Generative Artificial Intelligence (GAI) shows remarkable productivity and creativity in Mobile Edge Networks, such as the metaverse and the Industrial Internet of Things. Federated learning is a promising technique for effectively training GAI models in mobile edge networks due to its data distribution. However, there is a notable issue with communication consumption when training large GAI models like generative diffusion models in mobile edge networks. Additionally, the substantial energy consumption associated with training diffusion-based models, along with the limited resources of edge devices and complexities of network environments, pose challenges for improving the training efficiency of GAI models. To address this challenge, we propose an on-demand quantized energy-efficient federated diffusion approach for mobile edge networks. Specifically, we first design a dynamic quantized federated diffusion training scheme considering various demands from the edge devices. Then, we study an energy efficiency problem based on specific quantization requirements. Numerical results show that our proposed method significantly reduces system energy consumption and transmitted model size compared to both baseline federated diffusion and fixed quantized federated diffusion methods while effectively maintaining reasonable quality and diversity of generated data.

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