# Cold Diffusion for Speech Enhancement

arXiv: https://arxiv.org/abs/2211.02527 · HTML: https://mlsanity.com/paper/2211.02527/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 4 Nov 2022.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Real Time Speech Enhancement in the Waveform Domain](https://mlsanity.com/paper/2006.12847/) (2020)
- [SEGAN: Speech Enhancement Generative Adversarial Network](https://mlsanity.com/paper/1703.09452/) (2017)
- [DCCRN: Deep Complex Convolution Recurrent Network for Phase-Aware Speech Enhancement](https://mlsanity.com/paper/2008.00264/) (2020)
- [Conditional Diffusion Probabilistic Model for Speech Enhancement](https://mlsanity.com/paper/2202.05256/) (2022)
- [MetricGAN: Generative Adversarial Networks based Black-box Metric Scores Optimization for Speech Enhancement](https://mlsanity.com/paper/1905.04874/) (2019)
- [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022)
- [Universal Speech Enhancement with Score-based Diffusion](https://mlsanity.com/paper/2206.03065/) (2022)
- [A Study on Speech Enhancement Based on Diffusion Probabilistic Model](https://mlsanity.com/paper/2107.11876/) (2021)
- [Variational Autoencoder for Speech Enhancement with a Noise-Aware Encoder](https://mlsanity.com/paper/2102.08706/) (2021)
- [Unsupervised Speech Enhancement using Dynamical Variational Auto-Encoders](https://mlsanity.com/paper/2106.12271/) (2021)
- [Speech Denoising with Deep Feature Losses](https://mlsanity.com/paper/1806.10522/) (2018)
- [A Flow-Based Neural Network for Time Domain Speech Enhancement](https://mlsanity.com/paper/2106.09008/) (2021)
- [S-DCCRN: Super Wide Band DCCRN with learnable complex feature for speech enhancement](https://mlsanity.com/paper/2111.08387/) (2021)
- [WaveCRN: An Efficient Convolutional Recurrent Neural Network for End-to-end Speech Enhancement](https://mlsanity.com/paper/2004.04098/) (2020)
- [Disentanglement Learning for Variational Autoencoders Applied to Audio-Visual Speech Enhancement](https://mlsanity.com/paper/2105.08970/) (2021)

## Built on by (most cited first, 30 of 31)

- [A Survey on Audio Diffusion Models: Text To Speech Synthesis and Enhancement in Generative AI](https://mlsanity.com/paper/2303.13336/) (2023)
- [CoreDiff: Contextual Error-Modulated Generalized Diffusion Model for Low-Dose CT Denoising and Generalization](https://mlsanity.com/paper/2304.01814/) (2023)
- [Blind Audio Bandwidth Extension: A Diffusion-Based Zero-Shot Approach](https://mlsanity.com/paper/2306.01433/) (2023)
- [The Ethical Implications of Generative Audio Models: A Systematic Literature Review](https://mlsanity.com/paper/2307.05527/) (2023)
- [The Age of Synthetic Realities: Challenges and Opportunities](https://mlsanity.com/paper/2306.11503/) (2023)
- [Single and Few-step Diffusion for Generative Speech Enhancement](https://mlsanity.com/paper/2309.09677/) (2023)
- [Unsupervised speech enhancement with diffusion-based generative models](https://mlsanity.com/paper/2309.10450/) (2023)
- [Investigating the Design Space of Diffusion Models for Speech Enhancement](https://mlsanity.com/paper/2312.04370/) (2023)
- [A Multi-dimensional Deep Structured State Space Approach to Speech Enhancement Using Small-footprint Models](https://mlsanity.com/paper/2306.00331/) (2023)
- [Structured Diffusion Models with Mixture of Gaussians as Prior Distribution](https://mlsanity.com/paper/2410.19149/) (2024)
- [DDTSE: Discriminative Diffusion Model for Target Speech Extraction](https://mlsanity.com/paper/2309.13874/) (2023)
- [Diffusion-Based Speech Enhancement in Matched and Mismatched Conditions Using a Heun-Based Sampler](https://mlsanity.com/paper/2312.02683/) (2023)
- [Reconstruction of Sound Field through Diffusion Models](https://mlsanity.com/paper/2312.08821/) (2023)
- [Diffusion-based Unsupervised Audio-visual Speech Enhancement](https://mlsanity.com/paper/2410.05301/) (2024)
- [Diffusion-based speech enhancement with a weighted generative-supervised learning loss](https://mlsanity.com/paper/2309.10457/) (2023)
- [Variance-Preserving-Based Interpolation Diffusion Models for Speech Enhancement](https://mlsanity.com/paper/2306.08527/) (2023)
- [A Variance-Preserving Interpolation Approach for Diffusion Models with Applications to Single Channel Speech Enhancement and Recognition](https://mlsanity.com/paper/2405.16952/) (2024)
- [MGE-LDM: Joint Latent Diffusion for Simultaneous Music Generation and Source Extraction](https://mlsanity.com/paper/2505.23305/) (2025)
- [The Effect of Training Dataset Size on Discriminative and Diffusion-Based Speech Enhancement Systems](https://mlsanity.com/paper/2406.06160/) (2024)
- [A Survey of Deep Learning for Complex Speech Spectrograms](https://mlsanity.com/paper/2505.08694/) (2025)
- [Adaptive Deterministic Flow Matching for Target Speaker Extraction](https://mlsanity.com/paper/2510.16995/) (2025)
- [AnnoTheia: A Semi-Automatic Annotation Toolkit for Audio-Visual Speech Technologies](https://mlsanity.com/paper/2402.13152/) (2024)
- [Leveraging Discriminative Latent Representations for Conditioning GAN-Based Speech Enhancement](https://mlsanity.com/paper/2508.20859/) (2025)
- [Compose Yourself: Average-Velocity Flow Matching for One-Step Speech Enhancement](https://mlsanity.com/paper/2509.15952/) (2025)
- [Posterior sampling algorithms for unsupervised speech enhancement with recurrent variational autoencoder](https://mlsanity.com/paper/2309.10439/) (2023)
- [RestoreGrad: Signal Restoration Using Conditional Denoising Diffusion Models with Jointly Learned Prior](https://mlsanity.com/paper/2502.13574/) (2025)
- [Posterior Transition Modeling for Unsupervised Diffusion-Based Speech Enhancement](https://mlsanity.com/paper/2507.02391/) (2025)
- [A Cold Diffusion Approach for Percussive Dereverberation](https://mlsanity.com/paper/2605.10256/) (2026)
- [GenDiff: A Dose and Anatomy Aware Diffusion Model with Structural Prior Refinement for Low-Dose CT Reconstruction and Generalization](https://mlsanity.com/paper/2607.11941/) (2026)
- [Dose-Aware Cold Diffusion with Physics Consistency for Generalizable Low-Dose CT Reconstruction](https://mlsanity.com/paper/2609.18943/) (2026)

## Abstract (arXiv)

Diffusion models have recently shown promising results for difficult enhancement tasks such as the conditional and unconditional restoration of natural images and audio signals. In this work, we explore the possibility of leveraging a recently proposed advanced iterative diffusion model, namely cold diffusion, to recover clean speech signals from noisy signals. The unique mathematical properties of the sampling process from cold diffusion could be utilized to restore high-quality samples from arbitrary degradations. Based on these properties, we propose an improved training algorithm and objective to help the model generalize better during the sampling process. We verify our proposed framework by investigating two model architectures. Experimental results on benchmark speech enhancement dataset VoiceBank-DEMAND demonstrate the strong performance of the proposed approach compared to representative discriminative models and diffusion-based enhancement models.