Verlet Flows: Exact-Likelihood Integrators for Flow-Based Generative Models
arxiv(2024)
摘要
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.
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