图扩散模型能否准确捕获并生成子结构分布？
Do Graph Diffusion Models Accurately Capture and Generate Substructure Distributions?
AI总结：
本文研究图扩散模型在子结构分布捕获与生成上的不足，建立GNN表达能力与扩散模型性能的理论联系，并通过引入更强表达能力的GNN骨干网络显著提升子结构生成效果。
摘要：
扩散模型在图生成任务中已获得广泛应用；然而，关于它们在学习图分布方面的表达能力程度尚未被充分理解。与其他领域的模型不同，图扩散模型的流行骨干网络（如图Transformer）并不具备通用表达能力，无法准确建模复杂图数据的分布得分。我们的工作通过关注特定子结构的出现频率作为目标图分布的关键特征来应对这一局限性。当使用该指标评估现有模型时，我们发现它们在生成新图时无法保持训练集中观察到的子结构计数分布。为解决这一问题，我们建立了图神经网络（GNN）表达能力与图扩散模型整体性能之间的理论联系，证明更具表达能力的GNN骨干网络能够更好地捕获复杂分布模式。通过将先进GNN集成到骨干架构中，我们在子结构生成方面取得了显著改进。
英文摘要：
Diffusion models have gained popularity in graph generation tasks; however, the extent of their expressivity concerning the graph distributions they can learn is not fully understood. Unlike models in other domains, popular backbones for graph diffusion models, such as Graph Transformers, do not possess universal expressivity to accurately model the distribution scores of complex graph data. Our work addresses this limitation by focusing on the frequency of specific substructures as a key characteristic of target graph distributions. When evaluating existing models using this metric, we find that they fail to maintain the distribution of substructure counts observed in the training set when generating new graphs. To address this issue, we establish a theoretical connection between the expressivity of Graph Neural Networks (GNNs) and the overall performance of graph diffusion models, demonstrating that more expressive GNN backbones can better capture complex distribution patterns. By integrating advanced GNNs into the backbone architecture, we achieve significant improvements in substructure generation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
