On the Robustness of Normalizing Flows for Inverse Problems in Imaging

TL;DR

This paper investigates the causes of artifacts in normalizing flows for inverse imaging problems, revealing the role of out-of-distribution inputs and proposing a spline-based coupling layer to improve robustness and reduce artifacts.

Contribution

It identifies the 'exploding inverse' issue as a cause of artifacts and introduces a spline coupling layer as a simple remedy to enhance normalizing flow robustness in inverse imaging tasks.

Findings

Spline coupling layers reduce artifacts in normalizing flows.

Mahalanobis distance correlates with artifact likelihood.

Proposed method improves super-resolution and low-light image enhancement.

Abstract

Conditional normalizing flows can generate diverse image samples for solving inverse problems. Most normalizing flows for inverse problems in imaging employ the conditional affine coupling layer that can generate diverse images quickly. However, unintended severe artifacts are occasionally observed in the output of them. In this work, we address this critical issue by investigating the origins of these artifacts and proposing the conditions to avoid them. First of all, we empirically and theoretically reveal that these problems are caused by "exploding inverse" in the conditional affine coupling layer for certain out-of-distribution (OOD) conditional inputs. Then, we further validated that the probability of causing erroneous artifacts in pixels is highly correlated with a Mahalanobis distance-based OOD score for inverse problems in imaging. Lastly, based on our investigations, we propose a remark to avoid exploding inverse and then based on it, we suggest a simple remedy that substitutes the affine coupling layers with the modified rational quadratic spline coupling layers in normalizing flows, to encourage the robustness of generated image samples. Our experimental results demonstrated that our suggested methods effectively suppressed critical artifacts occurring in normalizing flows for super-resolution space generation and low-light image enhancement.