Existing imitation learning (IL) methods such as inverse reinforcement learning (IRL) usually have a double-loop training process, alternating between learning a reward function and a policy and tend to suffer long training time and high variance. In this work, we identify the benefits of differentiable physics simulators and propose a new IL method, i.e., Imitation Learning as State Matching via Differentiable Physics (ILD), which gets rid of the double-loop design and achieves significant improvements in final performance, convergence speed, and stability. The proposed ILD incorporates the differentiable physics simulator as a physics prior into its computational graph for policy learning. ILD unrolls the dynamics by sampling actions from a parameterized policy and minimizing the distance between the expert trajectory and the agent trajectory. It back-propagates the gradient into the policy via temporal physics operators, which improves the transferability to unseen environments and yields higher final performance. ILD has a single-loop structure that stabilizes and speeds up training. It dynamically selects learning objectives for each state during optimization to simplify the complex optimization land-scape. Experiments show that ILD outperforms state-of-the-art methods in continuous control tasks with Brax, and can be applied to deformable object manipulation tasks, generalized to unseen configurations.11The link to the code: https://github.com/sail-sg/ILD