PointDiffermer is a robust point cloud registration method that leverages graph neural Partial Differential Equations (PDEs) and heat kernel signatures. The method first uses graph neural PDE modules to extract high-dimensional features from point clouds by aggregating information from the 3D point neighborhood, enhancing the robustness of the feature representations. It then incorporates heat kernel signatures into an attention mechanism to efficiently obtain corresponding keypoints. Finally, a Singular Value Decomposition (SVD) module with learnable weights predicts the transformation between two point clouds. Empirical experiments on various datasets demonstrate that PointDiffermer achieves state-of-the-art performance for point cloud registration and exhibits better robustness to additive noise and 3D shape perturbations. The method is motivated by the robustness of graph neural PDE learning for representing graph-structured data and the shape isometry-invariance of heat kernel signatures. The main contributions include designing a 3D point cloud representation module, proposing a robust registration method using graph neural diffusion and heat kernel signatures, and demonstrating superior performance compared to baselines in both normal and challenging scenarios.PointDiffermer is a robust point cloud registration method that leverages graph neural Partial Differential Equations (PDEs) and heat kernel signatures. The method first uses graph neural PDE modules to extract high-dimensional features from point clouds by aggregating information from the 3D point neighborhood, enhancing the robustness of the feature representations. It then incorporates heat kernel signatures into an attention mechanism to efficiently obtain corresponding keypoints. Finally, a Singular Value Decomposition (SVD) module with learnable weights predicts the transformation between two point clouds. Empirical experiments on various datasets demonstrate that PointDiffermer achieves state-of-the-art performance for point cloud registration and exhibits better robustness to additive noise and 3D shape perturbations. The method is motivated by the robustness of graph neural PDE learning for representing graph-structured data and the shape isometry-invariance of heat kernel signatures. The main contributions include designing a 3D point cloud representation module, proposing a robust registration method using graph neural diffusion and heat kernel signatures, and demonstrating superior performance compared to baselines in both normal and challenging scenarios.