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We propose advances that address two key challenges in future trajectory prediction: (i) multimodality in both training data and predictions and (ii) constant time inference regardless of number of agents. Existing trajectory predictions are fundamentally limited by lack of diversity in training data, which is difficult to acquire with sufficient coverage of possible modes. Our first contribution is an automatic method to simulate diverse trajectories in the top-view. It uses pre-existing datasets and maps as initialization, mines existing trajectories to represent realistic driving behaviors and uses a multi-agent vehicle dynamics simulator to generate diverse new trajectories that cover various modes and are consistent with scene layout constraints. Our second contribution is a novel method that generates diverse predictions while accounting for scene semantics and multi-agent interactions, with constant-time inference independent of the number of agents. We propose a convLSTM with novel state pooling operations and losses to predict scene-consistent states of multiple agents in a single forward pass, along with a CVAE for diversity. We validate our proposed multi-agent trajectory prediction approach by training and testing on the proposed simulated dataset and existing real datasets of traffic scenes. In both cases, our approach outperforms SOTA methods by a large margin, highlighting the benefits of both our diverse dataset simulation and constant-time diverse trajectory prediction methods.