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Building reliable object detectors that can detect out-of-distribution (OOD) objects is critical yet underexplored. One of the key challenges is that models lack supervision signals from unknown data, producing overconfident predictions on OOD objects. We propose a new unknown-aware object detection framework through Spatial-Temporal Unknown Distillation (STUD), which distills unknown objects from videos in the wild and meaningfully regularizes the model's decision boundary. STUD first identifies the unknown candidate object proposals in the spatial dimension, and then aggregates the candidates across multiple video frames to form a diverse set of unknown objects near the decision boundary. Alongside, we employ an energy-based uncertainty regularization loss, which contrastively shapes the uncertainty space between the in-distribution and distilled unknown objects. STUD establishes the state-of-the-art performance on OOD detection tasks for object detection, reducing the FPR95 score by over 10% compared to the previous best method.