# Image Degradation Modeling for Real-World Super Resolution via Conditional Normalizing Flow
## 1 Introduction  
Image super resolution (SR) targets the recovery of a visually pleasing high-resolution (HR) image from its low-resolution (LR) version. With the rapid development of deep learning and convolution neural networks (CNNs), CNN-based methods [1, 2, 3, 4, 5] have made impressive SR performance gains in recent years. However, most of the existing methods are trained supervisedly on synthetic paired datasets where LR images are commonly obtained by bicubic interpolation from HR images. Even though this kind of data acquisition could provide fine results in clean settings, it causes a data distribution mismatch between real-world images and synthetic images. Bicubic down-sampling would alter image characteristics, as visible corruptions such as sensor noise in natural images are reduced in the meantime. On the other hand, the real-world image degradation is much more complicated than a single down-sampling process. Thus, the state-of-the-art SR methods trained on the synthetic datasets cannot perform as well as expected in real-world scenarios. In order to improve the generalization ability of SR models, many works have been proposed [6; 7; 8; 9; 10]. Generally, image degradation could be formulated as a combination of blurring and noise addition. Following the definition, [PERSON] et al. [6] introduced anisotropic Gaussian blur kernels as well as additive white Gaussian noise into HR-LR pair generation to simulate real image characteristics. They then proposed and trained a CNN model, SRMD [6], for blind super resolution. Since SRMD takes degradation maps as input as well, SRMD has to find suitable degradation parameters on real images via a grid search strategy, which is time-consuming. Recently, some works have made efforts to collect paired image datasets from real-world scenarios. [PERSON] et al. [7] captured the images of 100 city scenes printed on postcards based on two imaging systems (DSLR and smartphone) at different focal lengths and obtained a real-world paired dataset known as City100 [7]. [PERSON] et al. [8] collected paired HR-LR images on the same scene by adjusting the focal length of a digital camera. They also developed a registration algorithm to align the image pairs. A real-world SR dataset named RealSR [8] was built with three different scale factors. However, obtaining such paired training datasets requires expensive digital camera devices and needs complex image post-processing to align LR and HR images. As a result, the number of image pairs and the diversity of scenes are insufficient. City100 [7] only contains 100 aligned HR-LR image pairs, while RealSR [8] contains 559 scenes in total, which limits the further applications of SR models into a wider range of scenarios. Besides collecting real-world datasets, there are some methods [9; 11; 12] proposed to construct HR-LR images using unsupervised or semi-supervised learning. These methods utilize a Generative Adversarial Network (GAN) to learn the distribution of real-world LR images. However, training a GAN based network to model the degradation process with unpaired LR and HR images suffers from training instability and may lead to undesired results. Furthermore, given an HR image, only one generated LR result can be predicted once the network is trained, which does not take account for the fact that multiple LR images from one scene may have the same HR version. As discussed above, to improve the performance of existing SR models in real-world scenarios lies in how to effectively build training SR datasets that is close to reality. To address this issue, we propose a method based on conditional normalizing flow named IDFlow to investigate image degradation modeling (IDM). Unlike deterministic mapping learning in [9; 12], IDFlow takes IDM as the problem of learning a conditional probability distribution of degraded LR images given the HR versions. It learns the distribution from the existing real-world datasets and is trained with a single negative log likelihood (NLL) loss in a supervised manner.