Verlet Flows: Exact-Likelihood Integrators for Flow-Based Generative Models

• URL: http://arxiv.org/abs/2405.02805v1
• Date: Sun, 5 May 2024 03:47:56 GMT
• Title: Verlet Flows: Exact-Likelihood Integrators for Flow-Based Generative Models
• Authors: Ezra Erives, Bowen Jing, Tommi Jaakkola,
• Abstract summary: We present Verlet flows, a class of CNFs on an augmented state-space inspired by symplectic from Hamiltonian dynamics. 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.
• Score: 4.9425328004453375
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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