Graph Signal Diffusion Models for Wireless Resource Allocation

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.

The aggressive densification of modern wireless networks necessitates judicious resource allocation to mitigate severe mutual interference. However, classical iterative algorithms remain computationally prohibitive for real-time applications requiring rapid responsiveness. While recent deep learning-based methods show promise, they typically function as task-specific solvers lacking the flexibility to adapt to different objectives and scenarios without expensive retraining. To address these limitations, we propose a graph foundation model for resource allocation (GFM-RA) based on a pre-training and fine-tuning paradigm to extract unified representations, thereby enabling rapid adaptation to different objectives and scenarios. Specifically, we introduce an interference-aware Transformer architecture with a bias projector that injects interference topologies into global attention mechanisms. Furthermore, we develop a hybrid self-supervised pre-training strategy that synergizes masked edge prediction with negative-free Teacher-Student contrastive learning, enabling the model to capture transferable structural representations from massive unlabeled datasets. Extensive experiments demonstrate that the proposed framework achieves state-of-the-art performance and scales effectively with increased model capacity. Crucially, leveraging its unified representations, the foundation model exhibits exceptional sample efficiency, enabling robust few-shot adaptation to diverse and unsupervised downstream objectives in out-of-distribution (OOD) scenarios. These results demonstrate the promise of pre-trained foundation models for adaptable wireless resource allocation and provide a strong foundation for future research on generalizable learning-based wireless optimization.

Graph Neural Networks (GNNs) have emerged as a powerful tool for wireless resource allocation that leverages the underlying graph structure of communication networks. Their transferability property enables models trained on small-scale graphs to generalize to large-scale deployments with little performance deterioration, a desirable property for currently growing networks. Wireless networks are sparse regimes, where a single node is connected to a small number of other users. This work establishes theoretical results for transferability of GNNs over graphs derived from sparse Random Geometric Graphs (RGGs). In particular, we focus on conflict graphs of RGGs used to model interference among links. Our approach considers the closeness between RGGs and Deterministic Grid Graphs (DGG) to establish bounds in the performance loss when a model is transferred across scales. We validate our theoretical findings through the problem of link scheduling, demonstrating that our learned policies consistently outperform existing benchmarks at scale. Finally, we examine the impact of our theoretical assumptions on empirical performance.