  In this paper, we propose Multiresolution Equivariant Graph Variational
Autoencoders (MGVAE), the first hierarchical generative model to learn and
generate graphs in a multiresolution and equivariant manner. At each resolution
level, MGVAE employs higher order message passing to encode the graph while
learning to partition it into mutually exclusive clusters and coarsening into a
lower resolution that eventually creates a hierarchy of latent distributions.
MGVAE then constructs a hierarchical generative model to variationally decode
into a hierarchy of coarsened graphs. Importantly, our proposed framework is
end-to-end permutation equivariant with respect to node ordering. MGVAE
achieves competitive results with several generative tasks including general
graph generation, molecular generation, unsupervised molecular representation
learning to predict molecular properties, link prediction on citation graphs,
and graph-based image generation.
