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Diffusion models have achieved state-of-the-art performance in generatingmany different kinds of data, including images, text, and videos. Despite theirsuccess, there has been limited research on how the underlying diffusionprocess and the final convergent prior can affect generative performance; thisresearch has also been limited to continuous data types and a score-baseddiffusion framework. To fill this gap, we explore how different discretediffusion kernels (which converge to different prior distributions) affect theperformance of diffusion models for graphs. To this end, we developed a novelformulation of a family of discrete diffusion kernels which are easilyadjustable to converge to different Bernoulli priors, and we study the effectof these different kernels on generative performance. We show that the qualityof generated graphs is sensitive to the prior used, and that the optimal choicecannot be explained by obvious statistics or metrics, which challenges theintuitions which previous works have suggested.

Complex Preferences for Different Convergent Priors in Discrete Graph Diffusion