Autonomous micro-mobility vehicles (MMVs) such as wheelchairs, scooters, and bicycles have the potential to improve mobility access and support safe low-speed transportation in pedestrian-shared spaces. Achieving MMV autonomy will require realistic, predictable MMV motion. However, many existing autonomous vehicle stacks rely on simplified kinematic models that fail to capture key MMV characteristics such as tire slip, friction, and wheel layouts, limiting realism and gradient-based optimization. In this paper, we explore differentiable formulations of dynamics models for autonomous micro-mobility systems. We first construct DiffKBM, a differentiable version of the kinematic bicycle model (KBM). Then, we introduce DiffGM3, a differentiable formulation of the General Micro-Mobility Model (GM3), a unified tire-based dynamics formulation for micro-mobility vehicles that supports a wide range of MMV configurations. DiffKBM and DiffGM3 enable end-to-end differentiable optimization through MMV dynamics, making them suitable for integration into differentiable autonomy stacks. We evaluate these dynamics models in both open-loop and closed-loop settings: (1) open-loop trajectory matching, where DiffKBM and DiffGM3 are integrated as a dynamics layer within DiffStack and optimized to reproduce real-world MMV trajectories, and (2) closed-loop autonomous navigation, where DiffKBM and DiffGM3 are paired with a differentiable MPC controller in CrowdNav pedestrian scenarios. In the open-loop setting, DiffGM3 outperforms DiffKBM in reproducing trajectories with improvements in ADE and NLL across bicycle, scooter, and motorcycle modes, and reductions in planning loss for bicycle and motorcycle trajectories. We also find that, in closed-loop settings, DiffGM3 improves on DiffKBM's CrowdNav performance by producing 55\% fewer collisions and a 75\% lower discomfort frequency for the bicycle mode.

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