Rectified Schrödinger Bridge Matching for Few-Step Visual Navigation

• URL: http://arxiv.org/abs/2604.05673v1
• Date: Tue, 07 Apr 2026 10:22:27 GMT
• Title: Rectified Schrödinger Bridge Matching for Few-Step Visual Navigation
• Abstract summary: Visual navigation is a core challenge in Embodied AI, requiring autonomous agents to translate high-dimensional sensory observations into long-horizon action trajectories.<n>We propose Rectified Schrdinger Bridge Matching (RSBM), a framework that exploits a shared velocity-field structure between Schrdinger Bridges and deterministic transport.<n>RSBM achieves over 94% and 92% success rate in merely 3 stage training, substantially narrowing the gap between high-fidelity generative policies and the low-latency demands of Embodied AI.
• Score: 18.319705014361908
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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