Latent Graph Diffusion: A Unified Framework for Generation and
  Prediction on Graphs
Zhou Cai Xiyuan Wang Muhan Zhang
In this paper, we propose the first framework that enables solving graph
learning tasks of all levels (node, edge and graph) and all types (generation,
regression and classification) with one model. We first propose Latent Graph
Diffusion (LGD), a generative model that can generate node, edge, and
graph-level features of all categories simultaneously. We achieve this goal by
embedding the graph structures and features into a latent space leveraging a
powerful encoder which can also be decoded, then training a diffusion model in
the latent space. LGD is also capable of conditional generation through a
specifically designed cross-attention mechanism. Then we formulate prediction
tasks including regression and classification as (conditional) generation,
which enables our LGD to solve tasks of all levels and all types with provable
guarantees. We verify the effectiveness of our framework with extensive
experiments, where our models achieve state-of-the-art or highly competitive
results across generation and regression tasks.