# Boosting Fast and High-Quality Speech Synthesis with Linear Diffusion

arXiv: https://arxiv.org/abs/2306.05708 · HTML: https://mlsanity.com/paper/2306.05708/

## Key facts

- Cited by 4 papers in the map (data through 7 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 22 of its 25 references that are in the map.
- First posted on arXiv 9 Jun 2023.

## Placed in

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

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [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)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [LibriTTS: A Corpus Derived from LibriSpeech for Text-to-Speech](https://mlsanity.com/paper/1904.02882/) (2019)
- [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)
- [MelGAN: Generative Adversarial Networks for Conditional Waveform Synthesis](https://mlsanity.com/paper/1910.06711/) (2019)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [FastDiff: A Fast Conditional Diffusion Model for High-Quality Speech Synthesis](https://mlsanity.com/paper/2204.09934/) (2022)
- [BDDM: Bilateral Denoising Diffusion Models for Fast and High-Quality Speech Synthesis](https://mlsanity.com/paper/2203.13508/) (2022)
- [DiffGAN-TTS: High-Fidelity and Efficient Text-to-Speech with Denoising Diffusion GANs](https://mlsanity.com/paper/2201.11972/) (2022)
- [LVCNet: Efficient Condition-Dependent Modeling Network for Waveform Generation](https://mlsanity.com/paper/2102.10815/) (2021)

## Built on by (most cited first, 4 of 4)

- [VoiceFlow: Efficient Text-to-Speech with Rectified Flow Matching](https://mlsanity.com/paper/2309.05027/) (2023)
- [Survey of Video Diffusion Models: Foundations, Implementations, and Applications](https://mlsanity.com/paper/2504.16081/) (2025)
- [Optimizing Multilingual Text-To-Speech with Accents & Emotions](https://mlsanity.com/paper/2506.16310/) (2025)
- [SSG-Dit: A Spatial Signal Guided Framework for Controllable Video Generation](https://mlsanity.com/paper/2508.17062/) (2025)

## Abstract (arXiv)

Denoising Diffusion Probabilistic Models have shown extraordinary ability on various generative tasks. However, their slow inference speed renders them impractical in speech synthesis. This paper proposes a linear diffusion model (LinDiff) based on an ordinary differential equation to simultaneously reach fast inference and high sample quality. Firstly, we employ linear interpolation between the target and noise to design a diffusion sequence for training, while previously the diffusion path that links the noise and target is a curved segment. When decreasing the number of sampling steps (i.e., the number of line segments used to fit the path), the ease of fitting straight lines compared to curves allows us to generate higher quality samples from a random noise with fewer iterations. Secondly, to reduce computational complexity and achieve effective global modeling of noisy speech, LinDiff employs a patch-based processing approach that partitions the input signal into small patches. The patch-wise token leverages Transformer architecture for effective modeling of global information. Adversarial training is used to further improve the sample quality with decreased sampling steps. We test proposed method with speech synthesis conditioned on acoustic feature (Mel-spectrograms). Experimental results verify that our model can synthesize high-quality speech even with only one diffusion step. Both subjective and objective evaluations demonstrate that our model can synthesize speech of a quality comparable to that of autoregressive models with faster synthesis speed (3 diffusion steps).