Composing Normalizing Flows for Inverse Problems

• URL: http://arxiv.org/abs/2002.11743v3
• Date: Mon, 14 Jun 2021 18:00:48 GMT
• Title: Composing Normalizing Flows for Inverse Problems
• Authors: Jay Whang, Erik M. Lindgren, Alexandros G. Dimakis
• Abstract summary: We propose a framework for approximate inference that estimates the target conditional as a composition of two flow models. Our method is evaluated on a variety of inverse problems and is shown to produce high-quality samples with uncertainty.
• Score: 89.06155049265641
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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