The cultural heritage field has developed rapidly based on the use of digital technologies for protecting cultural relics. The point cloud data of cultural relics obtained using three-dimensional laser scanning equipment inevitably contain considerable noise, which directly affects the subsequent processing of the point cloud data. To effectively remove noise points from the disordered point cloud and ensure enhanced recover of point cloud data, a new point cloud denoising algorithm based on the unsupervised network was proposed. First, the outliers are classified and removed from the upper network. Then, a spatial prior term was introduced to guide the data points in the noise cloud to converge to the optimal mode closest to the real point cloud in the multimode on the manifold, enabling the distribution of clean point cloud from the point cloud data of outlier noise points; moreover, the unsupervised denoising of the fine point cloud was realized. Finally, the chamfer distance between the denoised point clouds was estimated for quantitative evaluations. Compared with some classic algorithms, the proposed algorithm can effectively maintain the geometric characteristics of the point cloud model during denoising, and shows a good denoising effect on the point cloud data of cultural relics. The denoised point cloud model considerably restores the original clean point cloud model, which is crucial for the follow-up link of the digital protection of cultural relics.