Generating realistic simulations is critical for autonomous system applications such as self-driving and human-robot interactions. However, autonomous driving simulators nowadays still have difficulty in generating controllable, diverse, and rule-compliant behaviors for road participants: Rule-based models cannot produce diverse behaviors and require careful tuning, whereas learning-based methods imitate the policy from data but are not designed to follow the rules explicitly. Besides, the real-world datasets are by nature ``single-outcome", making the learning method hard to generate diverse behaviors. In this paper, we leverage Signal Temporal Logic (STL) and diffusion models to learn controllable, diverse, and rule-aware policy. We first calibrate the STL on the real-world data, then generate diverse synthetic data using trajectory optimization, and finally learn the rectified diffusion policy on the augmented dataset. We test our approach on the NuScenes dataset and show that our approach can achieve the most diverse rule-compliant trajectories compared to other baselines, with a runtime 1/17X to the second-best approach. In the closed-loop testing, our approach reaches the highest diversity, rule satisfaction rate, and the least collision rate. A case study also shows that our approach can generate varied characteristics conditional on different STL parameters. The annotation tool, augmented dataset, and code are available at https://github.com/mengyuest/pSTL-diffusion-policy.
