# SB-RF: Schr"odinger Bridge Rectified Flow for One-Step Robust Speech Enhancement

arXiv: https://arxiv.org/abs/2606.05575 · HTML: https://mlsanity.com/paper/2606.05575/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 29 of its 41 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 29 of 29)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [High-Fidelity Audio Compression with Improved RVQGAN](https://mlsanity.com/paper/2306.06546/) (2023)
- [MUSAN: A Music, Speech, and Noise Corpus](https://mlsanity.com/paper/1510.08484/) (2015)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [AISHELL-1: An Open-Source Mandarin Speech Corpus and A Speech Recognition Baseline](https://mlsanity.com/paper/1709.05522/) (2017)
- [DNSMOS: A Non-Intrusive Perceptual Objective Speech Quality metric to evaluate Noise Suppressors](https://mlsanity.com/paper/2010.15258/) (2020)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [Speech Enhancement and Dereverberation with Diffusion-based Generative Models](https://mlsanity.com/paper/2208.05830/) (2022)
- [SEGAN: Speech Enhancement Generative Adversarial Network](https://mlsanity.com/paper/1703.09452/) (2017)
- [WHAM!: Extending Speech Separation to Noisy Environments](https://mlsanity.com/paper/1907.01160/) (2019)
- [Conditional Diffusion Probabilistic Model for Speech Enhancement](https://mlsanity.com/paper/2202.05256/) (2022)
- [The Schr"odinger Bridge between Gaussian Measures has a Closed Form](https://mlsanity.com/paper/2202.05722/) (2022)
- [ICASSP 2022 Deep Noise Suppression Challenge](https://mlsanity.com/paper/2202.13288/) (2022)
- [MP-SENet: A Speech Enhancement Model with Parallel Denoising of Magnitude and Phase Spectra](https://mlsanity.com/paper/2305.13686/) (2023)
- [WenetSpeech4TTS: A 12,800-hour Mandarin TTS Corpus for Large Speech Generation Model Benchmark](https://mlsanity.com/paper/2406.05763/) (2024)
- [A variance modeling framework based on variational autoencoders for speech enhancement](https://mlsanity.com/paper/1902.01605/) (2019)
- [Reducing the Prior Mismatch of Stochastic Differential Equations for Diffusion-based Speech Enhancement](https://mlsanity.com/paper/2302.14748/) (2023)
- [Schrodinger Bridges Beat Diffusion Models on Text-to-Speech Synthesis](https://mlsanity.com/paper/2312.03491/) (2023)
- [Variational Autoencoder for Speech Enhancement with a Noise-Aware Encoder](https://mlsanity.com/paper/2102.08706/) (2021)
- [Schr"odinger Bridge for Generative Speech Enhancement](https://mlsanity.com/paper/2407.16074/) (2024)
- [FlowSE: Flow Matching-based Speech Enhancement](https://mlsanity.com/paper/2508.06840/) (2025)
- [A consolidated view of loss functions for supervised deep learning-based speech enhancement](https://mlsanity.com/paper/2009.12286/) (2020)
- [MeanFlowSE: one-step generative speech enhancement via conditional mean flow](https://mlsanity.com/paper/2509.14858/) (2025)
- [Flowing Straighter with Conditional Flow Matching for Accurate Speech Enhancement](https://mlsanity.com/paper/2508.20584/) (2025)
- [VoiceRestore: Flow-Matching Transformers for Speech Recording Quality Restoration](https://mlsanity.com/paper/2501.00794/) (2025)
- [Compose Yourself: Average-Velocity Flow Matching for One-Step Speech Enhancement](https://mlsanity.com/paper/2509.15952/) (2025)

## Abstract (arXiv)

Generative models have shown promising results for speech enhancement (SE), but they often rely on multi-step inference, limiting low-latency deployment. We propose SB-RF, a one-step generative framework that integrates Rectified Flow (RF) with Schr"odinger Bridge (SB) theory. During training, SB-RF samples intermediate states from an SB time marginal and trains a conditional velocity field with the RF velocity-matching objective. At inference, SB-RF starts from the noisy observation and applies a single Euler update. Experiments show that SB-RF achieves competitive performance among generative methods on the VoiceBank-DEMAND benchmark. To further assess performance beyond this standard setting, we evaluate SB-RF on a simulated low signal-to-noise ratio test set using an expanded training dataset. Under these conditions, SB-RF achieves superior performance over the compared baselines, supporting its potential for real-world applications.