Since prediction plays a significant role in enhancing the performance of decision making and planning procedures, the requirement of advanced methods of prediction becomes urgent. Although many literatures propose methods to make prediction on a single agent, there is still a challenging and open problem on how to make prediction for multi-agent systems. In this work, by leveraging the power of statistics and information theory, we propose a novel deep latent variable model based on Wasserstein auto-encoder, which is able to learn a complex probabilistic distribution. Models such as neural networks cannot guarantee the satisfaction of dynamic system constraints directly. Therefore, we also propose a novel generative model structure to enable our approach to satisfy the kinematic constraints automatically. We test our model on both numerical examples and a real-world application to demonstrate its accuracy and efficiency. The results show that the proposed model achieves a better prediction accuracy than the other state-of-the-art methods under common evaluation metrics. Moreover, we introduce statistics to evaluate if the generative model literally learns the interaction patterns between different agents in the environments.