Sample from What You See: Visuomotor Policy Learning via Diffusion Bridge with Observation-Embedded Stochastic Differential Equation

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. We introduce BridgePolicy, 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. To 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.