HOG-Diff: Higher-Order Guided Diffusion for Graph Generation

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 achievements in graph generation, but these models are typically adapted from image generation frameworks and overlook inherent higher-order topology, leaving them ill-suited for capturing the topological properties of graphs. 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 exhibits a stronger theoretical guarantee than classical diffusion frameworks. Extensive experiments on both molecular and generic graph generation tasks demonstrate that our method consistently outperforms or remains competitive with state-of-the-art baselines. Our code is available at https://github.com/Yiminghh/HOG-Diff.