Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint

Abstract

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.

References in corpus (3)

• Guided Image Generation with Conditional Invertible Neural Networks
• Stabilizing Invertible Neural Networks Using Mixture Models
• Annealed Flow Transport Monte Carlo

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