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Due to the limited availability of actual large-scale datasets, realistic synthetic trajectory data play a crucial role in various research domains, including spatiotemporal data mining and data management, and domain-driven research related to transportation planning and urban analytics. Existing generation methods rely on predefined heuristics and cannot learn the unknown underlying generative mechanisms. This work introduces two end-to-end approaches for trajectory generation. The first approach comprises deep generative VAE-like models that factorize global and local semantics (habits vs. random routing change). We further enhance this approach by developing novel inference strategies based on variational inference and constrained optimization to ensure the validity of spatiotemporal aspects. This novel deep neural network architecture implements generative and inference models with dynamic latent priors. The second approach introduces a language model (LM) inspired generation as another benchmarking and foundational approach. The LM-inspired approach conceptualizes trajectories as sentences with the aim of predicting the likelihood of subsequent locations on a trajectory, given the locations as context. As a result, the LM-inspired approach implicitly learns the inherent spatiotemporal structure and other embedded semantics within the trajectories. These proposed methods demonstrate substantial quantitative and qualitative improvements over existing approaches, as evidenced by extensive experimental evaluations.