Point Cloud Resampling with Learnable Heat Diffusion

Generative diffusion models have shown empirical successes in point cloud resampling, generating a denser and more uniform distribution of points from sparse or noisy 3D point clouds by progressively refining noise into structure. However, existing diffusion models employ manually predefined schemes, which often fail to recover the underlying point cloud structure due to the rigid and disruptive nature of the geometric degradation. To address this issue, we propose a novel learnable heat diffusion framework for point cloud resampling, which directly parameterizes the marginal distribution for the forward process by learning the adaptive heat diffusion schedules and local filtering scales of the time-varying heat kernel, and consequently, generates an adaptive conditional prior for the reverse process. Unlike previous diffusion models with a fixed prior, the adaptive conditional prior selectively preserves geometric features of the point cloud by minimizing a refined variational lower bound, guiding the points to evolve towards the underlying surface during the reverse process. Extensive experimental results demonstrate that the proposed point cloud resampling achieves state-of-the-art performance in representative reconstruction tasks including point cloud denoising and upsampling.