Generalized Normalizing Flows via Markov Chains

Normalizing flows, diffusion normalizing flows, and variational autoencoders are powerful generative models, but their coupling can be challenging. This Element provides a unified framework to handle these approaches via Markov chains, which improve the expressivity of the network and allow for generating multimodal distributions from unimodal ones.

Format: Paperback / softback
Length: 75 pages
Publication date: 02 February 2023
Publisher: Cambridge University Press

Normalizing flows, diffusion normalizing flows, and variational autoencoders are powerful generative models that offer a unified framework for handling these approaches through Markov chains. The authors view stochastic normalizing flows as a pair of Markov chains that satisfy certain properties, demonstrating how many state-of-the-art models for data generation fall into this framework. Numerical simulations confirm that incorporating stochastic layers enhances the network's expressivity, enabling the generation of multimodal distributions from unimodal ones. The Markov chain perspective allows for a mathematically sound coupling of deterministic layers, such as invertible neural networks, with stochastic layers, including Metropolis-Hasting layers, Langevin layers, variational autoencoders, and diffusion normalizing flows. This framework provides a valuable mathematical tool for combining these diverse approaches.

Normalizing flows, diffusion normalizing flows, and variational autoencoders are powerful generative models that offer a unified framework for handling these approaches through Markov chains. The authors view stochastic normalizing flows as a pair of Markov chains that satisfy certain properties, demonstrating how many state-of-the-art models for data generation fall into this framework. Numerical simulations confirm that incorporating stochastic layers enhances the network's expressivity, enabling the generation of multimodal distributions from unimodal ones. The Markov chain perspective allows for a mathematically sound coupling of deterministic layers, such as invertible neural networks, with stochastic layers, including Metropolis-Hasting layers, Langevin layers, variational autoencoders, and diffusion normalizing flows. This framework provides a valuable mathematical tool for combining these diverse approaches.

ISBN-13: 9781009331005