Distributed Artificial Intelligence (AI) model training over mobile edge networks encounters significant challenges due to the data and resource heterogeneity of edge devices. The former hampers the convergence rate of the global model, while the latter diminishes the devices' resource utilization efficiency. In this paper, we propose a generative AI-empowered federated learning to address these challenges by leveraging the idea of FIlling the MIssing (FIMI) portion of local data. Specifically, FIMI can be considered as a resource-aware data augmentation method that effectively mitigates the data heterogeneity while ensuring efficient FL training. We first quantify the relationship between the training data amount and the learning performance. We then study the FIMI optimization problem with the objective of minimizing the device-side overall energy consumption subject to required learning performance constraints. The decomposition-based analysis and the cross-entropy searching method are leveraged to derive the solution, where each device is assigned suitable AI-synthetic data and resource utilization policy. Experiment results demonstrate that FIMI can save up to 50% of the device-side energy to achieve the target global test accuracy in comparison with the existing methods. Meanwhile, FIMI can significantly enhance the converged global accuracy under the non-independently-and-identically distribution (non-IID) data.