# Continuous-Time Acoustic Modelling with Neural Controlled Differential Equations

arXiv: https://arxiv.org/abs/2609.11725 · HTML: https://mlsanity.com/paper/2609.11725/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [WavLM: Large-Scale Self-Supervised Pre-Training for Full Stack Speech Processing](https://mlsanity.com/paper/2110.13900/) (2021)
- [Natural TTS Synthesis by Conditioning WaveNet on Mel Spectrogram Predictions](https://mlsanity.com/paper/1712.05884/) (2017)
- [Conditional Variational Autoencoder with Adversarial Learning for End-to-End Text-to-Speech](https://mlsanity.com/paper/2106.06103/) (2021)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech](https://mlsanity.com/paper/2105.06337/) (2021)
- [F5-TTS: A Fairytaler that Fakes Fluent and Faithful Speech with Flow Matching](https://mlsanity.com/paper/2410.06885/) (2024)
- [Glow-TTS: A Generative Flow for Text-to-Speech via Monotonic Alignment Search](https://mlsanity.com/paper/2005.11129/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [NaturalSpeech 3: Zero-Shot Speech Synthesis with Factorized Codec and Diffusion Models](https://mlsanity.com/paper/2403.03100/) (2024)
- [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)
- [Matcha-TTS: A fast TTS architecture with conditional flow matching](https://mlsanity.com/paper/2309.03199/) (2023)
- [Seen and Unseen emotional style transfer for voice conversion with a new emotional speech dataset](https://mlsanity.com/paper/2010.14794/) (2020)
- [StyleTTS: A Style-Based Generative Model for Natural and Diverse Text-to-Speech Synthesis](https://mlsanity.com/paper/2205.15439/) (2022)
- [Attentive Neural Controlled Differential Equations for Time-series Classification and Forecasting](https://mlsanity.com/paper/2109.01876/) (2021)
- [Phoneme-Level BERT for Enhanced Prosody of Text-to-Speech with Grapheme Predictions](https://mlsanity.com/paper/2301.08810/) (2023)
- [Towards Controllable Speech Synthesis in the Era of Large Language Models: A Systematic Survey](https://mlsanity.com/paper/2412.06602/) (2024)
- [Training Data Augmentation for Dysarthric Automatic Speech Recognition by Text-to-Dysarthric-Speech Synthesis](https://mlsanity.com/paper/2406.08568/) (2024)
- [TTSDS -- Text-to-Speech Distribution Score](https://mlsanity.com/paper/2407.12707/) (2024)
- [On the Relevance of Phoneme Duration Variability of Synthesized Training Data for Automatic Speech Recognition](https://mlsanity.com/paper/2310.08132/) (2023)

## Abstract (arXiv)

Text-to-speech (TTS) models commonly address text--speech alignment by expanding phone-level encoder states to frame-level decoder inputs using predicted durations. While this length-regulation step resolves alignment structurally, this use of duration typically changes only where and how often latent states appear, not the values of the states themselves. This paper proposes a continuous-time mechanism for duration-aware acoustic modelling in TTS using neural controlled differential equations (CDEs). We formulate the phone representation as a temporally parameterised control path and use a neural acoustic vector field to produce a continuous-time hidden state whose values evolve with phonetic content and duration-derived timing. The resulting trajectory can be sampled at discrete points and integrated into a standard acoustic decoder pipeline. Objective results contrast CDEs and typical recurrent models. Subjective results suggest that CDE-based models evaluating one phone per step can improve rank-order agreement between synthesised and reference emotion intensity while maintaining comparable emotion-expression quality to a strong baseline. Additional experiments with half-phone step-sizes suggest that temporal resolution changes the trade-off between style tracking and absolute calibration. These results position CDEs as a promising design space for continuous-time and duration-aware style-sensitive TTS.