Generalized Normalizing Flows via Markov Chains

TL;DR

This paper introduces a unified Markov chain framework for various generative models like normalizing flows and VAEs, enhancing their expressivity and ability to generate complex distributions.

Contribution

It provides a novel mathematical framework that unifies stochastic and deterministic generative models via Markov chains, enabling new combinations and insights.

Findings

Including stochastic layers improves model expressivity.

The framework allows coupling different types of layers mathematically.

Numerical simulations demonstrate better generation of multimodal distributions.

Abstract

Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This chapter provides a unified framework to handle these approaches via Markov chains. We consider stochastic normalizing flows as a pair of Markov chains fulfilling some properties and show how many state-of-the-art models for data generation fit into this framework. Indeed numerical simulations show that including stochastic layers improves the expressivity of the network and allows for generating multimodal distributions from unimodal ones. The Markov chains point of view enables us to couple both deterministic layers as invertible neural networks and stochastic layers as Metropolis-Hasting layers, Langevin layers, variational autoencoders and diffusion normalizing flows in a mathematically sound way. Our framework establishes a useful mathematical tool to combine the various approaches.