TOPS: Reshaping Flow Source and Transport for Multi-Task Robot Manipulation

Flow-based policies for language-conditioned multi-task manipulation commonly share a single Gaussian source prior and a common linear transport path across tasks. However, reliably executing multiple tasks with distinct motion requirements remains challenging for a shared policy. We introduce TOPS (Task-Oriented Priors and Schedules), which adapts the flow source prior and interpolation schedule to each task without modifying the network architecture. TOPS first constructs multimodal task sources from reverse-mapped expert action sequences, allowing language instructions to select where generation begins. Guided by source-target covariance mismatch, it then slows the transition toward expert actions early in denoising and accelerates it later along directions requiring expansion. Under a Gaussian endpoint model, our analysis shows that this schedule adjustment can lower an upper bound on velocity-prediction risk. Experiments on LIBERO, LIBERO-Plus, and CALVIN demonstrate improved performance across in-distribution, perturbation and cross-environment settings, alongside better data efficiency. Using one integration step, TOPS raises LIBERO-10 success from $53.44%$ to $69.67%$ compared with ten-step Standard Flow Matching (FM), while reducing inference time to approximately one-sixth of the baseline. TOPS also yields consistent gains when transferred to the large-scale flow-based π0.5 policy across all four evaluated settings. Real-world experiments further demonstrate improved task success, including an increase from $20%$ with standard FM to $80%$ with TOPS on the upper-drawer opening task.