# GLA-Grad: A Griffin-Lim Extended Waveform Generation Diffusion Model

arXiv: https://arxiv.org/abs/2402.15516 · HTML: https://mlsanity.com/paper/2402.15516/

## 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 22 of its 33 references that are in the map.
- First posted on arXiv 9 Feb 2024.

## Placed in

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

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (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)
- [HiFi-GAN: Generative Adversarial Networks for Efficient and High Fidelity Speech Synthesis](https://mlsanity.com/paper/2010.05646/) (2020)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [Speech Enhancement and Dereverberation with Diffusion-based Generative Models](https://mlsanity.com/paper/2208.05830/) (2022)
- [FastDiff: A Fast Conditional Diffusion Model for High-Quality Speech Synthesis](https://mlsanity.com/paper/2204.09934/) (2022)
- [Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Models](https://mlsanity.com/paper/2304.12526/) (2023)
- [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)
- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Prior](https://mlsanity.com/paper/2106.06406/) (2021)
- [Diffusion-based Generative Speech Source Separation](https://mlsanity.com/paper/2210.17327/) (2022)
- [SpecGrad: Diffusion Probabilistic Model based Neural Vocoder with Adaptive Noise Spectral Shaping](https://mlsanity.com/paper/2203.16749/) (2022)
- [An Introduction to Image Synthesis with Generative Adversarial Nets](https://mlsanity.com/paper/1803.04469/) (2018)
- [VAENAR-TTS: Variational Auto-Encoder based Non-AutoRegressive Text-to-Speech Synthesis](https://mlsanity.com/paper/2107.03298/) (2021)

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

- [GROOT: Generating Robust Watermark for Diffusion-Model-Based Audio Synthesis](https://mlsanity.com/paper/2407.10471/) (2024)
- [TA-V2A: Textually Assisted Video-to-Audio Generation](https://mlsanity.com/paper/2503.10700/) (2025)
- [MiSTR: Multi-Modal iEEG-to-Speech Synthesis with Transformer-Based Prosody Prediction and Neural Phase Reconstruction](https://mlsanity.com/paper/2508.03166/) (2025)
- [GLA-Grad++: An Improved Griffin-Lim Guided Diffusion Model for Speech Synthesis](https://mlsanity.com/paper/2511.22293/) (2025)
- [Toward Complex-Valued Neural Networks for Waveform Generation](https://mlsanity.com/paper/2603.11589/) (2026)
- [Brain-to-Speech: Prosody Feature Engineering and Transformer-Based Reconstruction](https://mlsanity.com/paper/2604.05751/) (2026)

## Abstract (arXiv)

Diffusion models are receiving a growing interest for a variety of signal generation tasks such as speech or music synthesis. WaveGrad, for example, is a successful diffusion model that conditionally uses the mel spectrogram to guide a diffusion process for the generation of high-fidelity audio. However, such models face important challenges concerning the noise diffusion process for training and inference, and they have difficulty generating high-quality speech for speakers that were not seen during training. With the aim of minimizing the conditioning error and increasing the efficiency of the noise diffusion process, we propose in this paper a new scheme called GLA-Grad, which consists in introducing a phase recovery algorithm such as the Griffin-Lim algorithm (GLA) at each step of the regular diffusion process. Furthermore, it can be directly applied to an already-trained waveform generation model, without additional training or fine-tuning. We show that our algorithm outperforms state-of-the-art diffusion models for speech generation, especially when generating speech for a previously unseen target speaker.