  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 module 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 the state-of-the-art
performance of FrePolad in terms of quality, diversity, and computational
efficiency.

Computer Vision and Pattern Recognition