Don't Throw Away the Solution: Training-Free Acceleration of Flow-Based Robot Policies

Standard samplers for flow-based robot policies generate each action chunk by sequential denoising and discard the solver trajectory at every replan, even though consecutive control cycles solve closely related problems. We introduce RePIC, a training-free sampler that turns this discarded trajectory into the initialization of the next solve. After an action prefix is executed, RePIC shifts the cached trajectory to the new horizon and re-aligns it to fresh noise with a closed-form correction that preserves the clean-action endpoint and needs no network evaluation. The pretrained velocity network then refines all transferred states under the new observation through batched fixed-point updates on the original integration grid, so an accurate initialization is converted into fewer sequential network calls. On Fast-WAM, RePIC reduces sequential calls per chunk from 10 to 2.2-2.6 and action-generation latency from 578 to 218ms on RoboTwin2.0 ($2.66\times$) and from 564 to 205ms on LIBERO ($2.75\times$) at comparable success; with system optimizations, RePIC-Flash reaches $5.71\times$. The same sampler accelerates ${\pi }_{0.5}$ and GR00T N1.5 by $1.14\times$ and $1.68\times$ without retraining. Transferred drafts start $24\times$ closer to the serial solution on the carried action steps, and on a physical robot Fast-WAM with RePIC succeeds in $77.5\%$ versus $66.3\%$ for the original sampler. These results show that the numerical path of a previous solve is a reusable resource for fast robot control. Code will be made publicly available.