This paper addresses unsupervised diffusion-based single-channel speech enhancement (SE). Prior work in this direction combines a score-based diffusion model trained on clean speech with a Gaussian noise model whose covariance is structured by non-negative matrix factorization (NMF). This combination is used within an iterative expectation-maximization (EM) scheme, in which a diffusion-based posterior-sampling E-step estimates the clean speech. We first revisit this framework and propose to explicitly model both speech and acoustic noise as latent variables, jointly sampling them in the E-step instead of sampling speech alone as in previous approaches. We then introduce a new semi-supervised SE framework that replaces the NMF noise prior with a diffusion-based noise model, learned jointly with the speech prior in a single conditional score model. Within this framework, we derive two variants: one that implicitly accounts for noise and one that explicitly treats noise as a latent variable. Experiments on WSJ0-QUT and VoiceBank-DEMAND show that explicit noise modeling systematically improves SE performance for both NMF-based and diffusion-based noise priors. Under matched conditions, the diffusion-based noise model attains the best overall quality and intelligibility among unsupervised methods, while under mismatched conditions the proposed NMF-based explicit-noise framework is more robust and suffers less degradation than several supervised baselines. Code, demo, and supplementary materials are publicly available.

翻译：本文针对无监督单通道语音增强（SE）中基于扩散的方法展开研究。现有相关工作将基于干净语音训练的分数扩散模型与协方差由非负矩阵分解（NMF）约束的高斯噪声模型相结合，并在迭代期望最大化（EM）框架中使用该组合；其中，基于扩散的后验采样E步用于估计干净语音。我们首先重新审视该框架，提出将语音和声学噪声均显式建模为隐变量，在E步中联合采样它们，而非如先前方法仅采样语音。随后，我们引入一种新的半监督SE框架，用基于扩散的噪声模型替代NMF噪声先验，并在单一条件分数模型中与语音先验联合学习。在此框架下，我们推导出两种变体：一种隐式处理噪声，另一种将噪声显式视为隐变量。在WSJ0-QUT和VoiceBank-DEMAND上的实验表明，无论对于基于NMF还是基于扩散的噪声先验，显式噪声建模均能系统性提升SE性能。在匹配条件下，基于扩散的噪声模型在无监督方法中取得最佳的整体质量和可懂度；而在失配条件下，所提出的基于NMF的显式噪声框架具有更强的鲁棒性，其性能退化程度低于多种监督基线方法。代码、演示及补充材料已公开提供。