# Discrete-Time Diffusion-Like Models for Speech Synthesis

arXiv: https://arxiv.org/abs/2509.18470 · HTML: https://mlsanity.com/paper/2509.18470/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 23 of its 30 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [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)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech](https://mlsanity.com/paper/2105.06337/) (2021)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Glow-TTS: A Generative Flow for Text-to-Speech via Monotonic Alignment Search](https://mlsanity.com/paper/2005.11129/) (2020)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Matcha-TTS: A fast TTS architecture with conditional flow matching](https://mlsanity.com/paper/2309.03199/) (2023)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [The T05 System for The VoiceMOS Challenge 2024: Transfer Learning from Deep Image Classifier to Naturalness MOS Prediction of High-Quality Synthetic Speech](https://mlsanity.com/paper/2409.09305/) (2024)
- [Flowtron: an Autoregressive Flow-based Generative Network for Text-to-Speech Synthesis](https://mlsanity.com/paper/2005.05957/) (2020)
- [VoiceFlow: Efficient Text-to-Speech with Rectified Flow Matching](https://mlsanity.com/paper/2309.05027/) (2023)
- [A Bayesian Multilevel Random-Effects Model for Estimating Noise in Image Sensors](https://mlsanity.com/paper/2004.11849/) (2020)

## Abstract (arXiv)

Diffusion models have attracted a lot of attention in recent years. These models view speech generation as a continuous-time process. For efficient training, this process is typically restricted to additive Gaussian noising, which is limiting. For inference, the time is typically discretized, leading to the mismatch between continuous training and discrete sampling conditions. Recently proposed discrete-time processes, on the other hand, usually do not have these limitations, may require substantially fewer inference steps, and are fully consistent between training/inference conditions. This paper explores some diffusion-like discrete-time processes and proposes some new variants. These include processes applying additive Gaussian noise, multiplicative Gaussian noise, blurring noise and a mixture of blurring and Gaussian noises. The experimental results suggest that discrete-time processes offer comparable subjective and objective speech quality to their widely popular continuous counterpart, with more efficient and consistent training and inference schemas.