Generalized Normalizing Flows via Markov Chains
This provides a mathematically sound tool for researchers in generative modeling to combine different approaches, though it is incremental as it unifies existing methods.
The paper tackles the challenge of unifying various generative models like normalizing flows, diffusion normalizing flows, and variational autoencoders by proposing a Markov chain framework, showing that including stochastic layers improves expressivity and enables generating multimodal distributions from unimodal ones.
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.