# Thunder : Unified Regression-Diffusion Speech Enhancement with a Single Reverse Step using Brownian Bridge

arXiv: https://arxiv.org/abs/2406.06139 · HTML: https://mlsanity.com/paper/2406.06139/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [FSD50K: An Open Dataset of Human-Labeled Sound Events](https://mlsanity.com/paper/2010.00475/) (2020)
- [Speech Enhancement and Dereverberation with Diffusion-based Generative Models](https://mlsanity.com/paper/2208.05830/) (2022)
- [Conditional Diffusion Probabilistic Model for Speech Enhancement](https://mlsanity.com/paper/2202.05256/) (2022)
- [MetricGAN+: An Improved Version of MetricGAN for Speech Enhancement](https://mlsanity.com/paper/2104.03538/) (2021)
- [StoRM: A Diffusion-based Stochastic Regeneration Model for Speech Enhancement and Dereverberation](https://mlsanity.com/paper/2212.11851/) (2022)
- [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022)
- [Analysing Diffusion-based Generative Approaches versus Discriminative Approaches for Speech Restoration](https://mlsanity.com/paper/2211.02397/) (2022)
- [Reducing the Prior Mismatch of Stochastic Differential Equations for Diffusion-based Speech Enhancement](https://mlsanity.com/paper/2302.14748/) (2023)
- [How Bad Are Artifacts?: Analyzing the Impact of Speech Enhancement Errors on ASR](https://mlsanity.com/paper/2201.06685/) (2022)
- [Glance and Gaze: A Collaborative Learning Framework for Single-channel Speech Enhancement](https://mlsanity.com/paper/2106.11789/) (2021)
- [VoiceID Loss: Speech Enhancement for Speaker Verification](https://mlsanity.com/paper/1904.03601/) (2019)
- [Diffusion-Based Speech Enhancement with Joint Generative and Predictive Decoders](https://mlsanity.com/paper/2305.10734/) (2023)
- [SNRi Target Training for Joint Speech Enhancement and Recognition](https://mlsanity.com/paper/2111.00764/) (2021)

## Built on by (most cited first, 6 of 6)

- [Robust One-step Speech Enhancement via Consistency Distillation](https://mlsanity.com/paper/2507.05688/) (2025)
- [Speech Enhancement Based on Drifting Models](https://mlsanity.com/paper/2604.24199/) (2026)
- [Accelerating Diffusion Sampling via Exploiting Local Transition Coherence](https://mlsanity.com/paper/2503.09675/) (2025)
- [Speech Enhancement based on cascaded two flows](https://mlsanity.com/paper/2508.06842/) (2025)
- [A Fast Solver for Interpolating Stochastic Differential Equation Diffusion Models for Speech Restoration](https://mlsanity.com/paper/2603.09508/) (2026)
- [DriftSE: Speech Enhancement with Generative Drifting](https://mlsanity.com/paper/2609.12252/) (2026)

## Abstract (arXiv)

Diffusion-based speech enhancement has shown promising results, but can suffer from a slower inference time. Initializing the diffusion process with the enhanced audio generated by a regression-based model can be used to reduce the computational steps required. However, these approaches often necessitate a regression model, further increasing the system's complexity. We propose Thunder, a unified regression-diffusion model that utilizes the Brownian bridge process which can allow the model to act in both modes. The regression mode can be accessed by setting the diffusion time step closed to 1. However, the standard score-based diffusion modeling does not perform well in this setup due to gradient instability. To mitigate this problem, we modify the diffusion model to predict the clean speech instead of the score function, achieving competitive performance with a more compact model size and fewer reverse steps.