Graph-Aware Diffusion for Signal Generation

2025-10-06

AI Summary

Existing methods for generating graph signals under unknown distributions—e.g., in recommendation systems or sensor networks—either neglect graph structure or lack generality. Method: We propose Graph-Aware Diffusion (GAD), a diffusion-based generative model explicitly incorporating graph topology. GAD designs a forward process grounded in the graph heat equation and time-warping coefficients, ensuring the terminal distribution converges to a Gaussian Markov Random Field parameterized by the graph Laplacian. The reverse process is formulated as a sequence of graph-aware denoising steps, jointly ensuring theoretical soundness and structural fidelity. Crucially, GAD is the first diffusion model to explicitly embed graph differential operators into its core mechanism, unifying signal covariance modeling and dynamic evolution. Results: Experiments on synthetic data and real-world traffic speed and temperature sensing networks demonstrate that GAD significantly outperforms both structure-agnostic and domain-specific baselines, validating its generality, effectiveness, and principled integration of graph geometry.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

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.

Problem

• Generating graph signals from unknown distributions on given graphs
• Incorporating graph structure into diffusion models for signal generation
• Overcoming limitations of existing methods that ignore graph structure

Innovation

• Graph-aware diffusion model for signal generation
• Forward process incorporates graph via heat equation
• Time-warped coefficient mitigates exponential drift decay