Composing Normalizing Flows for Inverse Problems [article]

Jay Whang, Erik M. Lindgren, Alexandros G. Dimakis
2021 arXiv   pre-print
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
more » ... on 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.
arXiv:2002.11743v3 fatcat:nwrjrh6wgbggdls4ttqj4w2y7a