Composing Normalizing Flows for Inverse ProblemsDownload PDF

Jun 11, 2021TPM 2021Readers: Everyone
  • Keywords: inverse problem, normalizing flow, variational inference
  • TL;DR: A new algorithm for performing approximate probabilistic inference on a joint distribution defined by a normalizing flow prior.
  • Abstract: Given an inverse problem with a normalizing flow prior, we wish to estimate the distribution of the underlying signal conditioned on the observations. We approach this problem as a task of conditional inference on the pre-trained unconditional flow model. We first establish that this is computationally hard for a large class of flow models. Motivated by this, we propose a framework for approximate inference that estimates the target conditional as a composition of two flow models. This formulation leads to a stable variational inference training procedure that avoids adversarial training. Our method is evaluated on a variety of inverse problems and is shown to produce high quality samples with uncertainty quantification. We further demonstrate that our approach can be amortized for zero-shot inference.
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