# A Multi-Scale Deep Back-Projection Backbone for Face Super-Resolution with Diffusion Models
## 5 Experiment
### Comparison with Other Algorithms on Face Images  
BPSR3 was compared to the original baseline SR3 [23] using the face datasets CelebA [39] and FFHQ [40] on the 64 \(\times\) 64 \(\rightarrow\) 256 \(\times\) 256 (\(4\times\)) task. For baseline SR3, we followed SR3 to set \(mult\_size=\) {1, 2, 4, 8, 8} and \(N_{BC}=64\). We used two residual blocks and a dropout with a value of 0.2. Except for these special parameters above, in the non-basic network parameters part of the diffusion model, the settings of SR3 were exactly the same as those of BPSR3.  
We used about 30k of CelebA facial images to SR3 and BPSR3. For evaluation, we selected the first 10 images of FFHQ and computed the average PSNR and SSIM of their reconstructions. We saved the evaluation metrics and checkpoints every 10k iterations until we reached 0.5 M iterations. Figure 7 shows the comparison curves of model convergence speed and reconstruction effect.  
It is easy to observe from Figure 7 that the PSNR and SSIM of BPSR3 fluctuate widely in the first 200 k iterations but stabilize at a higher value after 200 k. SR3 has almost no large variation between 0.5 M in PSNR, while its optimal value is far from the general level of BPSR3; in the SSIM performance, although SR3 also shows an upward trend, it still does not reach the general level of BPSR3. This indicates that SR3 converges slower than BPSR3.  
We computed the parameter counts for SR3 and BPSR3 to be approximately 97 M and 25 M, respectively. Remarkably, the latter constitutes nearly a quarter of the former, indicating that we achieved superior reconstructions using a simpler model.  
Furthermore, we evaluated several advanced algorithms on the same validation dataset, including Latent-Diffusion [20], SwinIR [41], RealESRGAN [42], and BSRGAN [43]. Among them, Latent-Diffusion is based on the diffusion model, SwinIR is based on Vision Transformer, and RealESRGAN and BSRGAN are based on GAN.  
For evaluation, we measured PSNR, SSIM, and FID. We determined the optimal values for the training process of BPSR3 and its base model SR3. For the other models, we used the default options as given by the authors in the GitHub code.  
According to Table 1, it can be found that the BPSR3 proposed in this paper is optimal in all indicators, which shows its effectiveness. Further, we present Figure 8 to demonstrate the reconstruction results of some of the algorithms in Table 1 for a qualitative analysis. A more representative sample with more significant differences was selected for presentation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Based** & **Models** & **PSNR\(\uparrow\)** & **SSIM\(\uparrow\)** & **FID\(\downarrow\)** \\ \hline Transformer & SwinIR [41] & 26.29 & 0.7796 & 113.652 \\ Transformer & SwinIR (Large) [41] & 27.20 & 0.8093 & 97.976 \\ GAN & RealESRGAN [42] & 26.42 & 0.7856 & 152.281 \\ GAN & BSRGAN [43] & 26.99 & 0.7901 & 120.312 \\ Diffusion model & SR3 (The basic one) [23] & 20.24 & 0.7174 & 77.147 \\ Diffusion model & Latent-Diffusion [20] & 26.47 & 0.7829 & 110.297 \\ Diffusion model & BPSR3 (Ours) & **30.37** & **0.8597** & **65.238** \\ \hline \hline \end{tabular}
\end{table}
Table 1: The average performance of BPSR3 versus other SR reconstruction algorithms validated on the first 10 images of FFHQ (64 \(\times\) 64 \(\times\) 256 \(\times\) 256).  
Figure 7: Performance comparison of SR3 and BPSR3 on the FFHQ validation set, where (**a**) compares the reconstructed PSNR, and (**b**) compares SSIM. The red dotted line represents BPSR3, and the green dotted line represents SR3.  
Figure 8 demonstrates that, apart from the SR3 and BPSR3 algorithms, the reconstructed images tend to exhibit excessive smoothness. While SR3 maintains the overall shape of the original image, there is a noticeable variation in the primary hue. On the other hand, our BPSR3 reconstructions closely resemble the reference HR image, offering the most faithful restoration results.