Stochastic Normalizing Flows

TL;DR

This paper introduces stochastic normalizing flows, extending continuous normalizing flows with stochastic differential equations to improve likelihood estimation, variational inference, and sampling efficiency.

Contribution

It presents a novel framework combining SDEs and rough path theory for training neural SDEs and optimizing hyperparameters in stochastic MCMC.

Findings

Efficient training of neural SDEs as random neural ODEs

Construction of Markov chains for sampling from data distributions

Application of VI to hyperparameter optimization in stochastic MCMC

Abstract

We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the underlying Brownian motion is treated as a latent variable and approximated, enabling efficient training of neural SDEs as random neural ordinary differential equations. These SDEs can be used for constructing efficient Markov chains to sample from the underlying distribution of a given dataset. Furthermore, by considering families of targeted SDEs with prescribed stationary distribution, we can apply VI to the optimization of hyperparameters in stochastic MCMC.