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Leveraging Structural Knowledge in Diffusion Models for Source Localization in Data-Limited Graph Scenarios

The source localization problem in graph information propagation is crucial for managing various network disruptions, from misinformation spread to infrastructure failures. While recent deep generative approaches have shown promise in this domain, their effectiveness is limited by the scarcity of real-world propagation data. This paper introduces SIDSL (\textbf{S}tructure-prior \textbf{I}nformed \textbf{D}iffusion model for \textbf{S}ource \textbf{L}ocalization), a novel framework that addresses three key challenges in limited-data scenarios: unknown propagation patterns, complex topology-propagation relationships, and class imbalance between source and non-source nodes. SIDSL incorporates topology-aware priors through graph label propagation and employs a propagation-enhanced conditional denoiser with a GNN-parameterized label propagation module (GNN-LP). Additionally, we propose a structure-prior biased denoising scheme that initializes from structure-based source estimations rather than random noise, effectively countering class imbalance issues. Experimental results across four real-world datasets demonstrate SIDSL's superior performance, achieving 7.5-13.3% improvements in F1 scores compared to state-of-the-art methods. Notably, when pretrained with simulation data of synthetic patterns, SIDSL maintains robust performance with only 10% of training data, surpassing baselines by more than 18.8%. These results highlight SIDSL's effectiveness in real-world applications where labeled data is scarce.

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