Physical intelligence requires embodied agents to ground language in observations and execute actions while retaining useful skills. Vision-language-action (VLA) policies offer a shared interface, but task-specific post-training often produces separate specialists. Consolidation is difficult: mixed-task reinforcement learning provides sparse trajectory-level credit, while offline distillation may miss student-visited observations and endpoint distillation does not supervise intermediate action-generation states. We introduce VLA Multi-teacher On-Policy Distillation (VLA-MOPD), a protocol for consolidating flow-matching VLA specialists. After acquiring task or suite experts, a shared student collects robot rollouts and queries the instruction-routed frozen teacher at each visited observation and intermediate ordinary differential equation (ODE) state. Detached per-flow-step transition targets supervise valid action chunks through a masked local matching loss; an optional reference-policy term supports retention on other tasks. Starting from one trajectory per LIBERO task, VLA-MOPD raises mean success-once from 75.4% to 98.9%, compared with 98.15% for endpoint action distillation. It improves mean RoboTwin 2.0 success from 73.0% to 89.3%; on a Piper robot, two consolidation rounds improve average success from 70.0% to 90.0%. In a near-matched Spatial-adaptation study, reference matching limits the Object suite decrease to 3.0 points, versus 13.2 without the reference term.

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