# ResGrad: Residual Denoising Diffusion Probabilistic Models for Text to Speech

arXiv: https://arxiv.org/abs/2212.14518 · HTML: https://mlsanity.com/paper/2212.14518/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 40 of its 51 references that are in the map.
- First posted on arXiv 30 Dec 2022.

## Placed in

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

## Builds on (most cited first, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (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)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [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)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [FastSpeech 2: Fast and High-Quality End-to-End Text to Speech](https://mlsanity.com/paper/2006.04558/) (2020)
- [LibriTTS: A Corpus Derived from LibriSpeech for Text-to-Speech](https://mlsanity.com/paper/1904.02882/) (2019)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech](https://mlsanity.com/paper/2105.06337/) (2021)
- [MelGAN: Generative Adversarial Networks for Conditional Waveform Synthesis](https://mlsanity.com/paper/1910.06711/) (2019)
- [Glow-TTS: A Generative Flow for Text-to-Speech via Monotonic Alignment Search](https://mlsanity.com/paper/2005.11129/) (2020)
- [BigVGAN: A Universal Neural Vocoder with Large-Scale Training](https://mlsanity.com/paper/2206.04658/) (2022)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [Efficient Neural Audio Synthesis](https://mlsanity.com/paper/1802.08435/) (2018)
- [Parallel WaveNet: Fast High-Fidelity Speech Synthesis](https://mlsanity.com/paper/1711.10433/) (2017)
- [A Survey on Neural Speech Synthesis](https://mlsanity.com/paper/2106.15561/) (2021)
- [DiffSinger: Singing Voice Synthesis via Shallow Diffusion Mechanism](https://mlsanity.com/paper/2105.02446/) (2021)
- [ProDiff: Progressive Fast Diffusion Model For High-Quality Text-to-Speech](https://mlsanity.com/paper/2207.06389/) (2022)
- [FastDiff: A Fast Conditional Diffusion Model for High-Quality Speech Synthesis](https://mlsanity.com/paper/2204.09934/) (2022)
- [SampleRNN: An Unconditional End-to-End Neural Audio Generation Model](https://mlsanity.com/paper/1612.07837/) (2016)

## Built on by (most cited first, 21 of 21)

- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [AudioLDM 2: Learning Holistic Audio Generation with Self-supervised Pretraining](https://mlsanity.com/paper/2308.05734/) (2023)
- [PromptTTS 2: Describing and Generating Voices with Text Prompt](https://mlsanity.com/paper/2309.02285/) (2023)
- [CoMoSpeech: One-Step Speech and Singing Voice Synthesis via Consistency Model](https://mlsanity.com/paper/2305.06908/) (2023)
- [SemantiCodec: An Ultra Low Bitrate Semantic Audio Codec for General Sound](https://mlsanity.com/paper/2405.00233/) (2024)
- [Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Series](https://mlsanity.com/paper/2410.19538/) (2024)
- [Schrodinger Bridges Beat Diffusion Models on Text-to-Speech Synthesis](https://mlsanity.com/paper/2312.03491/) (2023)
- [Generating Visual Scenes from Touch](https://mlsanity.com/paper/2309.15117/) (2023)
- [ReFlow-TTS: A Rectified Flow Model for High-fidelity Text-to-Speech](https://mlsanity.com/paper/2309.17056/) (2023)
- [U-DiT TTS: U-Diffusion Vision Transformer for Text-to-Speech](https://mlsanity.com/paper/2305.13195/) (2023)
- [Improving Diffusion Models for ECG Imputation with an Augmented Template Prior](https://mlsanity.com/paper/2310.15742/) (2023)
- [A Diffusion Model for Regular Time Series Generation from Irregular Data with Completion and Masking](https://mlsanity.com/paper/2510.06699/) (2025)
- [SonicVisionLM: Playing Sound with Vision Language Models](https://mlsanity.com/paper/2401.04394/) (2024)
- [Bailing-TTS: Chinese Dialectal Speech Synthesis Towards Human-like Spontaneous Representation](https://mlsanity.com/paper/2408.00284/) (2024)
- [ProSE: Diffusion Priors for Speech Enhancement](https://mlsanity.com/paper/2503.06375/) (2025)
- [DreamAudio: Customized Text-to-Audio Generation with Diffusion Models](https://mlsanity.com/paper/2509.06027/) (2025)
- [GuidedBridge: Training-freely Improving Bridge Models with Prior Guidance](https://mlsanity.com/paper/2606.03119/) (2026)
- [MIMII-Gen: Generative Modeling Approach for Simulated Evaluation of Anomalous Sound Detection System](https://mlsanity.com/paper/2409.18542/) (2024)
- [Audio Generation Through Score-Based Generative Modeling: Design Principles and Implementation](https://mlsanity.com/paper/2506.08457/) (2025)
- [Improving Robustness of Diffusion-Based Zero-Shot Speech Synthesis via Stable Formant Generation](https://mlsanity.com/paper/2409.09311/) (2024)
- [Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias](https://mlsanity.com/paper/2606.30821/) (2026)

## Abstract (arXiv)

Denoising Diffusion Probabilistic Models (DDPMs) are emerging in text-to-speech (TTS) synthesis because of their strong capability of generating high-fidelity samples. However, their iterative refinement process in high-dimensional data space results in slow inference speed, which restricts their application in real-time systems. Previous works have explored speeding up by minimizing the number of inference steps but at the cost of sample quality. In this work, to improve the inference speed for DDPM-based TTS model while achieving high sample quality, we propose ResGrad, a lightweight diffusion model which learns to refine the output spectrogram of an existing TTS model (e.g., FastSpeech 2) by predicting the residual between the model output and the corresponding ground-truth speech. ResGrad has several advantages: 1) Compare with other acceleration methods for DDPM which need to synthesize speech from scratch, ResGrad reduces the complexity of task by changing the generation target from ground-truth mel-spectrogram to the residual, resulting into a more lightweight model and thus a smaller real-time factor. 2) ResGrad is employed in the inference process of the existing TTS model in a plug-and-play way, without re-training this model. We verify ResGrad on the single-speaker dataset LJSpeech and two more challenging datasets with multiple speakers (LibriTTS) and high sampling rate (VCTK). Experimental results show that in comparison with other speed-up methods of DDPMs: 1) ResGrad achieves better sample quality with the same inference speed measured by real-time factor; 2) with similar speech quality, ResGrad synthesizes speech faster than baseline methods by more than 10 times. Audio samples are available at https://resgrad1.github.io/.