# Wavelet-Domain Diffusion

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.

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.