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The rapid advancement of Artificial Intelligence (AI) has introduced Deep Neural Network (DNN)-based tasks to the ecosystem of vehicular networks. These tasks are often computation-intensive, requiring substantial computation resources, which are beyond the capability of a single vehicle. To address this challenge, Vehicular Edge Computing (VEC) has emerged as a solution, offering computing services for DNN-based tasks through resource pooling via Vehicle-to-Vehicle/Infrastructure (V2V/V2I) communications. In this paper, we formulate the problem of joint DNN partitioning, task offloading, and resource allocation in VEC as a dynamic long-term optimization. Our objective is to minimize the DNN-based task completion time while guaranteeing the system stability over time. To this end, we first leverage a Lyapunov optimization technique to decouple the original long-term optimization with stability constraints into a per-slot deterministic problem. Afterwards, we propose a Multi-Agent Diffusion-based Deep Reinforcement Learning (MAD2RL) algorithm, incorporating the innovative use of diffusion models to determine the optimal DNN partitioning and task offloading decisions. Furthermore, we integrate convex optimization techniques into MAD2RL as a subroutine to allocate computation resources, enhancing the learning efficiency. Through simulations under real-world movement traces of vehicles, we demonstrate the superior performance of our proposed algorithm compared to existing benchmark solutions.

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