Where Precision Meets Efficiency: Transformation Diffusion Model for Point Cloud Registration

We propose a transformation diffusion model for point cloud registration to balance precision and efficiency. Our method formulates point cloud registration as a denoising diffusion process from noisy transformation to object transformation, which is represented by quaternion and translation. Specifically, in training stage, object transformation diffuses from ground-truth transformation to random distribution, and the model learns to reverse this noising process. In sampling stage, the model refines randomly generated transformation to the optimal transformation in a progressive way. We derive the variational bound in closed form for training and provide instantiation of the model. Our diffusion model maps transformation into latent space, and splits the transformation into two components (rotation and translation) based on the fact that they belong to different solution spaces. In addition, our work provides the following crucial findings: (i) Point cloud registration, one of the representative discriminative tasks, can be solved by a generative way and mapped into latent space to obtain new unified probabilistic formulation. (ii) Our model, Transformation Diffusion Model (TDM) can be a plug-and-play agent for point cloud registration, making our method applicable to different deep registration networks. Experimental results on synthetic and real-world datasets demonstrate that, in correspondence-free and correspondence-based scenarios, TDM can both achieve exceeding 60% performance improvements and higher efficiency simultaneously.