We present a new framework for point cloud denoising by patch-collaborative spectral analysis. A collaborative generalization of each surface patch is defined, combining similar patches from the denoised surface. The Laplace–Beltrami operator of the collaborative patch is then used to selectively smooth the surface in a robust manner that can gracefully handle high levels of noise, yet preserves sharp surface features. The resulting denoising algorithm competes favourably with state-of-the-art approaches, and extends patch-based algorithms from the image processing domain to point clouds of arbitrary sampling. We demonstrate the accuracy and noise-robustness of the proposed algorithm on standard benchmark models as well as range scans, and compare it to existing methods for point cloud denoising.