Graph Signal Diffusion Models for Wireless Resource Allocation

Abstract: We consider constrained ergodic resource optimization in wireless networks with graph-structured interference. We train a diffusion model policy to match expert conditional distributions over resource allocations. By leveraging a primal-dual (expert) algorithm, we generate primal iterates that serve as draws from the corresponding expert conditionals for each training network instance. We view the allocations as stochastic graph signals supported on known channel state graphs. We implement the diffusion model architecture as a U-Net hierarchy of graph neural network (GNN) blocks, conditioned on the channel states and additional node states. At inference, the learned generative model amortizes the iterative expert policy by directly sampling allocation vectors from the near-optimal conditional distributions. In a power-control case study, we show that time-sharing the generated power allocations achieves near-optimal ergodic sum-rate utility and near-feasible ergodic minimum-rates, with strong generalization and transferability across network states.