Graph Signal Diffusion Models for Wireless Resource Allocation

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.

Generative Diffusion Models for Resource Allocation in Wireless Networks

This paper proposes a supervised training algorithm for learning stochastic resource allocation policies with generative diffusion models (GDMs). We formulate the allocation problem as the maximization of an ergodic utility function subject to ergodic Quality of Service (QoS) constraints. Given samples from a stochastic expert policy that yields a near-optimal solution to the problem, we train a GDM policy to imitate the expert and generate new samples from the optimal distribution. We achieve near-optimal performance through sequential execution of the generated samples. To enable generalization to a family of network configurations, we parameterize the backward diffusion process with a graph neural network (GNN) architecture. We present numerical results in a case study of power control in multi-user interference networks.