# Graph-Aware Diffusion for Signal Generation

arXiv: https://arxiv.org/abs/2510.05036 · HTML: https://mlsanity.com/paper/2510.05036/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 37 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 22 of 22)

- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directions](https://mlsanity.com/paper/2109.12843/) (2021)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [Generative Diffusion Models on Graphs: Methods and Applications](https://mlsanity.com/paper/2302.02591/) (2023)
- [Estimating High Order Gradients of the Data Distribution by Denoising](https://mlsanity.com/paper/2111.04726/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Autoregressive Moving Average Graph Filtering](https://mlsanity.com/paper/1602.04436/) (2016)
- [Blurring-Sharpening Process Models for Collaborative Filtering](https://mlsanity.com/paper/2211.09324/) (2022)
- [Graph Unrolling Networks: Interpretable Neural Networks for Graph Signal Denoising](https://mlsanity.com/paper/2006.01301/) (2020)
- [A User Guide to Low-Pass Graph Signal Processing and its Applications](https://mlsanity.com/paper/2008.01305/) (2020)
- [Graph Signal Diffusion Model for Collaborative Filtering](https://mlsanity.com/paper/2311.08744/) (2023)
- [Robust Graph Filter Identification and Graph Denoising from Signal Observations](https://mlsanity.com/paper/2210.08488/) (2022)
- [Graph Signal Restoration Using Nested Deep Algorithm Unrolling](https://mlsanity.com/paper/2106.15910/) (2021)
- [Understanding Graph Neural Networks from Graph Signal Denoising Perspectives](https://mlsanity.com/paper/2006.04386/) (2020)
- [Bayesian Estimation of Graph Signals](https://mlsanity.com/paper/2103.15520/) (2021)
- [DiffSTOCK: Probabilistic relational Stock Market Predictions using Diffusion Models](https://mlsanity.com/paper/2403.14063/) (2024)
- [S-Diff: An Anisotropic Diffusion Model for Collaborative Filtering in Spectral Domain](https://mlsanity.com/paper/2501.00384/) (2024)
- [Equivariant Blurring Diffusion for Hierarchical Molecular Conformer Generation](https://mlsanity.com/paper/2410.20255/) (2024)
- [Point Cloud Resampling with Learnable Heat Diffusion](https://mlsanity.com/paper/2411.14120/) (2024)

## Built on by (most cited first, 8 of 8)

- [Generative Diffusion Models of Stochastic Graph Signals](https://mlsanity.com/paper/2607.06833/) (2026)
- [Stability of Flow Models for Graph Signals](https://mlsanity.com/paper/2607.07510/) (2026)
- [DiPhon: Diffusion on Graphons for Scalable Graph Generation](https://mlsanity.com/paper/2607.07232/) (2026)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)
- [Stable Filters for Generative Modeling of Graph Signals](https://mlsanity.com/paper/2609.18759/) (2026)
- [Graph-Spectral Flow Matching for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2609.36765/) (2026)
- [Graph Residual Conjugate Diffusion: SNR-Equalized Heat Flow for Graph Signals](https://mlsanity.com/paper/2609.39658/) (2026)
- [Colored Graph Signal Diffusion Models](https://mlsanity.com/paper/2610.17282/) (2026)

## Abstract (arXiv)

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.