Rectified Schr"odinger 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 Schr"odinger 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 Schr"odinger Bridge Matching (RSBM), a framework that exploits a shared velocity-field structure between standard Schr"odinger Bridges (varepsilon=1, maximum-entropy transport) and deterministic Optimal Transport (varepsilon→ 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 ≥ 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.