Rectified Schrödinger Bridge Matching for Few-Step Visual Navigation

Visual navigation is a core challenge in Embodied AI, requiring autonomous agents to translate high-dimensional sensory observations into continuous, long-horizon action trajectories. While generative policies based on diffusion models and Schrödinger Bridges (SB) effectively capture multimodal action distributions, they require dozens of integration steps due to high-variance stochastic transport, posing a critical barrier for real-time robotic control. We propose Rectified Schrödinger Bridge Matching (RSBM), a framework that exploits a shared velocity-field structure between standard Schrödinger Bridges (\varepsilon=1, maximum-entropy transport) and deterministic Optimal Transport (\varepsilon\to 0, as in Conditional Flow Matching), controlled by a single entropic regularization parameter \varepsilon. We prove two key results: (1) the conditional velocity field's functional form is invariant across the entire \varepsilon-spectrum (Velocity Structure Invariance), enabling a single network to serve all regularization strengths; and (2) reducing \varepsilon linearly decreases the conditional velocity variance, enabling more stable coarse-step ODE integration. Anchored to a learned conditional prior that shortens transport distance, RSBM operates at an intermediate \varepsilon that balances multimodal coverage and path straightness. Empirically, while standard bridges require \geq 10 steps to converge, RSBM achieves over 94% cosine similarity and 92% success rate in merely 3 integration steps -- without distillation or multi-stage training -- substantially narrowing the gap between high-fidelity generative policies and the low-latency demands of Embodied AI.