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.

翻译：条件归一化流能够生成多样化的图像样本用于求解逆问题。目前多数应用于成像逆问题的归一化流采用条件仿射耦合层，可快速生成多样化图像。然而，其输出偶尔会出现意外严重伪影。本文通过探究伪影根源并提出规避条件来解决这一关键问题。首先，我们从经验与理论层面揭示，此类问题源于特定分布外条件输入下条件仿射耦合层的"逆爆炸"现象。随后进一步验证，像素级错误伪影的产生概率与基于马氏距离的成像逆问题分布外评分高度相关。最终基于上述研究，我们提出避免逆爆炸的准则，并据此提出简单改进方案：将归一化流中的仿射耦合层替换为修正有理二次样条耦合层，以增强生成图像样本的鲁棒性。实验结果表明，该方法有效抑制了超分辨率空间生成与低光图像增强任务中归一化流产生的关键伪影。