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Currently, the generative model has garnered considerable attention due to its application in addressing the challenge of scarcity of abnormal samples in the industrial Internet of Things (IoT). However, challenges persist regarding the edge deployment of generative models and the optimization of joint edge AI-generated content (AIGC) tasks. In this paper, we focus on the edge optimization of AIGC task execution and propose GMEL, a generative model-driven industrial AIGC collaborative edge learning framework. This framework aims to facilitate efficient few-shot learning by leveraging realistic sample synthesis and edge-based optimization capabilities. First, a multi-task AIGC computational offloading model is presented to ensure the efficient execution of heterogeneous AIGC tasks on edge servers. Then, we propose an attention-enhanced multi-agent reinforcement learning (AMARL) algorithm aimed at refining offloading policies within the IoT system, thereby supporting generative model-driven edge learning. Finally, our experimental results demonstrate the effectiveness of the proposed algorithm in optimizing the total system latency of the edge-based AIGC task completion.