# Harmonizing Spectral Evolution in Conditional Flow Matching for TTS

arXiv: https://arxiv.org/abs/2609.34431 · HTML: https://mlsanity.com/paper/2609.34431/

## 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 15 of its 19 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

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

## Builds on (most cited first, 15 of 15)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [CNN Architectures for Large-Scale Audio Classification](https://mlsanity.com/paper/1609.09430/) (2016)
- [LibriTTS: A Corpus Derived from LibriSpeech for Text-to-Speech](https://mlsanity.com/paper/1904.02882/) (2019)
- [UTMOS: UTokyo-SaruLab System for VoiceMOS Challenge 2022](https://mlsanity.com/paper/2204.02152/) (2022)
- [Voicebox: Text-Guided Multilingual Universal Speech Generation at Scale](https://mlsanity.com/paper/2306.15687/) (2023)
- [F5-TTS: A Fairytaler that Fakes Fluent and Faithful Speech with Flow Matching](https://mlsanity.com/paper/2410.06885/) (2024)
- [Fr'echet Audio Distance: A Metric for Evaluating Music Enhancement Algorithms](https://mlsanity.com/paper/1812.08466/) (2018)
- [Matcha-TTS: A fast TTS architecture with conditional flow matching](https://mlsanity.com/paper/2309.03199/) (2023)
- [Diffusion Probabilistic Model Made Slim](https://mlsanity.com/paper/2211.17106/) (2022)
- [Boosting Diffusion Models with Moving Average Sampling in Frequency Domain](https://mlsanity.com/paper/2403.17870/) (2024)
- [Vistaar: Diverse Benchmarks and Training Sets for Indian Language ASR](https://mlsanity.com/paper/2305.15386/) (2023)
- [IndicVoices-R: Unlocking a Massive Multilingual Multi-speaker Speech Corpus for Scaling Indian TTS](https://mlsanity.com/paper/2409.05356/) (2024)

## Abstract (arXiv)

Conditional Flow Matching (CFM) models for text-to-speech (TTS) suffer from incoherent frequency evolution during inference. While similar spectral imbalances are addressed in diffusion models for other domains, those generic solutions fail to generalize to the inherently uncoordinated acoustic dynamics of CFM. We demonstrate that this issue can be effectively mitigated by introducing a novel training-free frequency-selective boosting strategy. Using the Discrete Wavelet Transform (DWT), our method dynamically modulates mel-spectrogram sub-bands during ODE integration, synchronizing spectral development by penalizing aggressive low-frequency growth and boosting lagging high-frequency details. Validated across diverse architectures (Matcha-TTS, F5-TTS, IndicF5), our approach reduces the required Number of Function Evaluations (NFE) from 32 to 26 and improves Frechet Audio Distance (FAD) by up to 61%, all without compromising mean opinion scores, speaker similarity, and speech intelligibility.