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Behavior prediction models have proliferated in recent years, especially in the popular real-world robotics application of autonomous driving, where representing the distribution over possible futures of moving agents is essential for safe and comfortable motion planning. In these models, the choice of coordinate frames to represent inputs and outputs has crucial trade offs which broadly fall into one of two categories. Agent-centric models transform inputs and perform inference in agent-centric coordinates. These models are intrinsically invariant to translation and rotation between scene elements, are best-performing on public leaderboards, but scale quadratically with the number of agents and scene elements. Scene-centric models use a fixed coordinate system to process all agents. This gives them the advantage of sharing representations among all agents, offering efficient amortized inference computation which scales linearly with the number of agents. However, these models have to learn invariance to translation and rotation between scene elements, and typically underperform agent-centric models. In this work, we develop knowledge distillation techniques between probabilistic motion forecasting models, and apply these techniques to close the gap in performance between agent-centric and scene-centric models. This improves scene-centric model performance by 13.2% on the public Argoverse benchmark, 7.8% on Waymo Open Dataset and up to 9.4% on a large In-House dataset. These improved scene-centric models rank highly in public leaderboards and are up to 15 times more efficient than their agent-centric teacher counterparts in busy scenes.