Graph generation is a critical yet challenging task, as empirical analyses require a deep understanding of complex, non-Euclidean structures. Diffusion models have recently made significant advances in graph generation, but these models are typically adapted from image generation frameworks and overlook inherent higher-order topology, limiting their ability to capture graph topology. In this work, we propose Higher-order Guided Diffusion (HOG-Diff), a principled framework that progressively generates plausible graphs with inherent topological structures. HOG-Diff follows a coarse-to-fine generation curriculum, guided by higher-order topology and implemented via diffusion bridges. We further prove that our model admits stronger theoretical guarantees than classical diffusion frameworks. Extensive experiments across eight graph generation benchmarks, spanning diverse domains and including large-scale settings, demonstrate the scalability of our method and its superior performance on both pairwise and higher-order topological metrics. Our project page is available \href{https://circle-group.github.io/research/hog-diff/}{here}.

翻译：图生成是一项关键但具有挑战性的任务，因为实证分析需要对复杂的非欧几里得结构有深入理解。扩散模型最近在图生成方面取得了显著进展，但这些模型通常是从图像生成框架改编而来，忽略了固有的高阶拓扑结构，从而限制了其捕捉图拓扑的能力。在本工作中，我们提出了高阶引导扩散（HOG-Diff），这是一个原则性的框架，能够逐步生成具有固有拓扑结构的合理图。HOG-Diff遵循从粗到细的生成课程，由高阶拓扑引导，并通过扩散桥实现。我们进一步证明，与经典扩散框架相比，我们的模型具有更强的理论保证。在涵盖不同领域（包括大规模设置）的八个图生成基准上进行的大量实验表明，我们的方法具有良好的可扩展性，并且在成对和高阶拓扑指标上均表现出优越的性能。我们的项目页面可\href{https://circle-group.github.io/research/hog-diff/}{在此}访问。