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

arXiv: https://arxiv.org/abs/2604.05673 · HTML: https://mlsanity.com/paper/2604.05673/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 36 of its 44 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 36)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [3D Diffuser Actor: Policy Diffusion with 3D Scene Representations](https://mlsanity.com/paper/2402.10885/) (2024)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [NaVid: Video-based VLM Plans the Next Step for Vision-and-Language Navigation](https://mlsanity.com/paper/2402.15852/) (2024)
- [BBDM: Image-to-image Translation with Brownian Bridge Diffusion Models](https://mlsanity.com/paper/2205.07680/) (2022)
- [ViNT: A Foundation Model for Visual Navigation](https://mlsanity.com/paper/2306.14846/) (2023)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [Let us Build Bridges: Understanding and Extending Diffusion Generative Models](https://mlsanity.com/paper/2208.14699/) (2022)
- [Diffusion Models for Reinforcement Learning: A Survey](https://mlsanity.com/paper/2311.01223/) (2023)
- [Simulating Diffusion Bridges with Score Matching](https://mlsanity.com/paper/2111.07243/) (2021)
- [GaussNav: Gaussian Splatting for Visual Navigation](https://mlsanity.com/paper/2403.11625/) (2024)
- [Light and Optimal Schr"odinger Bridge Matching](https://mlsanity.com/paper/2402.03207/) (2024)
- [A Behavioral Approach to Visual Navigation with Graph Localization Networks](https://mlsanity.com/paper/1903.00445/) (2019)
- [Generalized Schr"odinger Bridge Matching](https://mlsanity.com/paper/2310.02233/) (2023)
- [Aligned Diffusion Schr"odinger Bridges](https://mlsanity.com/paper/2302.11419/) (2023)
- [Entropic and displacement interpolation: a computational approach using the Hilbert metric](https://mlsanity.com/paper/1506.04255/) (2015)
- [Prior Does Matter: Visual Navigation via Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2504.10041/) (2025)
- [Visual Navigation in Real-World Indoor Environments Using End-to-End Deep Reinforcement Learning](https://mlsanity.com/paper/2010.10903/) (2020)
- [Adversarial Schr"odinger Bridge Matching](https://mlsanity.com/paper/2405.14449/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning to Navigate with Minimal Parameters: Decomposing Visual Navigation Through Closed-Form Geometric Interfaces](https://mlsanity.com/paper/2607.11029/) (2026)

## Abstract (arXiv)

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.