DiffLyap-MEC: Diffusion-Guided Lyapunov Optimization for Joint Offloading, Semantic Compression, and Resource Allocation in ISAC-Enabled 6G Edge Computing

Integrated sensing and communication (ISAC), semantic communication, and mobile edge computing (MEC) jointly create a high-dimensional, non-convex, and time-coupled resource allocation problem in sixth-generation (6G) networks that existing heuristics and deep reinforcement learning (DRL) methods solve either slowly or without stability guarantees. This study proposes DiffLyap-MEC, a framework that couples generative diffusion models with Lyapunov drift-plus-penalty optimization for online decision-making in ISAC-enabled multi-user, multi-server MEC systems. A mixed-integer non-linear program jointly optimizes task offloading ratios, semantic compression levels, ISAC beamforming, and edge CPU and bandwidth allocation under long-term energy-queue stability and sensing-accuracy constraints. Lyapunov theory decouples the long-term problem into per-slot subproblems with a provable O(1/V) optimality versus backlog trade-off, and a conditional denoising diffusion policy generates near-optimal offloading and beamforming decisions in a fixed number of reverse steps, with a closed-form water-filling solution embedded as a differentiable layer. Bounds on queue stability, policy convergence, and the distortion versus latency trade-off are derived. Simulations with 3GPP-compliant channel models show that DiffLyap-MEC reduces average end-to-end latency by 27.3% to 33.9% and energy consumption by 22.2% to 27.1% relative to proximal policy optimization (PPO), soft actor–critic (SAC), and Lyapunov-only baselines while maintaining 97.3% sensing accuracy at 0.74 ms inference time per slot on an NVIDIA RTX A6000 GPU with a batch size of one.