On the Robustness of Normalizing Flows for Inverse Problems in Imaging

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.

1. Introduction

Deep learning techniques have demonstrated great potential for solving ill-posed inverse problems in imaging [25], [31]. Among them, conditional normalizing flow (NF)-based methods have a unique advantage over other deep learning methods, which is the capability of generating diverse solutions for a given input. Conditional NFs [6] have been explored for various inverse problems in imaging such as super-resolution space generation [26], [14], [38], [13], [22], [29], [27], [28], low-light image enhancement [42], [41], guided image generation [3], [35], image dehazing [45], denoising [1], [24] and inpainting [24]. Most of these prior works with conditional NFs for image processing and lowlevel computer vision have focused on excellent performance with diverse solutions.