TILDE: Teacher-in-the-Loop Distillation from Embodied Foundation Models

Large-scale action pretraining equips Embodied Foundation Models (EFMs) with strong manipulation capabilities, with particular strengths in generalization and closed-loop robustness, but reproducing such pretraining requires substantial robot data and computation. To transfer these capabilities from pretrained EFMs to policies without action pretraining, we introduce TILDE (**T**eacher-**I**n-the-**L**oop **D**istillation from **E**FMs), which synergizes on-policy distillation at student-induced states with learning from teacher-executed recovery trajectories. We further propose AutoDAgger, an autonomous data aggregation pipeline in which a robotic reward model monitors task progress and triggers teacher intervention, thereby collecting recovery experience without human monitoring or manual control. AutoDAgger accelerates recovery-trajectory collection by more than $2\times$ compared with the human-in-the-loop method. By unifying learning from demonstrations, on-policy teacher supervision, and teacher's corrective behavior, TILDE improves task performance by up to $4.1\times$ over behavior cloning across three real-world tasks and supports effective cross-architecture distillation.