In this paper, we present SOCIA-$\nabla$, a diagnosis-driven multi-agent framework for automated simulator-code construction. SOCIA-$\nabla$ iteratively refines executable simulator code within a textual computation graph, where LLM-driven agents synthesize, execute, evaluate, diagnose, and repair simulators. A grounded simulator blueprint attributes behavioral residuals to candidate mechanisms and their spatial or interaction contexts, which are then converted into localized textual repair signals with history-aware memory and constraint projection. We evaluate SOCIA-$\nabla$ on the real-world LLMob personal-mobility benchmark and a controlled semi-synthetic geo-social mask-adoption benchmark. Across in-distribution simulation, out-of-distribution what-if generation, and geo-social diffusion, SOCIA-$\nabla$ achieves the strongest overall simulator fidelity. SOCIA-$\nabla$'s code and data are publicly available at https://github.com/cruiseresearchgroup/SOCIA-Nabla.

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