The digital construction of cultural heritage promotes communication and sharing of digital cultural resources across time and space. Digital storage serves as the foundation for the digital construction of cultural artifacts. In the digital storage of Dunhuang murals, image stitching plays a critical role in restoring the complete image of the cave murals. Traditional image stitching methods are constrained by the detection accuracy of feature points and are not fit for stitching low-texture murals. Despite deep learning-based image stitching methods, parallax misalignment and ghosting are still prevalent issues. For this reason, we perform the first Dunhuang mural stitching based on deep learning in this paper. This is in response to the need for digitizing and storing Dunhuang murals. Two mural stitching datasets are constructed, and we design a progressive regression image alignment network and a feature differential reconstruction soft-coded seam stitching network. We also introduce a soft-coded seam quality evaluation method. The algorithm presented in this paper achieves state-of-the-art alignment and stitching performance in the mural stitching task through unsupervised learning with a smaller number of model parameters, which provides technical support for the digitization and preservation of Dunhuang murals.