# Image Degradation Modeling for Real-World Super Resolution via Conditional Normalizing Flow
## 4 Experimental Results and Discussion
### Evaluation on Image Degradation Modeling  
To validate the effectiveness of the proposed IDFlow, we compared IDFlow with existing IDM methods. Firstly, since Bicubic is the most widely used degradation method for SR, we used it as the baseline. Moreover, learning-based methods KernelGAN [11] and DSGAN [9] were introduced for comparison. We also introduced a CNN-based IDM method named baselineCNN, which utilizes a CNN that has the same structure as the HR encoder of IDFlow with an additional convolution layer at the tail. baselineCNN tries to learn the direct mapping from HR to LR in a supervised manner. All the compared methods were trained on RealSR-Train and tested on RealSR-Test with 4\(\times\) down-sampling. During testing, the IDM methods take HR images in RealSR-Test as input to generate synthetic LR images. Subsequently, these images were used to calculate IQA metrics with LR images in RealSR-Test. The IQA results measure the similarity between the synthetic results and ground-truth LR images and thus can be used to evaluate image degradation performance. Table 2 shows the degradation performance results of the compared methods on RealSR-Test with 4\(\times\) down-sampling. It can be seen that IDFlow outperforms Bicubic,  
Figure 3: The effect of different \(\tau\) on degradation performance of IDFlow. PSNR, diversity, SSIM, and LPIPS results are reported. The results of DSGAN and KernelGAN are introduced as a reference. KernelGAN, and DSGAN on all the IQA metrics, demonstrating that IDFlow can effectively model the image degradation process. Benefiting from pixel-wisely supervision, baselineCNN achieves better degradation performance than IDFlow. The main purpose of image degradation modeling for SR is to generate realistic training datasets to improve SR performance. Thus, we introduced these compared IDM methods into 4\(\times\) SR model training to verify their effects on SR. The experimental scheme is shown in Figure 4. Different image degradation methods were first applied to generate synthetic 3450 HR-LR training image pairs based on the DF2K dataset with 4\(\times\) downsampling. Afterwards, different synthetic datasets were used to train a known SR model RRDBNet [4] with a scale of 4\(\times\) with the same training settings. SR models trained with Bicubic, DSGAN, baselineCNN, and IDFlow are named Bicubic-SR, DSGAN-SR, baselineCNN-SR, and IDFlow-SR. Specially, since KernelGAN needs no training process, it will generate SR images using ZSSR [17] during testing, denoted as K-ZSSR. After training, these trained SR models were tested on RealSR-Test. They took the LR images as input and generated 4\(\times\) SR results to compute IQA metrics PSNR/SSIM/LPIPS with HR ground truth. The SR performance results are reported in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **PSNR (dB) \(\uparrow\)** & **SSIM \(\uparrow\)** & **LPIPS \(\downarrow\)** \\ \hline Bicubic & 29.16 & 0.901 & 0.150 \\ KernelGAN & 30.01 & 0.928 & 0.077 \\ DSGAN & 32.23 & 0.953 & 0.049 \\ \hline baselineCNN & 34.00 & 0.963 & 0.038 \\ IDFlow & 33.44 & 0.959 & 0.042 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Degradation performance of different image degradation modeling methods on RealSR-Test with 4\(\times\) down-sampling. \(\uparrow\) indicates that the higher the value, the better the result. \(\downarrow\) indicates that the lower the value, the better the result. Figure 4: The scheme of SR model training and testing with different image degradation modeling methods. As shown in Table 3, K-ZSSR and DSGAN-SR achieved better results in terms of LPIPS than the baseline SR model Bicubic-SR, but obtained an obviously lower performance in terms of PSNR and SSIM. Even though baselineCNN learned a direct mapping from HR to LR, the corresponding SR model baselineCNN-SR could not achieve SR performance gains as expected.