Ancient murals are invaluable cultural heritage artifacts that frequently suffer from complex degradation due to environmental exposure and human activity. Most existing computational restoration methods rely on supervised learning and require large collections of clean reference murals, which are often unavailable or prohibitively expensive to acquire. To address this challenge, we propose the first unsupervised mural restoration method based on residual diffusion. Our approach operates solely on degraded murals and corresponding simulated degradation noise, both of which can be obtained without ground-truth supervision. Rather than directly reconstructing the original clean image, we simulate additional degradation on already-damaged murals and train the model to invert this process through residual-aware diffusion. Furthermore, we incorporate a low-rank prior during sampling to promote global structural consistency. Extensive experiments demonstrate that our method achieves performance on par with or superior to state-of-the-art supervised techniques, establishing the viability of unsupervised learning for high-quality mural restoration.