SE(3)-equivariance is a critical property for capturing pose information in 3D vision tasks, enabling models to handle transformations such as rotations and translations effectively. While equivariant diffusion models have recently demonstrated promise in 3D object reassembly due to their generative and denoising capabilities, they face key challenges when applied to this task. Specifically, traditional diffusion models rely on fixed input sizes, which limits their adaptability to varying part quantities, and their linear noise addition and removal processes struggle to address the inherently nonlinear transformations of 3D parts. To overcome these limitations, this paper proposes an SE(3)-equivariant diffusion model for pose denoising and 3D object reassembly from fragmented parts. The model incorporates an equivariant encoder to extract SE(3)-equivariant features, a Lie algebra mapping to linearize noise addition and removal, and an elastic diffusion framework capable of adapting to varying part quantities and nonlinear transformations. By leveraging these components, the method achieves accurate and robust pose predictions across diverse input configurations. Experiments conducted on the Breaking Bad dataset, a real-world RePAIR and a self-constructed 3D mannequin dataset demonstrate the effectiveness of the proposed model, outperforming state-of-the-art methods across metrics such as root mean square error and part accuracy. Ablation studies further validate the critical contributions of key modules, emphasizing their roles in improving accuracy and robustness for 3D part reassembly tasks.

Equivariant networks have recently made significant strides in computer vision tasks related to robotic grasping, molecule generation, and 6D pose tracking. In this paper, we explore 3D mesh object analysis based on an equivariant masked autoencoder to reduce the model dependence on large datasets and predict the pose transformation. We employ 3D reconstruction tasks under rotation and masking operations, such as segmentation tasks after rotation, as pretraining to enhance downstream task performance. To mitigate the computational complexity of the algorithm, we first utilize multiple non-overlapping 3D mesh patches with a fixed face size. We then design a rotation-equivariant self-attention mechanism to obtain advanced features. To improve the throughput of the encoder, we design a sparse token merging strategy. Our method achieves comparable performance on equivariant analysis tasks of mesh objects, such as 3D mesh pose transformation estimation, object classification and part segmentation on the ShapeNetCore16, Manifold40, COSEG-aliens, COSEG-vases and Human Body datasets. In the object classification task, we achieve superior performance even when only 10% of the original sample is used. We perform extensive ablation experiments to demonstrate the efficacy of critical design choices in our approach.