# Posterior Transition Modeling for Unsupervised Diffusion-Based Speech Enhancement

arXiv: https://arxiv.org/abs/2507.02391 · HTML: https://mlsanity.com/paper/2507.02391/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 22 of its 38 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 22 of 22)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Supervised Speech Separation Based on Deep Learning: An Overview](https://mlsanity.com/paper/1708.07524/) (2017)
- [Speech Enhancement and Dereverberation with Diffusion-based Generative Models](https://mlsanity.com/paper/2208.05830/) (2022)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Conditional Diffusion Probabilistic Model for Speech Enhancement](https://mlsanity.com/paper/2202.05256/) (2022)
- [StoRM: A Diffusion-based Stochastic Regeneration Model for Speech Enhancement and Dereverberation](https://mlsanity.com/paper/2212.11851/) (2022)
- [Universal Speech Enhancement with Score-based Diffusion](https://mlsanity.com/paper/2206.03065/) (2022)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [A Recurrent Variational Autoencoder for Speech Enhancement](https://mlsanity.com/paper/1910.10942/) (2019)
- [Diffusion Models for Audio Restoration](https://mlsanity.com/paper/2402.09821/) (2024)
- [Cold Diffusion for Speech Enhancement](https://mlsanity.com/paper/2211.02527/) (2022)
- [Unsupervised speech enhancement with diffusion-based generative models](https://mlsanity.com/paper/2309.10450/) (2023)
- [BUDDy: Single-Channel Blind Unsupervised Dereverberation with Diffusion Models](https://mlsanity.com/paper/2405.04272/) (2024)
- [Diffusion-Based Speech Enhancement in Matched and Mismatched Conditions Using a Heun-Based Sampler](https://mlsanity.com/paper/2312.02683/) (2023)
- [Diffusion-based Unsupervised Audio-visual Speech Enhancement](https://mlsanity.com/paper/2410.05301/) (2024)
- [UnDiff: Unsupervised Voice Restoration with Unconditional Diffusion Model](https://mlsanity.com/paper/2306.00721/) (2023)

## Abstract (arXiv)

We explore unsupervised speech enhancement using diffusion models as expressive generative priors for clean speech. Existing approaches guide the reverse diffusion process using noisy speech through an approximate, noise-perturbed likelihood score, combined with the unconditional score via a trade-off hyperparameter. In this work, we propose two alternative algorithms that directly model the conditional reverse transition distribution of diffusion states. The first method integrates the diffusion prior with the observation model in a principled way, removing the need for hyperparameter tuning. The second defines a diffusion process over the noisy speech itself, yielding a fully tractable and exact likelihood score. Experiments on the WSJ0-QUT and VoiceBank-DEMAND datasets demonstrate improved enhancement metrics and greater robustness to domain shifts compared to both supervised and unsupervised baselines.