HOG-Diff: Higher-Order Guided Diffusion for Graph Generation
Yiming Huang, Tolga Birdal
TL;DR
HOG-Diff introduces a novel diffusion-based framework for graph generation that explicitly incorporates higher-order topological structures, leading to improved scalability and performance across diverse benchmarks.
Contribution
The paper presents HOG-Diff, a new guided diffusion model that captures higher-order topology in graph generation, with stronger theoretical guarantees and superior empirical results.
Findings
Outperforms existing methods on multiple benchmarks
Effectively captures higher-order topological features
Scalable to large graphs across various domains
Abstract
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…
Peer Reviews
Decision·ICLR 2026 Poster
Introduces a Higher-Order Guided Diffusion model, which for the first time explicitly incorporates higher-order structures (e.g., cell complexes) into graph generation tasks, addressing the limitations of existing diffusion models in capturing graph topological properties. Designs a Cell Complex Filtering (CCF) operation to enable a coarse-to-fine generation process, simplifying the modeling of complex graph distributions. Achieves superior results on molecular datasets (QM9, ZINC250k) and ge
The proposed coarse-to-fine process and cell complex filtering could be computationally expensive, especially for large graphs or dense higher-order structures. No runtime is provided. Although the authors emphasize interpretability as a motivation, there are few visual or quantitative analyses explaining what “higher-order topology” the model actually captures or how it improves the generation quality.
- The idea of graph generation via lifted is refreshing. - The paper is built upon a solid mathematical formulation. - The theoretical foundations, including theorems and propositions, are well-presented, and the accompanying proofs provided in the appendix appear to be correct.
Despite its theoretical grounding, the paper suffers from significant weaknesses in its justification, clarity, and empirical evaluation. - **Clarity of Writing and Notation.** A primary concern is the clarity of the writing and the logical flow. The notation, in particular, seems inconsistent and potentially overloaded. For instance, Proposition 2 introduces the $p$-cell complex filtered graph $G_p$, where the subscript $p$ denotes the cell dimension. However, in subsequent sections, graphs ar
- The use of higher-order topological structures to guide the diffusion process represents a novel contribution. The alignment of the different diffusion stages with hierarchical graph structures seems an innovative way of capturing complex structural patterns. - The proposed framework is theoretically grounded and proves to be an effective extension of standard diffusion models to non-Euclidean domains. - Empirical results are competitive with state-of-the-art methods, showing the potential o
- The reported performance improvements are relatively modest. Without an accompanying analysis of computational efficiency or scalability, the practical advantages of introducing higher-order topology remain unclear. - The methodological presentation of the framework could be more intuitive. Although the paper explains how higher-order structures are obtained and integrated into the diffusion process, the overall exposition is difficult to follow, as it often mixes high-level intuition with th
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Taxonomy
TopicsAdvanced Graph Neural Networks · Advanced Computing and Algorithms · Advanced Image and Video Retrieval Techniques
MethodsDiffusion