EquiForm: Noise-Robust SE(3)-Equivariant Policy Learning from 3D Point Clouds

Visual imitation learning with 3D point clouds has advanced robotic manipulation by providing geometry-aware, appearance-invariant observations. However, point cloud-based policies remain highly sensitive to sensor noise, pose perturbations, and occlusion-induced artifacts, which distort geometric structure and break the equivariance assumptions required for robust generalization. Existing equivariant approaches primarily encode symmetry constraints into neural architectures, but do not explicitly correct noise-induced geometric deviations or enforce equivariant consistency in learned representations. We introduce EquiForm, a noise-robust SE(3)-equivariant policy learning framework for point cloud-based manipulation. EquiForm formalizes how noise-induced geometric distortions lead to equivariance deviations in observation-to-action mappings, and introduces a geometric denoising module to restore consistent 3D structure under noisy or incomplete observations. In addition, we propose a contrastive equivariant alignment objective that enforces representation consistency under both rigid transformations and noise perturbations. Built upon these components, EquiForm forms a flexible policy learning pipeline that integrates noise-robust geometric reasoning with modern generative models. We evaluate EquiForm on 16 simulated tasks and 4 real-world manipulation tasks across diverse objects and scene layouts. Compared to state-of-the-art point cloud imitation learning methods, EquiForm achieves an average improvement of 17.2% in simulation and 28.1% in real-world experiments, demonstrating strong noise robustness and spatial generalization.