In this paper we show how the task of motion tracking for physically simulated characters can be solved using supervised learning and optimizing a policy directly via back-propagation. To achieve this we make use of a world model trained to approximate a specific subset of the environment's transition function, effectively acting as a differentiable physics simulator through which the policy can be optimized to minimize the tracking error. Compared to popular model-free methods of physically simulated character control which primarily make use of Proximal Policy Optimization (PPO) we find direct optimization of the policy via our approach consistently achieves a higher quality of control in a shorter training time, with a reduced sensitivity to the rate of experience gathering, dataset size, and distribution.