograd trace computations while being significantly faster on toy densities.
Approximations in computing model likelihoods with continuous normalizing flows (CNFs) hinder the use of these models for importance sampling of Boltzmann distributions, where exact likelihoods are required. In this work, we present Verlet flows, a class of CNFs on an augmented state-space inspired by symplectic integrators from Hamiltonian dynamics. When used with carefully constructed Taylor-Verlet integrators, Verlet flows provide exact-likelihood generative models which generalize coupled flow architectures from a non-continuous setting while imposing minimal expressivity constraints. On experiments over toy densities, we demonstrate that the variance of the commonly used Hutchinson trace estimator is unsuitable for importance sampling, whereas Verlet flows perform comparably to full autograd trace computations while being significantly faster.