OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport

TL;DR

OT-Flow introduces a novel continuous normalizing flow method that uses optimal transport to simplify trajectories and achieves faster training and inference while maintaining competitive density estimation performance.

Contribution

The paper proposes OT-Flow, which combines optimal transport regularization with exact trace computation to improve efficiency and accuracy of continuous normalizing flows.

Findings

OT-Flow achieves 8x faster training and 24x faster inference.

It uses one-fourth the number of weights compared to state-of-the-art CNFs.

Performs competitively on high-dimensional density estimation tasks.

Abstract

A normalizing flow is an invertible mapping between an arbitrary probability distribution and a standard normal distribution; it can be used for density estimation and statistical inference. Computing the flow follows the change of variables formula and thus requires invertibility of the mapping and an efficient way to compute the determinant of its Jacobian. To satisfy these requirements, normalizing flows typically consist of carefully chosen components. Continuous normalizing flows (CNFs) are mappings obtained by solving a neural ordinary differential equation (ODE). The neural ODE's dynamics can be chosen almost arbitrarily while ensuring invertibility. Moreover, the log-determinant of the flow's Jacobian can be obtained by integrating the trace of the dynamics' Jacobian along the flow. Our proposed OT-Flow approach tackles two critical computational challenges that limit a more widespread use of CNFs. First, OT-Flow leverages optimal transport (OT) theory to regularize the CNF and enforce straight trajectories that are easier to integrate. Second, OT-Flow features exact trace computation with time complexity equal to trace estimators used in existing CNFs. On five high-dimensional density estimation and generative modeling tasks, OT-Flow performs competitively to state-of-the-art CNFs while on average requiring one-fourth of the number of weights with an 8x speedup in training time and 24x speedup in inference.