VQ-Flows: Vector Quantized Local Normalizing Flows

TL;DR

This paper introduces VQ-Flows, a novel framework combining vector quantized auto-encoders and local normalizing flows to better model complex data distributions on low-dimensional manifolds with non-trivial topology.

Contribution

It proposes a new statistical framework that learns a mixture of local flows over a data manifold using an atlas of charts via VQ-AE, enhancing expressivity while maintaining exact density evaluation.

Findings

Improved modeling of data on complex manifolds.

Enhanced expressivity over previous normalizing flow methods.

Validated through experiments on complex data distributions.

Abstract

Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their expressivity when the data distribution is supported on a low-dimensional manifold or has a non-trivial topology. We introduce a novel statistical framework for learning a mixture of local normalizing flows as "chart maps" over the data manifold. Our framework augments the expressivity of recent approaches while preserving the signature property of normalizing flows, that they admit exact density evaluation. We learn a suitable atlas of charts for the data manifold via a vector quantized auto-encoder (VQ-AE) and the distributions over them using a conditional flow. We validate experimentally that our probabilistic framework enables existing approaches to better model data distributions over complex manifolds.