Imitation learning with diffusion models has advanced robotic control by capturing multi-modal action distributions. However, existing approaches typically treat observations as high-level conditioning inputs to the denoising network, rather than integrating them into the stochastic dynamics of the diffusion process itself. As a result, sampling must begin from random Gaussian noise, weakening the coupling between perception and control and often yielding suboptimal performance. W e introduce Bridge-Policy, a generative visuomotor policy that explicitly embeds observations within the stochastic differential equation via a diffusion-bridge formulation. By constructing an observation-informed trajectory, BridgePolicy enables sampling to start from a rich, informative prior rather than random noise, substantially improving precision and reliability in control. A key challenge is that classical diffusion bridges connect distributions with matched dimensionality, whereas robotic observations are heterogeneous and multi-modal and do not naturally align with the action space. T o address this, we design a multi-modal fusion module and a semantic aligner that unify visual and state inputs and align observation and action representations, making the bridge applicable to heterogeneous robot data. Extensive experiments across 52 simulation tasks on three benchmarks and five real-world tasks demonstrate that BridgePolicy consistently outperforms state-of-the-art generative policies.

In robot manipulation, robot learning has become a prevailing approach. However, generative models within this field face a fundamental trade-off between the slow, iterative sampling of diffusion models and the architectural constraints of faster Flow-based methods, which often rely on explicit consistency losses. To address these limitations, we introduce MP1, which pairs 3D point-cloud inputs with the MeanFlow paradigm to generate action trajectories in one network function evaluation (1-NFE). By directly learning the interval-averaged velocity via the "MeanFlow Identity", our policy avoids any additional consistency constraints. This formulation eliminates numerical ODE-solver errors during inference, yielding more precise trajectories. MP1 further incorporates CFG for improved trajectory controllability while retaining 1-NFE inference without reintroducing structural constraints. Because subtle scene-context variations are critical for robot learning, especially in few-shot learning, we introduce a lightweight Dispersive Loss that repels state embeddings during training, boosting generalization without slowing inference. We validate our method on the Adroit and Meta-World benchmarks, as well as in real-world scenarios. Experimental results show MP1 achieves superior average task success rates, outperforming DP3 by 10.2% and FlowPolicy by 7.3%. Its average inference time is only 6.8 ms-19x faster than DP3 and nearly 2x faster than FlowPolicy. Our project page is available at https://mp1-2254.github.io/, and the code can be accessed at https://github.com/LogSSim/MP1.

Flow-matching-based policies have recently emerged as a promising approach for learning-based robot manipulation, offering significant acceleration in action sampling compared to diffusion-based policies. However, conventional flow-matching methods struggle with multi-modality, often collapsing to averaged or ambiguous behaviors in complex manipulation tasks. To address this, we propose the Variational Flow-Matching Policy (VFP), which introduces a variational latent prior for mode-aware action generation and effectively captures both task-level and trajectory-level multi-modality. VFP further incorporates Kantorovich Optimal Transport (K-OT) for distribution-level alignment and utilizes a Mixture-of-Experts (MoE) decoder for mode specialization and efficient inference. We comprehensively evaluate VFP on 41 simulated tasks and 3 real-robot tasks, demonstrating its effectiveness and sampling efficiency in both simulated and real-world settings. Results show that VFP achieves a 49% relative improvement in task success rate over standard flow-based baselines in simulation, and further outperforms them on real-robot tasks, while still maintaining fast inference and a compact model size. More details are available on our project page: https://sites.google.com/view/varfp/

Robots can acquire complex manipulation skills by learning policies from expert demonstrations, which is often known as vision-based imitation learning. Generating policies based on diffusion and flow matching models has been shown to be effective, particularly in robotic manipulation tasks. However, recursion-based approaches are inference inefficient in working from noise distributions to policy distributions, posing a challenging trade-off between efficiency and quality. This motivates us to propose FlowPolicy, a novel framework for fast policy generation based on consistency flow matching and 3D vision. Our approach refines the flow dynamics by normalizing the self-consistency of the velocity field, enabling the model to derive task execution policies in a single inference step. Specifically, FlowPolicy conditions on the observed 3D point cloud, where consistency flow matching directly defines straight-line flows from different time states to the same action space, while simultaneously constraining their velocity values, that is, we approximate the trajectories from noise to robot actions by normalizing the self-consistency of the velocity field within the action space, thus improving the inference efficiency. We validate the effectiveness of FlowPolicy in Adroit and Metaworld, demonstrating a 7$\times$ increase in inference speed while maintaining competitive average success rates compared to state-of-the-art methods. Code is available at https://github.com/zql-kk/FlowPolicy.