Generalized Normalizing Flows via Markov Chains

Paul Lyonel Hagemann, Johannes Hertrich, Gabriele Steidl

ISBN 10: 1009331000 / ISBN 13: 9781009331005

Published by Cambridge University Press, GB, 2023

About this Item

Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This Element provides a unified framework to handle these approaches via Markov chains. The authors 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 the coupling of 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. The authors' framework establishes a useful mathematical tool to combine the various approaches.

Seller Inventory # LU-9781009331005

Bibliographic Details

• Title: Generalized Normalizing Flows via Markov Chains
• Publisher: Cambridge University Press, GB
• Publication Date: 2023
• Language: English
• ISBN 10: 1009331000
• ISBN 13: 9781009331005
• Binding: Paperback
• Condition: New
• Weight: 94 grams

About this title

Synopsis

Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This Element provides a unified framework to handle these approaches via Markov chains. The authors 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 the coupling of 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. The authors' framework establishes a useful mathematical tool to combine the various approaches.