# Flowing Straighter with Conditional Flow Matching for Accurate Speech Enhancement

arXiv: https://arxiv.org/abs/2508.20584 · HTML: https://mlsanity.com/paper/2508.20584/

## Key facts

- Cited by 3 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 28 Aug 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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [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)
- [Deep Generative Learning via Schr"odinger Bridge](https://mlsanity.com/paper/2106.10410/) (2021)
- [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022)
- [The Schr"odinger Bridge between Gaussian Measures has a Closed Form](https://mlsanity.com/paper/2202.05722/) (2022)
- [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)
- [FlowAVSE: Efficient Audio-Visual Speech Enhancement with Conditional Flow Matching](https://mlsanity.com/paper/2406.09286/) (2024)
- [FlowSE: Flow Matching-based Speech Enhancement](https://mlsanity.com/paper/2508.06840/) (2025)
- [Investigating Training Objectives for Generative Speech Enhancement](https://mlsanity.com/paper/2409.10753/) (2024)
- [Diffusion-based Speech Enhancement with Schr"odinger Bridge and Symmetric Noise Schedule](https://mlsanity.com/paper/2409.05116/) (2024)
- [Hallucination in Perceptual Metric-Driven Speech Enhancement Networks](https://mlsanity.com/paper/2403.11732/) (2024)
- [WhiSQA: Non-Intrusive Speech Quality Prediction Using Whisper Encoder Features](https://mlsanity.com/paper/2508.02210/) (2025)

## Built on by (most cited first, 3 of 3)

- [Shortcut Flow Matching for Speech Enhancement: Step-Invariant flows via single stage training](https://mlsanity.com/paper/2509.21522/) (2025)
- [SB-RF: Schr"odinger Bridge Rectified Flow for One-Step Robust Speech Enhancement](https://mlsanity.com/paper/2606.05575/) (2026)
- [Discriminative Flow Matching: Beyond Time-Conditioning in Generative Restoration via Flow-State Representations](https://mlsanity.com/paper/2609.04525/) (2026)

## Abstract (arXiv)

Current flow-based generative speech enhancement methods learn curved probability paths which model a mapping between clean and noisy speech. Despite impressive performance, the implications of curved probability paths are unknown. Methods such as Schrodinger bridges focus on curved paths, where time-dependent gradients and variance do not promote straight paths. Findings in machine learning research suggest that straight paths, such as conditional flow matching, are easier to train and offer better generalisation. In this paper we quantify the effect of path straightness on speech enhancement quality. We report experiments with the Schrodinger bridge, where we show that certain configurations lead to straighter paths. Conversely, we propose independent conditional flow-matching for speech enhancement, which models straight paths between noisy and clean speech. We demonstrate empirically that a time-independent variance has a greater effect on sample quality than the gradient. Although conditional flow matching improves several speech quality metrics, it requires multiple inference steps. We rectify this with a one-step solution by inferring the trained flow-based model as if it was directly predictive. Our work suggests that straighter time-independent probability paths improve generative speech enhancement over curved time-dependent paths.