Shaping Without Tearing: Controllable Diffeomorphic Deformations for Topology-Preserving 3D Point Cloud Augmentation

Point cloud data augmentation is critical to improving the generalization of 3D deep learning models. However, existing methods often fail to preserve the underlying manifold structure, leading to semantic distortion or topology violation. This causes models to learn untrustworthy features, thereby limiting the representational ability of the model. To overcome these limitations, we propose ManiPoint, a novel point cloud augmentation framework based on diffeomorphism that explicitly preserves manifold structure during deformation. ManiPoint constructs diffeomorphic transformations via continuous differentiable mappings, ensuring topological consistency and geometric continuity between original and augmented data. To prevent excessive distortion and ensure semantic consistency, we introduce a controllable deformation mechanism that quantitatively constrains the augmentation magnitude and enables fine-grained control over the deformation space. We further provide theoretical analysis, indicating that, compared with topologically inconsistent methods, ManiPoint reduces empirical and vicinal risks by generating diverse and structurally reliable samples. Extensive experiments and visualizations on object-level datasets demonstrate that ManiPoint produces high-quality augmentations and consistently improves model robustness over existing baselines. Meanwhile, the scalability of our method was further verified on the scene-level datasets.