# Generative Diffusion Models of Stochastic Graph Signals

arXiv: https://arxiv.org/abs/2607.06833 · HTML: https://mlsanity.com/paper/2607.06833/

## Key facts

- Cited by 2 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 33 of its 44 references that are in the map.
- First posted on arXiv 7 Jul 2026.

## 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, 30 of 33)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement](https://mlsanity.com/paper/1903.06059/) (2019)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks](https://mlsanity.com/paper/1909.01865/) (2019)
- [UltraGCN: Ultra Simplification of Graph Convolutional Networks for Recommendation](https://mlsanity.com/paper/2110.15114/) (2021)
- [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)
- [Graph Neural Networks for Wireless Communications: From Theory to Practice](https://mlsanity.com/paper/2203.10800/) (2022)
- [Stationary signal processing on graphs](https://mlsanity.com/paper/1601.02522/) (2016)
- [Personalized Graph Signal Processing for Collaborative Filtering](https://mlsanity.com/paper/2302.02113/) (2023)
- [Link Scheduling using Graph Neural Networks](https://mlsanity.com/paper/2109.05536/) (2021)
- [DiffSG: A Generative Solver for Network Optimization with Diffusion Model](https://mlsanity.com/paper/2408.06701/) (2024)
- [Diffusion Model Based Resource Allocation Strategy in Ultra-Reliable Wireless Networked Control Systems](https://mlsanity.com/paper/2407.15784/) (2024)
- [DiffSTOCK: Probabilistic relational Stock Market Predictions using Diffusion Models](https://mlsanity.com/paper/2403.14063/) (2024)
- [Graph-Aware Diffusion for Signal Generation](https://mlsanity.com/paper/2510.05036/) (2025)
- [Deep Graph Unfolding for Beamforming in MU-MIMO Interference Networks](https://mlsanity.com/paper/2304.00446/) (2023)
- [Generative Diffusion Models for Resource Allocation in Wireless Networks](https://mlsanity.com/paper/2504.20277/) (2025)

## Built on by (most cited first, 2 of 2)

- [Stable Filters for Generative Modeling of Graph Signals](https://mlsanity.com/paper/2609.18759/) (2026)
- [Colored Graph Signal Diffusion Models](https://mlsanity.com/paper/2610.17282/) (2026)

## Abstract (arXiv)

Sampling stochastic signals supported on a graph underlies many graph machine learning tasks, including recommender systems, forecasting in financial markets, and wireless network optimization. In these settings, the target signals are realizations of unknown conditional distributions. However, prevailing approaches rely mostly on intricate, application-tailored designs that often regress to a conditional mean instead of sampling from the conditional law. This paper unifies such problems as conditional graph signal generative modeling and tackles them with a single denoising diffusion framework. We learn a reverse diffusion process, parametrized by graph neural networks (GNNs), that draws graph signals conditioned directly on the graph topology and on node-feature side information. The reverse process is realized by a novel architecture, the U-Graph Neural Network (U-GNN), which generalizes the image-convolutional U-Net to graph-structured signals. The U-GNN performs multi-resolution encoder--decoder processing in which pooling and unpooling reduce to a learned node selection, expressed by nested selection matrices, and a zero-padded lifting of coarse signals back to the full node set. The graph convolutions are carried out on the original graph, with a stride that sets their hop reach, so the U-GNN bypasses explicit graph coarsening at every resolution. We demonstrate our method on two generative tasks: stock price forecasting and optimal wireless resource allocation, with extensive numerical results in both domains.