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.

Mesh segmentation is a process of partitioning a mesh model into meaningful parts - a fundamental problem in various disciplines. This paper introduces a novel mesh segmentation method inspired by sparsity pursuit. Based on the local geometric and topological information of a given mesh, we build a Laplacian matrix whose Fiedler vector is used to characterize the uniformity among elements of the same segment. By analyzing the Fiedler vector, we reformulate the mesh segmentation problem as a ℓ0gradient minimization problem. To solve this problem efficiently, we adopt a coarse-to-fine strategy. A fast heuristic algorithm is first devised to find a rational coarse segmentation, and then an optimization algorithm based on the alternating direction method of multiplier (ADMM) is proposed to refine the segment boundaries within their local regions. To extract the inherent hierarchical structure of the given mesh, our method performs segmentation in a recursive way. Experimental results demonstrate that the presented method outperforms the state-of-the-art segmentation methods when evaluated on the Princeton Segmentation Benchmark, the LIFL/LIRIS Segmentation Benchmark and a number of other complex meshes.