Flowing straighter with conditional flow matching for accurate speech enhancement

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 Schrödinger 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 Schrödinger 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.