With the rapid convergence of artificial intelligence and mobile edge computing, edge intelligence is rapidly developing towards multi-dimensional perception and endogenous intelligence. As a promising enabling technology in edge intelligence, Artificial Intelligence Generated Content (AIGC) can provide mobile users with a variety of creative generation and personalized services, and further empower the paradigm shift of edge intelligence towards edge endogenous intelligence with its powerful reasoning and generalization capabilities. However, the large-scale parameters and fine-tuning process of AIGC make the existing task offloading schemes inappropriate in AIGC-empowered edge intelligence due to their high energy consumption and long waiting time. In this paper, we propose an energy-efficient task offloading scheme for AIGC-empowered edge intelligence. By considering the time cost and energy cost of the model fine-tuning process, the proposed scheme can accurately select the most suitable edge server and model to perform AIGC tasks, which further improves energy efficiency, service quality and user experience. Simulation results demonstrate that the proposed framework effectively minimizes the AIGC service failure rate and user waiting time compared to the baseline while ensuring efficient energy utilization.