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

Flow-based policies for language-conditioned multi-task manipulation commonly share a single $\text{Gaussian}$ source prior and a common linear transport path across tasks. However, reliably executing multi-task with distinct motion requirements remains challenging for a shared policy. We introduce $\text{TOPS}$ ($\text{T}$ask-$\text{O}$riented $\text{P}$riors and $\text{S}$chedules), 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 $\text{Gaussian}$ 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 ${\pi }_{0.5}$ 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 upper-drawer opening task.