  Graph generative models have broad applications in biology, chemistry and
social science. However, modelling and understanding the generative process of
graphs is challenging due to the discrete and high-dimensional nature of
graphs, as well as permutation invariance to node orderings in underlying graph
distributions. Current leading autoregressive models fail to capture the
permutation invariance nature of graphs for the reliance on generation ordering
and have high time complexity. Here, we propose a continuous-time generative
diffusion process for permutation invariant graph generation to mitigate these
issues. Specifically, we first construct a forward diffusion process defined by
a stochastic differential equation (SDE), which smoothly converts graphs within
the complex distribution to random graphs that follow a known edge probability.
Solving the corresponding reverse-time SDE, graphs can be generated from newly
sampled random graphs. To facilitate the reverse-time SDE, we newly design a
position-enhanced graph score network, capturing the evolving structure and
position information from perturbed graphs for permutation equivariant score
estimation. Under the evaluation of comprehensive metrics, our proposed
generative diffusion process achieves competitive performance in graph
distribution learning. Experimental results also show that GraphGDP can
generate high-quality graphs in only 24 function evaluations, much faster than
previous autoregressive models.
