<p>Ancient murals represent invaluable cultural heritage that often undergo complex degradation caused by environmental and human factors. Most existing computational restoration methods are supervised and require large datasets of clean reference murals, which are typically unavailable or costly to acquire. To address this issue, we propose an unsupervised mural restoration method based on residual diffusion. Our method only employs degraded murals and simulated degradation noise, both of which are easily accessible. Instead of directly reconstructing clean images, we apply further degradation to degraded murals and train the model to reverse this process via residual diffusion. In addition, we introduce a low-rank prior during sampling to suppress high-frequency measurement noise that is difficult to detect and locate. Extensive experiments demonstrate that our method performs comparably to or better than state-of-the-art supervised approaches, validating the feasibility of unsupervised learning for high-quality mural restoration.</p>