Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint
arXiv:2109.11375 · doi:10.1137/21M1450604
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.
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- Proximal Residual Flows for Bayesian Inverse Problems
- Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces
- Mixed Noise and Posterior Estimation with Conditional DeepGEM