Graph-Aware Diffusion for Signal Generation

• URL: http://arxiv.org/abs/2510.05036v1
• Date: Mon, 06 Oct 2025 17:11:32 GMT
• Title: Graph-Aware Diffusion for Signal Generation
• Authors: Sergio Rozada, Vimal K. B., Andrea Cavallo, Antonio G. Marques, Hadi Jamali-Rad, Elvin Isufi,
• Abstract summary: We study the problem of generating graph signals from unknown distributions defined over given graphs.<n>Our approach builds on generative diffusion models, which are well established in vision and graph generation.<n>We demonstrate the advantages of GAD on synthetic data, real traffic speed measurements, and a temperature sensor network.
• Score: 35.631095096228
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Learning Time-Varying Graphs from Incomplete Graph Signals [1.7430416823420511]
  We develop an efficient Alternating Direction Multiplier algorithm for solving the problem of imputing missing data from a graph.<n>We prove that the proposed ADMM scheme converges to and we derive a stationary point.
  arXiv  Detail & Related papers  (2025-10-19T11:12:13Z)
• Graph Signal Generative Diffusion Models [74.75869068073577]
  We introduce U-shaped encoder-decoder graph neural networks (U-GNNs) for graph signal generation using denoising diffusion processes.<n>The architecture learns node features at different resolutions with skip connections between the encoder and decoder paths.<n>We demonstrate the effectiveness of the diffusion model in probabilistic forecasting of stock prices.
  arXiv  Detail & Related papers  (2025-09-21T21:57:27Z)
• Overcoming Order in Autoregressive Graph Generation [12.351817671944515]
  Graph generation is a fundamental problem in various domains, including chemistry and social networks. Recent work has shown that molecular graph generation using recurrent neural networks (RNNs) is advantageous compared to traditional generative approaches.
  arXiv  Detail & Related papers  (2024-02-04T09:58:22Z)
• Graph Neural Networks with a Distribution of Parametrized Graphs [27.40566674759208]
  We introduce latent variables to parameterize and generate multiple graphs. We obtain the maximum likelihood estimate of the network parameters in an Expectation-Maximization framework.
  arXiv  Detail & Related papers  (2023-10-25T06:38:24Z)
• Supercharging Graph Transformers with Advective Diffusion [28.40109111316014]
  This paper proposes Advective Diffusion Transformer (AdvDIFFormer), a physics-inspired graph Transformer model designed to address this challenge.<n>We show that AdvDIFFormer has provable capability for controlling generalization error with topological shifts.<n> Empirically, the model demonstrates superiority in various predictive tasks across information networks, molecular screening and protein interactions.
  arXiv  Detail & Related papers  (2023-10-10T08:40:47Z)
• Dynamic Causal Explanation Based Diffusion-Variational Graph Neural Network for Spatio-temporal Forecasting [60.03169701753824]
  We propose a novel Dynamic Diffusion-al Graph Neural Network (DVGNN) fortemporal forecasting. The proposed DVGNN model outperforms state-of-the-art approaches and achieves outstanding Root Mean Squared Error result.
  arXiv  Detail & Related papers  (2023-05-16T11:38:19Z)
• Graph Generation with Diffusion Mixture [57.78958552860948]
  Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. We propose a generative framework that models the topology of graphs by explicitly learning the final graph structures of the diffusion process.
  arXiv  Detail & Related papers  (2023-02-07T17:07:46Z)
• Graph Condensation via Receptive Field Distribution Matching [61.71711656856704]
  This paper focuses on creating a small graph to represent the original graph, so that GNNs trained on the size-reduced graph can make accurate predictions. We view the original graph as a distribution of receptive fields and aim to synthesize a small graph whose receptive fields share a similar distribution.
  arXiv  Detail & Related papers  (2022-06-28T02:10:05Z)
• Learning Graph Structure from Convolutional Mixtures [119.45320143101381]
  We propose a graph convolutional relationship between the observed and latent graphs, and formulate the graph learning task as a network inverse (deconvolution) problem. In lieu of eigendecomposition-based spectral methods, we unroll and truncate proximal gradient iterations to arrive at a parameterized neural network architecture that we call a Graph Deconvolution Network (GDN) GDNs can learn a distribution of graphs in a supervised fashion, perform link prediction or edge-weight regression tasks by adapting the loss function, and they are inherently inductive.
  arXiv  Detail & Related papers  (2022-05-19T14:08:15Z)
• Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations [57.15855198512551]
  We propose a novel score-based generative model for graphs with a continuous-time framework. We show that our method is able to generate molecules that lie close to the training distribution yet do not violate the chemical valency rule.
  arXiv  Detail & Related papers  (2022-02-05T08:21:04Z)
• Non-separable Spatio-temporal Graph Kernels via SPDEs [69.4678086015418]
  A lack of justified graph kernels for principled-temporal modelling has held back their use in graph problems.<n>We leverage a link between partial differential equations (SPDEs) and onsepa-temporal graphs, introduce a framework for deriving graph kernels via SPDEs.<n>We show that by providing novel tools for GP modelling on graphs, we outperform pre-existing graph kernels in real-world applications.
  arXiv  Detail & Related papers  (2021-11-16T14:53:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.