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.

翻译：生成式扩散模型在点云重采样中已展现出实证成功，通过将噪声逐步细化为结构，可从稀疏或含噪声的三维点云生成更密集且分布更均匀的点集。然而，现有扩散模型采用人工预定义的方案，由于几何退化的刚性及破坏性，往往难以恢复潜在的点云结构。为解决此问题，我们提出一种新颖的可学习热扩散框架用于点云重采样，该框架通过学习时变热核的自适应热扩散调度与局部滤波尺度，直接参数化前向过程的边缘分布，进而为反向过程生成自适应条件先验。与先前具有固定先验的扩散模型不同，该自适应条件先验通过最小化精化的变分下界，选择性地保留点云的几何特征，从而在反向过程中引导点向潜在表面演化。大量实验结果表明，所提出的点云重采样方法在点云去噪与上采样等典型重建任务中取得了最先进的性能。