提出一种融合图结构的扩散模型，用于生成复杂关系的数据信号。
Graph-Aware Diffusion for Signal Generation
- 用热方程建模图信号扩散过程，引入时间扭曲系数改善衰减问题。
- 理论证明其收敛至由图拉普拉斯定义的高斯马尔可夫随机场。
- 在交通速度、温感网络等真实数据上表现优于传统方法，适合图信号生成场景。
我们研究在给定图结构上从未知分布中生成图信号的问题，该问题在推荐系统和传感器网络等领域具有重要意义。现有方法要么忽略图结构，要么仅针对特定领域设计图感知机制。本文提出一种基于扩散模型的新方法（GAD），其前向过程通过热方程融入图结构，并引入时间扭曲系数以缓解漂移项的指数衰减。理论分析表明，该过程收敛至由图拉普拉斯参数化的高斯马尔可夫随机场，后向过程可解释为一系列图信号去噪问题。实验在合成数据、真实交通速度数据及温度传感器网络上验证了GAD的有效性，显著优于基线方法。
原文摘要 · Abstract (English)
We study the problem of generating graph signals from unknown distributions defined over given graphs, relevant to domains such as recommender systems or sensor networks. Our approach builds on generative diffusion models, which are well established in vision and graph generation but remain underexplored for graph signals. Existing methods lack generality, either ignoring the graph structure in the forward process or designing graph-aware mechanisms tailored to specific domains. We adopt a forward process that incorporates the graph through the heat equation. Rather than relying on the standard formulation, we consider a time-warped coefficient to mitigate the exponential decay of the drift term, yielding a graph-aware generative diffusion model (GAD). We analyze its forward dynamics, proving convergence to a Gaussian Markov random field with covariance parametrized by the graph Laplacian, and interpret the backward dynamics as a sequence of graph-signal denoising problems. Finally, we demonstrate the advantages of GAD on synthetic data, real traffic speed measurements, and a temperature sensor network.
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