# Diffusion-based Frameworks for Unsupervised Speech Enhancement

arXiv: https://arxiv.org/abs/2601.09931 · HTML: https://mlsanity.com/paper/2601.09931/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2026.

## Built on by (most cited first, 2 of 2)

- [SSNAPS: Audio-Visual Separation of Speech and Background Noise with Diffusion Inverse Sampling](https://mlsanity.com/paper/2602.01394/) (2026)
- [Audio-visual Contrastive Alignment for Diffusion-based Visual-conditioned Speech Enhancement](https://mlsanity.com/paper/2606.23712/) (2026)

## Abstract (arXiv)

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.