  Diffusion models have achieved state-of-the-art performance in generating
many different kinds of data, including images, text, and videos. Despite their
success, there has been limited research on how the underlying diffusion
process and the final convergent prior can affect generative performance; this
research has also been limited to continuous data types and a score-based
diffusion framework. To fill this gap, we explore how different discrete
diffusion kernels (which converge to different prior distributions) affect the
performance of diffusion models for graphs. To this end, we developed a novel
formulation of a family of discrete diffusion kernels which are easily
adjustable to converge to different Bernoulli priors, and we study the effect
of these different kernels on generative performance. We show that the quality
of generated graphs is sensitive to the prior used, and that the optimal choice
cannot be explained by obvious statistics or metrics, which challenges the
intuitions which previous works have suggested.
