  Trajectory prediction and generation are vital for autonomous robots
navigating dynamic environments. While prior research has typically focused on
either prediction or generation, our approach unifies these tasks to provide a
versatile framework and achieve state-of-the-art performance. Diffusion models,
which are currently state-of-the-art for learned trajectory generation in
long-horizon planning and offline reinforcement learning tasks, rely on a
computationally intensive iterative sampling process. This slow process impedes
the dynamic capabilities of robotic systems. In contrast, we introduce
Trajectory Conditional Flow Matching (T-CFM), a novel data-driven approach that
utilizes flow matching techniques to learn a solver time-varying vector field
for efficient and fast trajectory generation. We demonstrate the effectiveness
of T-CFM on three separate tasks: adversarial tracking, real-world aircraft
trajectory forecasting, and long-horizon planning. Our model outperforms
state-of-the-art baselines with an increase of 35% in predictive accuracy and
142% increase in planning performance. Notably, T-CFM achieves up to
100$\times$ speed-up compared to diffusion-based models without sacrificing
accuracy, which is crucial for real-time decision making in robotics.
