  Point cloud upsampling (PCU) enriches the representation of raw point clouds,
significantly improving the performance in downstream tasks such as
classification and reconstruction. Most of the existing point cloud upsampling
methods focus on sparse point cloud feature extraction and upsampling module
design. In a different way, we dive deeper into directly modelling the gradient
of data distribution from dense point clouds. In this paper, we proposed a
conditional denoising diffusion probability model (DDPM) for point cloud
upsampling, called PUDM. Specifically, PUDM treats the sparse point cloud as a
condition, and iteratively learns the transformation relationship between the
dense point cloud and the noise. Simultaneously, PUDM aligns with a dual
mapping paradigm to further improve the discernment of point features. In this
context, PUDM enables learning complex geometry details in the ground truth
through the dominant features, while avoiding an additional upsampling module
design. Furthermore, to generate high-quality arbitrary-scale point clouds
during inference, PUDM exploits the prior knowledge of the scale between sparse
point clouds and dense point clouds during training by parameterizing a rate
factor. Moreover, PUDM exhibits strong noise robustness in experimental
results. In the quantitative and qualitative evaluations on PU1K and PUGAN,
PUDM significantly outperformed existing methods in terms of Chamfer Distance
(CD) and Hausdorff Distance (HD), achieving state of the art (SOTA)
performance.
