Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint
This work addresses a domain-specific problem in machine learning for inverse problems, offering incremental improvements to stochastic normalizing flows.
The paper tackles the challenge of improving normalizing flows for inverse problems by introducing a Markov chain viewpoint, generalizing them to handle distributions without densities and posterior sampling, and demonstrates performance through numerical examples.
To overcome topological constraints and improve the expressiveness of normalizing flow architectures, Wu, Köhler and Noé introduced stochastic normalizing flows which combine deterministic, learnable flow transformations with stochastic sampling methods. In this paper, we consider stochastic normalizing flows from a Markov chain point of view. In particular, we replace transition densities by general Markov kernels and establish proofs via Radon-Nikodym derivatives which allows to incorporate distributions without densities in a sound way. Further, we generalize the results for sampling from posterior distributions as required in inverse problems. The performance of the proposed conditional stochastic normalizing flow is demonstrated by numerical examples.