Deterministic Point Cloud Diffusion for Denoising

Diffusion-based generative models have achieved remarkable success in image restoration by learning to iteratively refine noisy data toward clean signals. Inspired by this progress, recent efforts have begun exploring their potential in 3D domains. However, applying diffusion models to point cloud denoising introduces several challenges. Unlike images, clean and noisy point clouds are characterized by structured displacements. As a result, it is unsuitable to establish a transform mapping in the forward phase by diffusing Gaussian noise, as this approach disregards the inherent geometric relationship between the point sets. Furthermore, the stochastic nature of Gaussian noise introduces additional complexity, complicating geometric reasoning and hindering surface recovery during the reverse denoising process. In this paper, we introduce a deterministic noise-free diffusion framework that formulates point cloud denoising as a two-phase residual diffusion process. In the forward phase, directional residuals are injected into clean surfaces to construct a degradation trajectory that encodes both local displacements and their global evolution. In the reverse phase, a U-Net-based network iteratively estimates and removes these residuals, effectively retracing the degradation path backward to recover the underlying surface. By decomposing the denoising task into directional residual computation and sequential refinement, our method enables faithful surface recovery while mitigating common artifacts such as over-smoothing and under-smoothing. Extensive experiments on synthetic and real-world datasets demonstrate that our method achieves state-of-the-art performance in both quantitative metrics and visual quality.