Mural restoration moves diffusion into the wavelet domain: 32.04 dB PSNR and inference cut from 35.31 to 9.56 seconds
Synopsis
Digital restoration of Dunhuang murals no longer denoises only in pixel space. Pixel-domain diffusion must handle global structure and local brushwork at once, which is costly and can drift in color and style. WDCRF first applies a 2D discrete wavelet transform to split a damaged mural into one low-frequency and three high-frequency subbands, then lets a conditional diffusion model rebuild all four coefficient sets directly in the wavelet domain, using the damaged coefficients themselves as the conditioning signal, and finally synthesizes the image by inverse wavelet transform. On the Dunhuang Mural dataset it reaches 32.04 dB PSNR and 0.922 SSIM, ahead of EdgeConnect, WaveDiff, PGRDiff and LRDiff; on DhMurals it reaches 18.95 dB PSNR and 0.7598 SSIM.
Interpretation
The generative step of mural restoration moves from pixel space into the wavelet domain, so the diffusion model no longer processes the image at full resolution. Earlier diffusion-based mural restoration ran mainly in the pixel domain, where iterative denoising had to perform global structural reasoning and local texture synthesis in the same high-dimensional space. On the Dunhuang Mural dataset the wavelet-domain scheme reaches 32.04 dB total PSNR and 0.922 SSIM, above PGRDiff at 26.44 dB and 0.763, URDiff at 26.29 dB and 0.763, WaveDiff at 27.98 dB and 0.811, and LRDiff at 28.47 dB and 0.791.
A damaged mural is first split into low-frequency and high-frequency components, then rebuilt jointly by one conditional diffusion model. Wavelet methods handle frequency decomposition and noise suppression well but lack the generative capacity to synthesize plausible content over large damaged regions, while diffusion models generate strongly but cost too much compute and memory when applied directly to high-resolution murals. A single-level 2D discrete wavelet transform separates the input into one low-frequency approximation subband A and three high-frequency detail subbands V, H and D, each halved in spatial size along both axes; the damaged coefficients condition the reverse denoising, and the restored coefficients return to the spatial domain through inverse wavelet transform.
Wavelet-domain diffusion reaches the best or near-best overall scores on both structural and perceptual measures. A pixel-domain baseline runs under the same U-Net backbone and training settings, providing the comparison that isolates the frequency-domain design. In the ablation, the spatial-domain DDPM variant scores 29.20 dB PSNR, 0.898 SSIM and 35.31 seconds of inference, while the full WDCRF scores 32.04 dB, 0.922 and 9.56 seconds; on DhMurals the totals are 18.95 dB PSNR, 0.7598 SSIM, 0.2078 LPIPS and 85.360 FID.
Perspective
The report covers restoration experiments on the Dunhuang Mural dataset and the DhMurals dataset, with inputs resized to 512×512 pixels and evaluation by PSNR, SSIM, LPIPS and FID. The intended readers are researchers and engineers working on image restoration, generative models or cultural heritage digitization, interested in whether frequency-domain generation can preserve structure while lowering the spatial dimension of each denoising step. Training used 8 TITAN V GPUs, and the authors state the model can also run on a single GPU; inference uses 100 DDIM sampling steps against 1000 diffusion steps during training.
On the severe-damage range of the DhMurals dataset (missing ratio at least 40%), CMAMRNet reaches 17.31 dB PSNR and 0.6819 SSIM while WDCRF reaches 16.67 dB and 0.6860, and the authors note CMAMRNet is slightly better under large missing regions while WDCRF has the best overall average. On the Dunhuang Mural dataset at 10%–20% and 20%–30% missing ratios, CMAMRNet scores 29.30 dB and 28.77 dB PSNR against WDCRF's 27.96 dB and 26.35 dB. These per-range differences show the advantage varies with damage severity, and no validation beyond these datasets is reported.