# Flowing Straighter with Conditional Flow Matching for Accurate Speech Enhancement

## TL;DR

This paper investigates the impact of path straightness in flow-based speech enhancement models, demonstrating that straight, time-independent paths lead to better quality and simpler inference compared to curved paths.

## Contribution

It introduces independent conditional flow matching for speech enhancement, showing that straight paths improve performance and proposing a one-step inference method for efficiency.

## Key findings

- Straight paths improve speech enhancement quality.
- Time-independent variance has a significant impact on sample quality.
- One-step inference achieves comparable results to multi-step methods.

## Abstract

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.