KoopmanFlow: Spectrally Decoupled Generative Control Policy via Koopman Structural Bias

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.

SVLL: Staged Vision-Language Learning for Physically Grounded Embodied Task Planning

Embodied task planning demands vision-language models to generate action sequences that are both visually grounded and causally coherent over time. However, existing training paradigms face a critical trade-off: joint end-to-end training often leads to premature temporal binding, while standard reinforcement learning methods suffer from optimization instability. To bridge this gap, we present Staged Vision-Language Learning (SVLL), a unified three-stage framework for robust, physically-grounded embodied planning. In the first two stages, SVLL decouples spatial grounding from temporal reasoning, establishing robust visual dependency before introducing sequential action history. In the final stage, we identify a key limitation of standard Direct Preference Optimization (DPO), its purely relative nature -- optimizing only the preference gap between winning and losing trajectories while neglecting absolute likelihood constraints on optimal path, often yields unsafe or hallucinated behaviors. To address this, we further introduce Bias-DPO, a novel alignment objective that injects an inductive bias toward expert trajectories by explicitly maximizing likelihood on ground-truth actions while penalizing overconfident hallucinations. By anchoring the policy to the expert manifold and mitigating causal misalignment, SVLL, powered by Bias-DPO, ensures strict adherence to environmental affordances and effectively suppresses physically impossible shortcuts. Finally, extensive experiments on the interactive AI2-THOR benchmark and real-world robotic deployments demonstrate that SVLL outperforms both state-of-the-art open-source (e.g., Qwen2.5-VL-7B) and closed-source models (e.g., GPT-4o, Gemini-2.0-flash) in task success rate, while significantly reducing physical constraint violations.