  We propose FrePolad: frequency-rectified point latent diffusion, a point
cloud generation pipeline integrating a variational autoencoder (VAE) with a
denoising diffusion probabilistic model (DDPM) for the latent distribution.
FrePolad simultaneously achieves high quality, diversity, and flexibility in
point cloud cardinality for generation tasks while maintaining high
computational efficiency. The improvement in generation quality and diversity
is achieved through (1) a novel frequency rectification via spherical harmonics
designed to retain high-frequency content while learning the point cloud
distribution; and (2) a latent DDPM to learn the regularized yet complex latent
distribution. In addition, FrePolad supports variable point cloud cardinality
by formulating the sampling of points as conditional distributions over a
latent shape distribution. Finally, the low-dimensional latent space encoded by
the VAE contributes to FrePolad's fast and scalable sampling. Our quantitative
and qualitative results demonstrate FrePolad's state-of-the-art performance in
terms of quality, diversity, and computational efficiency. Project page:
https://chenliang-zhou.github.io/FrePolad/.
