Keywords: Normalizing flows, ODE, neural ODE, universal approximation
TL;DR: We we invertible neural networks to approximate solutions to ODEs to show they are universal density approximators.
Abstract: Normalizing flows are powerful invertible probabilistic models that can be used to translate two probability distributions, in a way that allows us to efficiently track the change of probability density. However, to trade for computational efficiency in sampling and in evaluating the log-density, special parameterization designs have been proposed at the cost of representational expressiveness. In this work, we propose to use ODEs as a framework to establish universal approximation theory for certain families of flow-based models.