Flows for simultaneous manifold learning and density estimation

TL;DR

The paper introduces manifold-learning flows (M-flows), a novel generative model that jointly learns data manifolds and their probability densities, improving data representation and inference over traditional models.

Contribution

It presents a new class of models combining aspects of flows, GANs, autoencoders, and energy-based models, with a specialized training algorithm for manifold and density learning.

Findings

M-flows effectively learn the data manifold

They enable better inference than standard flows

The model improves tasks like denoising and out-of-distribution detection

Abstract

We introduce manifold-learning flows (M-flows), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs, autoencoders, and energy-based models, they have the potential to represent datasets with a manifold structure more faithfully and provide handles on dimensionality reduction, denoising, and out-of-distribution detection. We argue why such models should not be trained by maximum likelihood alone and present a new training algorithm that separates manifold and density updates. In a range of experiments we demonstrate how M-flows learn the data manifold and allow for better inference than standard flows in the ambient data space.