Composing Normalizing Flows for Inverse Problems
This work addresses a computational bottleneck in inverse problems for researchers and practitioners in fields like imaging or signal processing, offering a stable and efficient inference method.
The paper tackles the challenge of estimating the distribution of signals in inverse problems using normalizing flow priors, proposing a framework that composes two flow models for approximate inference, which produces high-quality samples with uncertainty quantification and enables zero-shot inference.
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.