Mural restoration stops asking only where damage is: a continuous severity field lifts PSNR by 3.27 dB

The input to semi-transparent mural restoration shifts from a binary mask of where damage lies to a continuous severity value per pixel, letting the network distinguish mild and severe locations inside one damaged region. Earlier diffusion-based mural restoration largely treated damage as missing-region completion, and a binary mask gave only the damaged support without encoding continuously varying severity inside it. On the fixed 100-image Dunhuang test split, keeping the asynchronous restoration structure unchanged and swapping the binary mask for predicted soft Alpha raised PSNR from 27.3421 dB to 30.6122 dB, SSIM from 0.8740 to 0.9253, and lowered LPIPS from 0.1151 to 0.0712.

The diffusion process no longer gives the whole image one shared time progress; each pixel carries its own local restoration progress while common start and end points are preserved. Standard diffusion assigns a shared timestep across the image, leaving spatially different restoration dynamics to be handled implicitly by network features. In the trajectory sensitivity experiment, asynchronous local time improved results under both Alpha states: PSNR rose from 30.6401 dB to 31.1265 dB with the linear state and from 29.1956 dB to 31.5152 dB with the composition-consistent state.

Severity is first estimated from the degraded image and coarse mask, then corrected within bounds so isolated high-severity responses do not dominate. The coarse estimate gives only approximate severity, and an average regression loss lets numerous easy pixels obscure a small number of large local errors. The refinement branch works as a residual logit, recovering the coarse estimate exactly when its output is zero and constraining severity to between 0 and 1 after a sigmoid; training adds a top-tail loss on the largest errors, a one-sided penalty on positive severity errors, and a neighborhood spike penalty.

Local progress is mapped to a dynamic Alpha state constrained by terminal severity, which progressively activates the image-space residual so intermediate states stay on the same semi-transparent degradation trajectory. Local progress alone states each location's relative restoration degree but does not directly specify the corresponding intermediate degradation state. The state starts at 0, ends at the terminal severity, is monotonic in local progress, and follows the Alpha composition law; at weak degradation its first-order approximation is the linear rule, with the nonlinear correction growing as severity increases.

Experiments use the Dunhuang mural dataset with a fixed split of 400 training and 100 test images, where degradation is synthesized by blending real damage patches and their transparency maps with intact murals across ten categories: salt crystallization, discoloration, cracking, fading, detachment, insect damage, mold, scratches, soot deposition and water stains. Comparisons cover IR-SDE, StrDiffusion, RDDM, LRDiff and PGRDiff, with PGRDiff the closest baseline to the degradation setting. Metrics are PSNR, SSIM and LPIPS; FID is excluded because it is not reported consistently across the main result tables. The method addresses semi-transparent damage that still retains part of the pigment and contours, and is not a complete physical model of material deterioration or chemical reactions.

A clear gap remains between predicted and ground-truth severity, with ground-truth Alpha giving 3.2539 dB higher PSNR than predicted Alpha, which marks severity estimation as an important bottleneck. The composition-consistent Alpha state does not outperform the linear state under every temporal setting, and its independent performance contribution still needs evaluation under a unified training protocol. Fine lines, dense textures and severely degraded regions still show reduced edge sharpness, texture displacement or local contrast differences, and LPIPS remains higher than PGRDiff. The authors propose extending evaluation across sites, materials and degradation types and studying domain generalization and uncertainty in severity estimation.