# WaveGrad 2: Iterative Refinement for Text-to-Speech Synthesis

arXiv: https://arxiv.org/abs/2106.09660 · HTML: https://mlsanity.com/paper/2106.09660/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 17 Jun 2021.

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [SpecAugment: A Simple Data Augmentation Method for Automatic Speech Recognition](https://mlsanity.com/paper/1904.08779/) (2019)
- [Natural TTS Synthesis by Conditioning WaveNet on Mel Spectrogram Predictions](https://mlsanity.com/paper/1712.05884/) (2017)
- [FastSpeech 2: Fast and High-Quality End-to-End Text to Speech](https://mlsanity.com/paper/2006.04558/) (2020)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Tacotron: Towards End-to-End Speech Synthesis](https://mlsanity.com/paper/1703.10135/) (2017)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [MelGAN: Generative Adversarial Networks for Conditional Waveform Synthesis](https://mlsanity.com/paper/1910.06711/) (2019)
- [Parallel WaveGAN: A fast waveform generation model based on generative adversarial networks with multi-resolution spectrogram](https://mlsanity.com/paper/1910.11480/) (2019)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Parallel WaveNet: Fast High-Fidelity Speech Synthesis](https://mlsanity.com/paper/1711.10433/) (2017)
- [GANSynth: Adversarial Neural Audio Synthesis](https://mlsanity.com/paper/1902.08710/) (2019)
- [High Fidelity Speech Synthesis with Adversarial Networks](https://mlsanity.com/paper/1909.11646/) (2019)
- [End-to-End Adversarial Text-to-Speech](https://mlsanity.com/paper/2006.03575/) (2020)
- [ClariNet: Parallel Wave Generation in End-to-End Text-to-Speech](https://mlsanity.com/paper/1807.07281/) (2018)
- [Non-Attentive Tacotron: Robust and Controllable Neural TTS Synthesis Including Unsupervised Duration Modeling](https://mlsanity.com/paper/2010.04301/) (2020)
- [Multi-band MelGAN: Faster Waveform Generation for High-Quality Text-to-Speech](https://mlsanity.com/paper/2005.05106/) (2020)
- [Zoneout: Regularizing RNNs by Randomly Preserving Hidden Activations](https://mlsanity.com/paper/1606.01305/) (2016)
- [FloWaveNet : A Generative Flow for Raw Audio](https://mlsanity.com/paper/1811.02155/) (2018)
- [Wave-Tacotron: Spectrogram-free end-to-end text-to-speech synthesis](https://mlsanity.com/paper/2011.03568/) (2020)
- [DurIAN: Duration Informed Attention Network For Multimodal Synthesis](https://mlsanity.com/paper/1909.01700/) (2019)
- [VocGAN: A High-Fidelity Real-time Vocoder with a Hierarchically-nested Adversarial Network](https://mlsanity.com/paper/2007.15256/) (2020)
- [HooliGAN: Robust, High Quality Neural Vocoding](https://mlsanity.com/paper/2008.02493/) (2020)
- [WaveNODE: A Continuous Normalizing Flow for Speech Synthesis](https://mlsanity.com/paper/2006.04598/) (2020)

## Built on by (most cited first, 30 of 65)

- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022)
- [Negative-prompt Inversion: Fast Image Inversion for Editing with Text-guided Diffusion Models](https://mlsanity.com/paper/2305.16807/) (2023)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [StyleTTS 2: Towards Human-Level Text-to-Speech through Style Diffusion and Adversarial Training with Large Speech Language Models](https://mlsanity.com/paper/2306.07691/) (2023)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Matcha-TTS: A fast TTS architecture with conditional flow matching](https://mlsanity.com/paper/2309.03199/) (2023)
- [FastDiff: A Fast Conditional Diffusion Model for High-Quality Speech Synthesis](https://mlsanity.com/paper/2204.09934/) (2022)
- [GENIE: Higher-Order Denoising Diffusion Solvers](https://mlsanity.com/paper/2210.05475/) (2022)
- [Flow Matching Policy Gradients](https://mlsanity.com/paper/2507.21053/) (2025)
- [Guided-TTS: A Diffusion Model for Text-to-Speech via Classifier Guidance](https://mlsanity.com/paper/2111.11755/) (2021)
- [A Complete Survey on Generative AI (AIGC): Is ChatGPT from GPT-4 to GPT-5 All You Need?](https://mlsanity.com/paper/2303.11717/) (2023)
- [VideoGen: A Reference-Guided Latent Diffusion Approach for High Definition Text-to-Video Generation](https://mlsanity.com/paper/2309.00398/) (2023)
- [A Survey on Audio Diffusion Models: Text To Speech Synthesis and Enhancement in Generative AI](https://mlsanity.com/paper/2303.13336/) (2023)
- [SEEDS: Exponential SDE Solvers for Fast High-Quality Sampling from Diffusion Models](https://mlsanity.com/paper/2305.14267/) (2023)
- [Guided-TTS 2: A Diffusion Model for High-quality Adaptive Text-to-Speech with Untranscribed Data](https://mlsanity.com/paper/2205.15370/) (2022)
- [E3 TTS: Easy End-to-End Diffusion-based Text to Speech](https://mlsanity.com/paper/2311.00945/) (2023)
- [GECCO: Geometrically-Conditioned Point Diffusion Models](https://mlsanity.com/paper/2303.05916/) (2023)
- [ESPnet2-TTS: Extending the Edge of TTS Research](https://mlsanity.com/paper/2110.07840/) (2021)
- [DiffV2S: Diffusion-based Video-to-Speech Synthesis with Vision-guided Speaker Embedding](https://mlsanity.com/paper/2308.07787/) (2023)
- [Talking Face Generation with Multilingual TTS](https://mlsanity.com/paper/2205.06421/) (2022)
- [The Ethical Implications of Generative Audio Models: A Systematic Literature Review](https://mlsanity.com/paper/2307.05527/) (2023)
- [SimpleSpeech 2: Towards Simple and Efficient Text-to-Speech with Flow-based Scalar Latent Transformer Diffusion Models](https://mlsanity.com/paper/2408.13893/) (2024)

## Abstract (arXiv)

This paper introduces WaveGrad 2, a non-autoregressive generative model for text-to-speech synthesis. WaveGrad 2 is trained to estimate the gradient of the log conditional density of the waveform given a phoneme sequence. The model takes an input phoneme sequence, and through an iterative refinement process, generates an audio waveform. This contrasts to the original WaveGrad vocoder which conditions on mel-spectrogram features, generated by a separate model. The iterative refinement process starts from Gaussian noise, and through a series of refinement steps (e.g., 50 steps), progressively recovers the audio sequence. WaveGrad 2 offers a natural way to trade-off between inference speed and sample quality, through adjusting the number of refinement steps. Experiments show that the model can generate high fidelity audio, approaching the performance of a state-of-the-art neural TTS system. We also report various ablation studies over different model configurations. Audio samples are available at https://wavegrad.github.io/v2.