Data-driven methods have great advantages in modeling complicated human behavioral dynamics and dealing with many human-robot interaction applications. However, collecting massive and annotated real-world human datasets has been a laborious task, especially for highly interactive scenarios. On the other hand, algorithmic data generation methods are usually limited by their model capacities, making them unable to offer realistic and diverse data needed by various application users. In this work, we study trajectory-level data generation for multi-human or human-robot interaction scenarios and propose a learning-based automatic trajectory generation model, which we call Multi-Agent TRajectory generation with dIverse conteXts (MATRIX). MATRIX is capable of generating interactive human behaviors in realistic diverse contexts. We achieve this goal by modeling the explicit and interpretable objectives so that MATRIX can generate human motions based on diverse destinations and heterogeneous behaviors. We carried out extensive comparison and ablation studies to illustrate the effectiveness of our approach across various metrics. We also presented experiments that demonstrate the capability of MATRIX to serve as data augmentation for imitation-based motion planning.