# Image Degradation Modeling for Real-World Super Resolution via Conditional Normalizing Flow
## 4 Experimental Results and Discussion  
### Evaluation on Image Degradation Stochasticity  
In this section, we conduct analyses on the image degradation stochasticity of IDFlow. Figure 2 shows the multiple degraded LR examples generated by IDFlow with blur degradation modeling given the same HR image with 4\(\times\) down-sampling. For each HR image, the first row lists the zoomed details of five degraded LR images. The second row presents the first LR image as well as absolute pixel-value difference maps between the first LR image and the other four images, to highlight the differences between LR images.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & \multirow{2}{*}{**Number**} & \multicolumn{2}{c}{**Avg. Resolution**} & \multirow{2}{*}{**Format**} \\ \cline{3-4} \cline{5-5}  & & **HR** & & **LR** \\ \hline DF2K & 3450 & (1446, 1942) & - & PNG \\ RealSR-Train & 459 & (1312, 1527) & (328, 381) & PNG \\ RealSR-Test & 100 & (1247, 1569) & (312, 392) & PNG \\ DPED-Train & 5614 & - & (768, 1024) & PNG \\ DPED-Test & 100 & - & (256, 511) & PNG \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summarized information about image datasets.  
From these maps, it can be seen that both of these synthetic LR images retain the overall structural information similar to the original HR image. Meanwhile, the LR images are different in the areas with more high-frequency information, which is consistent with the real-world image degradation. This shows that the image degradation realized by IDFlow has the characteristics of diversity and stochasticity.  
Furthermore, by adjusting the value of sampling temperature \(\tau\), we can control the diversity and stochasticity of IDFlow. We conduct experiments on RealSR-Test. For each \(\tau\), IDFlow takes an HR image as input and generates one synthetic LR image. The synthetic LR images are used to calculate IQA metrics PSNR, SSIM, and LPIPS with the LR images in RealSR-Test. IQA metrics can reflect the degradation performance of IDFlow. To illustrate the diversity of IDFlow, we let IDFlow generate 10 LR images for each testing HR image, and we then compute the pixel standard deviation of these LR images for each HR image. The average of the pixel standard deviations of all tested images in RealSR-Test can be regarded as the diversity. If the diversity is larger, the difference between any two LR images becomes larger. The results are reported in Figure 3. We also introduce the results of  
Figure 2: Random samples generated by IDFlow with \(\times\)4 down-sampling using a sampling temperature \(\tau=0.7\). For each HR image in the first column, the first row presents zoomed local regions of five synthetic LR examples.The second row presents the absolute pixel-value difference maps between the first LR image and the rest of the images.  
two learning-based image degradation modeling methods KernelGAN [11] and DSGAN [9] for comparison. They are trained with Real-Train and then used for testing.  
Since KernelGAN and DSGAN can only produce one LR image given an HR image, the diversity of these methods are zero, and the results of the IQA metrics will not change with the sampling temperature. As for IDFlow, when sampling temperature \(\tau\) decreases, the generated results are pixel-wisely closer to the original images, the curve of the PSNR shows an increasing trend, and the diversity of the generated results decreases accordingly. At the same time, the structural similarity and perceptual similarity of the generated results have not changed significantly. Specially, when \(\tau=0\), the diversity decreases to zero, which means each HR image could only have one LR image generated by IDFlow, which is the same as KernelGAN and DSGAN. Thus, we set the \(\tau=0.7\) as a tradeoff between fidelity and diversity.