Diffusion Models Generate Stochastic Graph Signals for Complex Tasks

Many machine learning tasks on graphs, such as recommender systems, financial market forecasting, and wireless network optimization, rely on sampling stochastic signals supported on a graph. Current methods often create intricate, application-specific designs that tend to predict a conditional mean rather than sampling from the full conditional distribution. This research unifies these diverse problems under a single framework: conditional graph signal generative modeling, tackled using denoising diffusion models. The core of the approach involves learning a reverse diffusion process, which is parameterized by graph neural networks (GNNs). This process is designed to draw graph signals conditioned directly on the graph's topology and any available node-feature side information. A key innovation is the introduction of the U-Graph Neural Network (U-GNN) architecture. The U-GNN extends the well-known image-convolutional U-Net to handle graph-structured signals, performing multi-resolution encoder-decoder processing. Its pooling and unpooling operations are implemented as learned node selections and zero-padded lifting of coarse signals, bypassing explicit graph coarsening at each resolution. The method's efficacy is demonstrated through extensive numerical experiments on two distinct generative tasks: predicting stock prices and optimizing wireless resource allocation, showcasing its versatility and performance in both domains.