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.

翻译：扩散模型已在生成图像、文本和视频等各类数据中取得了最先进的性能。尽管取得了成功，但关于底层扩散过程及最终收敛先验如何影响生成性能的研究仍十分有限；此类研究亦仅局限于连续数据类型与基于分数的扩散框架。为填补这一空白，我们探究了不同离散扩散核（其收敛至不同先验分布）如何影响图扩散模型的性能。为此，我们提出了一类离散扩散核的新颖公式，该公式可轻松调整以收敛至不同伯努利先验，并研究了这些不同核函数对生成性能的影响。研究表明，生成图的质量对所用先验分布敏感，且最优选择无法通过明显的统计量或指标解释，这对先前工作提出的直觉认知构成了挑战。