Artificial Intelligence Generated Content (AIGC) powered by Generative Diffusion Models (GDMs) has emerged as a transformative paradigm for automated content creation. To satisfy the stringent latency requirements of AIGC services in many edge intelligence scenarios (e.g., smart cities), Mobile Edge Computing (MEC) provides critical computational support by deploying GDMs at edge servers (ES) close to end users. This paper investigates an MEC-enabled AIGC network comprising multiple ES, wireless access points (APs), and mobile users (UEs) with heterogeneous latency and accuracy demands. We formulate a Joint Communication Association and Computation Offloading (JCACO) game, where each UE strategically selects its serving AP, ES, and inference steps to minimize the overall service completion time while meeting accuracy constraints. The problem is challenging due to the network dynamics and the incomplete information. We prove that the JCACO game is a potential game under both complete and stochastic information settings, ensuring the existence of Nash Equilibrium (NE) in both cases. To derive the NE efficiently, we develop a distributed Multi-Agent Stochastic Learning (MASL) algorithm that provably converges to the NE with strict performance guarantees. Unlike conventional best-response schemes, MASL requires neither the knowledge of other players' strategies nor global network information, making it fully distributed and adaptive to dynamic environments. We further provide a strict theoretical convergence analysis for MASL by using Ordinary Differential Equations (ODEs). Simulation results demonstrate that MASL significantly reduces service completion time compared with benchmark methods while satisfying accuracy constraints, confirming its effectiveness and practicality for real-world MEC-enabled AIGC networks.

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