# Fast Flow-based Visuomotor Policies via Conditional Optimal Transport Couplings

## Motivation

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## Abstract

Diffusion and flow matching policies have recently demonstrated remarkable performance in robotic applications by accurately capturing multimodal robot trajectory distributions. However, their computationally expensive inference, due to the numerical integration of an ODE or SDE, limits their applicability as real-time controllers for robots. We introduce a methodology that utilizes conditional Optimal Transport couplings between noise and samples to enforce straight solutions in the flow ODE for robot action generation tasks. We show that naively coupling noise and samples fails in conditional tasks and propose incorporating condition variables into the coupling process to improve few-step performance. The proposed few-step policy achieves a 4% higher success rate with a 10x speed-up compared to Diffusion Policy on a diverse set of simulation tasks. Moreover, it produces high-quality and diverse action trajectories within 1-2 steps on a set of real-world robot tasks. Our method also retains the same training complexity as Diffusion Policy and vanilla Flow Matching, in contrast to distillation-based approaches.

## Real-world experiments

COT Policy solves real-world tasks with 1–2 NFE while CFM often requires more than 10.

CFM Policy
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NFE= 1
COT Policy (ours)
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NFE = 1
CFM Policy
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NFE= 1
COT Policy (Ours)
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NFE = 1

COT Policy is able to uncover multiple modes with NFE=1 and adapt to disturbances in real-time.

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Moreover, COT couplings result in policies that solve complex and long horizon tasks using only a few NFE.

COT Policy - NFE=2
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COT Policy - NFE=5
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