# Graph Signal Generative Diffusion Models

arXiv: https://arxiv.org/abs/2509.17250 · HTML: https://mlsanity.com/paper/2509.17250/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 21 Sep 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [Graph Neural Networks: Architectures, Stability and Transferability](https://mlsanity.com/paper/2008.01767/) (2020)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Denoising Diffusion Recommender Model](https://mlsanity.com/paper/2401.06982/) (2024)
- [Graph Signal Diffusion Model for Collaborative Filtering](https://mlsanity.com/paper/2311.08744/) (2023)
- [Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning](https://mlsanity.com/paper/2310.17360/) (2023)
- [Conditional Denoising Diffusion Probabilistic Models for Data Reconstruction Enhancement in Wireless Communications](https://mlsanity.com/paper/2310.19460/) (2023)
- [DGDNN: Decoupled Graph Diffusion Neural Network for Stock Movement Prediction](https://mlsanity.com/paper/2401.01846/) (2024)
- [DiffSTOCK: Probabilistic relational Stock Market Predictions using Diffusion Models](https://mlsanity.com/paper/2403.14063/) (2024)
- [Generative Diffusion Models for Resource Allocation in Wireless Networks](https://mlsanity.com/paper/2504.20277/) (2025)

## Built on by (most cited first, 5 of 5)

- [Graph Signal Diffusion Models for Wireless Resource Allocation](https://mlsanity.com/paper/2604.05175/) (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)
- [Graph-Spectral Flow Matching for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2609.36765/) (2026)

## Abstract (arXiv)

We introduce U-shaped encoder-decoder graph neural networks (U-GNNs) for stochastic graph signal generation using denoising diffusion processes. The architecture learns node features at different resolutions with skip connections between the encoder and decoder paths, analogous to the convolutional U-Net for image generation. The U-GNN is prominent for a pooling operation that leverages zero-padding and avoids arbitrary graph coarsening, with graph convolutions layered on top to capture local dependencies. This technique permits learning feature embeddings for sampled nodes at deeper levels of the architecture that remain convolutional with respect to the original graph. Applied to stock price prediction -- where deterministic forecasts struggle to capture uncertainties and tail events that are paramount -- we demonstrate the effectiveness of the diffusion model in probabilistic forecasting of stock prices.