PointDifferormer is a robust point cloud registration method that combines graph neural partial differential equations (PDEs) and heat kernel signatures. The method first extracts high-dimensional features from point clouds using graph neural PDE modules, which aggregate information from the 3D point neighborhood to enhance feature representation. Then, heat kernel signatures are incorporated into an attention mechanism to efficiently obtain corresponding keypoints. A singular value decomposition (SVD) module with learnable weights is used to predict the transformation between two point clouds. Empirical experiments on a 3D point cloud dataset show that PointDifferormer achieves state-of-the-art performance in point cloud registration and exhibits better robustness to additive noise and 3D shape perturbations. The method is motivated by the robustness of graph neural PDEs in representing graph-structured data and the isometry-invariance of heat kernel signatures. The main contributions include designing a 3D point cloud representation module based on graph neural PDE learning, proposing a robust 3D point cloud registration method using graph neural diffusion modules and an attention mechanism with heat kernel signatures, and empirically demonstrating that the method outperforms other baselines under normal and noisy conditions. The model is evaluated on multiple datasets, including vReLoc, Boreas, and KITTI, showing superior performance in terms of registration accuracy and robustness. The method is also tested on datasets with lower overlaps, such as 3DMatch and 3DLoMatch, achieving state-of-the-art results. The computational complexity of the model is higher than other baselines, but the inference time is still acceptable for real-time applications.PointDifferormer is a robust point cloud registration method that combines graph neural partial differential equations (PDEs) and heat kernel signatures. The method first extracts high-dimensional features from point clouds using graph neural PDE modules, which aggregate information from the 3D point neighborhood to enhance feature representation. Then, heat kernel signatures are incorporated into an attention mechanism to efficiently obtain corresponding keypoints. A singular value decomposition (SVD) module with learnable weights is used to predict the transformation between two point clouds. Empirical experiments on a 3D point cloud dataset show that PointDifferormer achieves state-of-the-art performance in point cloud registration and exhibits better robustness to additive noise and 3D shape perturbations. The method is motivated by the robustness of graph neural PDEs in representing graph-structured data and the isometry-invariance of heat kernel signatures. The main contributions include designing a 3D point cloud representation module based on graph neural PDE learning, proposing a robust 3D point cloud registration method using graph neural diffusion modules and an attention mechanism with heat kernel signatures, and empirically demonstrating that the method outperforms other baselines under normal and noisy conditions. The model is evaluated on multiple datasets, including vReLoc, Boreas, and KITTI, showing superior performance in terms of registration accuracy and robustness. The method is also tested on datasets with lower overlaps, such as 3DMatch and 3DLoMatch, achieving state-of-the-art results. The computational complexity of the model is higher than other baselines, but the inference time is still acceptable for real-time applications.