  Generative modeling of set-structured data, such as point clouds, requires
reasoning over local and global structures at various scales. However, adopting
multi-scale frameworks for ordinary sequential data to a set-structured data is
nontrivial as it should be invariant to the permutation of its elements. In
this paper, we propose SetVAE, a hierarchical variational autoencoder for sets.
Motivated by recent progress in set encoding, we build SetVAE upon attentive
modules that first partition the set and project the partition back to the
original cardinality. Exploiting this module, our hierarchical VAE learns
latent variables at multiple scales, capturing coarse-to-fine dependency of the
set elements while achieving permutation invariance. We evaluate our model on
point cloud generation task and achieve competitive performance to the prior
arts with substantially smaller model capacity. We qualitatively demonstrate
that our model generalizes to unseen set sizes and learns interesting subset
relations without supervision. Our implementation is available at
https://github.com/jw9730/setvae.
