KoopmanFlow: Spectrally Decoupled Generative Control Policy via Koopman Structural Bias
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866917341504208896 |
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| author | Yao, Chengsi Wang, Ge Kang, Kai Yan, Shenhao Yang, Jiahao Feng, Fan Cai, Honghao Zeng, Xianxian Chen, Rongjun Zhao, Yiming Han, Yatong Li, Xi |
| author_facet | Yao, Chengsi Wang, Ge Kang, Kai Yan, Shenhao Yang, Jiahao Feng, Fan Cai, Honghao Zeng, Xianxian Chen, Rongjun Zhao, Yiming Han, Yatong Li, Xi |
| contents | Generative Control Policies (GCPs) show immense promise in robotic manipulation but struggle to simultaneously model stable global motions and high-frequency local corrections. While modern architectures extract multi-scale spatial features, their underlying Probability Flow ODEs apply a uniform temporal integration schedule. Compressed to a single step for real-time Receding Horizon Control (RHC), uniform ODE solvers mathematically smooth over sparse, high-frequency transients entangled within low-frequency steady states. To decouple these dynamics without accumulating pipelined errors, we introduce KoopmanFlow, a parameter-efficient generative policy guided by a Koopman-inspired structural inductive bias. Operating in a unified multimodal latent space with visual context, KoopmanFlow bifurcates generation at the terminal stage. Because visual conditioning occurs before spectral decomposition, both branches are visually guided yet temporally specialized. A macroscopic branch anchors slow-varying trajectories via single-step Consistency Training, while a transient branch uses Flow Matching to isolate high-frequency residuals stimulated by sudden visual cues (e.g., contacts or occlusions). Guided by an explicit spectral prior and optimized via a novel asymmetric consistency objective, KoopmanFlow establishes a fused co-training mechanism. This allows the variant branch to absorb localized dynamics without multi-stage error accumulation. Extensive experiments show KoopmanFlow significantly outperforms state-of-the-art baselines in contact-rich tasks requiring agile disturbance rejection. By trading a surplus latency buffer for a richer structural prior, KoopmanFlow achieves superior control fidelity and parameter efficiency within real-time deployment limits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13781 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | KoopmanFlow: Spectrally Decoupled Generative Control Policy via Koopman Structural Bias Yao, Chengsi Wang, Ge Kang, Kai Yan, Shenhao Yang, Jiahao Feng, Fan Cai, Honghao Zeng, Xianxian Chen, Rongjun Zhao, Yiming Han, Yatong Li, Xi Robotics Generative Control Policies (GCPs) show immense promise in robotic manipulation but struggle to simultaneously model stable global motions and high-frequency local corrections. While modern architectures extract multi-scale spatial features, their underlying Probability Flow ODEs apply a uniform temporal integration schedule. Compressed to a single step for real-time Receding Horizon Control (RHC), uniform ODE solvers mathematically smooth over sparse, high-frequency transients entangled within low-frequency steady states. To decouple these dynamics without accumulating pipelined errors, we introduce KoopmanFlow, a parameter-efficient generative policy guided by a Koopman-inspired structural inductive bias. Operating in a unified multimodal latent space with visual context, KoopmanFlow bifurcates generation at the terminal stage. Because visual conditioning occurs before spectral decomposition, both branches are visually guided yet temporally specialized. A macroscopic branch anchors slow-varying trajectories via single-step Consistency Training, while a transient branch uses Flow Matching to isolate high-frequency residuals stimulated by sudden visual cues (e.g., contacts or occlusions). Guided by an explicit spectral prior and optimized via a novel asymmetric consistency objective, KoopmanFlow establishes a fused co-training mechanism. This allows the variant branch to absorb localized dynamics without multi-stage error accumulation. Extensive experiments show KoopmanFlow significantly outperforms state-of-the-art baselines in contact-rich tasks requiring agile disturbance rejection. By trading a surplus latency buffer for a richer structural prior, KoopmanFlow achieves superior control fidelity and parameter efficiency within real-time deployment limits. |
| title | KoopmanFlow: Spectrally Decoupled Generative Control Policy via Koopman Structural Bias |
| topic | Robotics |
| url | https://arxiv.org/abs/2603.13781 |