# Schr"odinger Bridge Consistency Trajectory Models for Speech Enhancement

arXiv: https://arxiv.org/abs/2507.11925 · HTML: https://mlsanity.com/paper/2507.11925/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 25 of its 32 references that are in the map.
- First posted on arXiv 16 Jul 2025.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [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)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [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)
- [Real Time Speech Enhancement in the Waveform Domain](https://mlsanity.com/paper/2006.12847/) (2020)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Conditional Diffusion Probabilistic Model for Speech Enhancement](https://mlsanity.com/paper/2202.05256/) (2022)
- [StoRM: A Diffusion-based Stochastic Regeneration Model for Speech Enhancement and Dereverberation](https://mlsanity.com/paper/2212.11851/) (2022)
- [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022)
- [An Investigation of Incorporating Mamba for Speech Enhancement](https://mlsanity.com/paper/2405.06573/) (2024)
- [MP-SENet: A Speech Enhancement Model with Parallel Denoising of Magnitude and Phase Spectra](https://mlsanity.com/paper/2305.13686/) (2023)
- [DPT-FSNet: Dual-path Transformer Based Full-band and Sub-band Fusion Network for Speech Enhancement](https://mlsanity.com/paper/2104.13002/) (2021)
- [Diffusion Models for Audio Restoration](https://mlsanity.com/paper/2402.09821/) (2024)
- [Reducing the Prior Mismatch of Stochastic Differential Equations for Diffusion-based Speech Enhancement](https://mlsanity.com/paper/2302.14748/) (2023)
- [Schr"odinger Bridge for Generative Speech Enhancement](https://mlsanity.com/paper/2407.16074/) (2024)
- [CMGAN: Conformer-Based Metric-GAN for Monaural Speech Enhancement](https://mlsanity.com/paper/2209.11112/) (2022)
- [Consistency Diffusion Bridge Models](https://mlsanity.com/paper/2410.22637/) (2024)
- [Investigating Training Objectives for Generative Speech Enhancement](https://mlsanity.com/paper/2409.10753/) (2024)
- [Objective Measures of Perceptual Audio Quality Reviewed: An Evaluation of Their Application Domain Dependence](https://mlsanity.com/paper/2110.11438/) (2021)
- [SE-Bridge: Speech Enhancement with Consistent Brownian Bridge](https://mlsanity.com/paper/2305.13796/) (2023)

## Built on by (most cited first, 4 of 4)

- [Schr"odinger Bridge Mamba for One-Step Speech Enhancement](https://mlsanity.com/paper/2510.16834/) (2025)
- [Speech Enhancement Based on Drifting Models](https://mlsanity.com/paper/2604.24199/) (2026)
- [HybridSB-MoE: Dual-Domain Schr"odinger Bridges with Scene-Adaptive Expert Routing for Speech Enhancement](https://mlsanity.com/paper/2608.12715/) (2026)
- [DriftSE: Speech Enhancement with Generative Drifting](https://mlsanity.com/paper/2609.12252/) (2026)

## Abstract (arXiv)

Speech enhancement (SE) utilizing diffusion models is a promising technology that improves speech quality in noisy speech data. Furthermore, the Schr"odinger bridge (SB) has recently been used in diffusion-based SE to improve speech quality by resolving a mismatch between the endpoint of the forward process and the starting point of the reverse process. However, the SB still exhibits slow inference owing to the necessity of a large number of function evaluations (NFE) for inference to obtain high-quality results. While Consistency Models (CMs) address this issue by employing consistency training that uses distillation from pretrained models in the field of image generation, it does not improve generation quality when the number of steps increases. As a solution to this problem, Consistency Trajectory Models (CTMs) not only accelerate inference speed but also maintain a favorable trade-off between quality and speed. Furthermore, SoundCTM demonstrates the applicability of CTM techniques to the field of sound generation. In this paper, we present Schr"odinger bridge Consistency Trajectory Models (SBCTM) by applying the CTM's technique to the Schr"odinger bridge for SE. Additionally, we introduce a novel auxiliary loss, including a perceptual loss, into the original CTM's training framework. As a result, SBCTM achieves an approximately 16x improvement in the real-time factor (RTF) compared to the conventional Schr"odinger bridge for SE. Furthermore, the favorable trade-off between quality and speed in SBCTM allows for time-efficient inference by limiting multi-step refinement to cases where 1-step inference is insufficient. Our code, pretrained models, and audio samples are available at https://github.com/sony/sbctm/.