Rectified Schr\"odinger Bridge Matching for Few-Step Visual Navigation

TL;DR

This paper introduces RSBM, a novel framework that improves visual navigation by enabling high-quality, low-step trajectory generation through a unified Schr"odinger Bridge approach with a shared velocity structure.

Contribution

RSBM exploits a shared velocity-field structure across the entire entropic regularization spectrum, enabling efficient, stable, and multimodal trajectory generation in fewer steps.

Findings

RSBM achieves over 94% cosine similarity in 3 steps.

Standard Schr"odinger Bridges require 10 or more steps to converge.

RSBM narrows the gap between generative policies and real-time control demands.

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 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 ($\varepsilon\to 0$, 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.