Rectified Schrödinger Bridge Matching for Few-Step Visual Navigation
Summary: arXiv:2604.05673v1 Announce Type: cross
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.
In this article, we introduce a novel framework known as Rectified Schrödinger Bridge Matching (RSBM). This innovative approach leverages a shared velocity-field structure that exists between standard Schrödinger Bridges and deterministic Optimal Transport. The framework is governed by a single entropic regularization parameter, denoted as ε. Our research demonstrates two fundamental results:
- Velocity Structure Invariance: We prove that the functional form of the conditional velocity field remains invariant across the entire ε-spectrum. This means that a single network can effectively serve all regularization strengths.
- Conditional Velocity Variance Reduction: We show that by reducing ε, the conditional velocity variance decreases linearly, which facilitates more stable coarse-step Ordinary Differential Equation (ODE) integration.
RSBM is anchored to a learned conditional prior that reduces the transport distance, allowing it to function at an intermediate ε value. This balance between multimodal coverage and path straightness is crucial for enhancing performance in visual navigation tasks.
Empirical results indicate that while standard bridges typically require ten or more steps to achieve convergence, RSBM remarkably accomplishes over 94% cosine similarity and a 92% success rate in just three integration steps. This achievement is significant as it occurs without the need for distillation or multi-stage training, thereby substantially closing the gap between high-fidelity generative policies and the low-latency requirements of Embodied AI.
The implications of RSBM extend beyond theoretical advancements; they present practical opportunities for improving the efficiency and effectiveness of autonomous agents in various applications. As the demand for real-time robotic control continues to rise, the ability to execute complex navigation tasks in fewer steps represents a pivotal advancement in the field of AI.
In conclusion, the introduction of Rectified Schrödinger Bridge Matching marks a significant milestone in addressing the challenges faced in visual navigation for autonomous agents. By streamlining the integration process and enhancing performance metrics, RSBM paves the way for future research and application in the realm of Embodied AI.