Generative Diffusion Models of Stochastic Graph Signals

2026-07-07

AI Summary

Existing approaches struggle to effectively sample from the conditional distribution of stochastic graph signals, often being limited to regressing the conditional mean or relying on task-specific designs. This work proposes a unified framework for conditional graph signal generation based on denoising diffusion mechanisms. Its key innovation is the U-GNN architecture, which generalizes U-Net to the graph domain by employing learnable nested node selection matrices to enable multi-resolution encoding and decoding without explicit graph coarsening. The architecture further integrates stride-based graph convolutions and zero-padded upsampling operations. Evaluated on stock price forecasting and wireless resource allocation tasks, the proposed method significantly outperforms existing regression and generative baselines, demonstrating its effectiveness in modeling complex conditional distributions of graph signals.

Abstract

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.

Problem

• stochastic graph signals
• conditional generative modeling
• graph signal sampling
• diffusion models
• graph neural networks

Innovation

• diffusion models
• graph neural networks
• U-GNN
• conditional generation
• stochastic graph signals