# Kinetic-Optimal Scheduling with Moment Correction for Metric-Induced Discrete Flow Matching in Zero-Shot Text-to-Speech

arXiv: https://arxiv.org/abs/2605.09386 · HTML: https://mlsanity.com/paper/2605.09386/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 36 of its 41 references that are in the map.
- First posted on arXiv 10 May 2026.

## Placed in

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

## Builds on (most cited first, 30 of 36)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [WavLM: Large-Scale Self-Supervised Pre-Training for Full Stack Speech Processing](https://mlsanity.com/paper/2110.13900/) (2021)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [SoundStream: An End-to-End Neural Audio Codec](https://mlsanity.com/paper/2107.03312/) (2021)
- [Neural Codec Language Models are Zero-Shot Text to Speech Synthesizers](https://mlsanity.com/paper/2301.02111/) (2023)
- [High Fidelity Neural Audio Compression](https://mlsanity.com/paper/2210.13438/) (2022)
- [LibriTTS: A Corpus Derived from LibriSpeech for Text-to-Speech](https://mlsanity.com/paper/1904.02882/) (2019)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [High-Fidelity Audio Compression with Improved RVQGAN](https://mlsanity.com/paper/2306.06546/) (2023)
- [UTMOS: UTokyo-SaruLab System for VoiceMOS Challenge 2022](https://mlsanity.com/paper/2204.02152/) (2022)
- [F5-TTS: A Fairytaler that Fakes Fluent and Faithful Speech with Flow Matching](https://mlsanity.com/paper/2410.06885/) (2024)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Seed-TTS: A Family of High-Quality Versatile Speech Generation Models](https://mlsanity.com/paper/2406.02430/) (2024)
- [CosyVoice 2: Scalable Streaming Speech Synthesis with Large Language Models](https://mlsanity.com/paper/2412.10117/) (2024)
- [Emilia: An Extensive, Multilingual, and Diverse Speech Dataset for Large-Scale Speech Generation](https://mlsanity.com/paper/2407.05361/) (2024)
- [MaskGCT: Zero-Shot Text-to-Speech with Masked Generative Codec Transformer](https://mlsanity.com/paper/2409.00750/) (2024)
- [Vocos: Closing the gap between time-domain and Fourier-based neural vocoders for high-quality audio synthesis](https://mlsanity.com/paper/2306.00814/) (2023)
- [CosyVoice 3: Towards In-the-wild Speech Generation via Scaling-up and Post-training](https://mlsanity.com/paper/2505.17589/) (2025)
- [Paraformer: Fast and Accurate Parallel Transformer for Non-autoregressive End-to-End Speech Recognition](https://mlsanity.com/paper/2206.08317/) (2022)
- [Qwen3-TTS Technical Report](https://mlsanity.com/paper/2601.15621/) (2026)
- [SoundStorm: Efficient Parallel Audio Generation](https://mlsanity.com/paper/2305.09636/) (2023)
- [Spark-TTS: An Efficient LLM-Based Text-to-Speech Model with Single-Stream Decoupled Speech Tokens](https://mlsanity.com/paper/2503.01710/) (2025)
- [IndexTTS2: A Breakthrough in Emotionally Expressive and Duration-Controlled Auto-Regressive Zero-Shot Text-to-Speech](https://mlsanity.com/paper/2506.21619/) (2025)
- [Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspective](https://mlsanity.com/paper/2412.03487/) (2024)
- [FUDOKI: Discrete Flow-based Unified Understanding and Generation via Kinetic-Optimal Velocities](https://mlsanity.com/paper/2505.20147/) (2025)
- [FireRedTTS-2: Towards Long Conversational Speech Generation for Podcast and Chatbot](https://mlsanity.com/paper/2509.02020/) (2025)

## Built on by (most cited first, 1 of 1)

- [Mask, Sample, Revise: A Revisable CTMC Inference Stack for Guided Discrete Flow Matching Text-to-Speech](https://mlsanity.com/paper/2606.13989/) (2026)

## Abstract (arXiv)

Metric-induced discrete flow matching (MI-DFM) exploits token-latent geometry for discrete generation, but its practical use is limited by two issues: heuristic schedulers requiring hyperparameter search, and finite-step path-tracking error from its first-order continuous-time Markov chain (CTMC) solver. We address both issues. First, we derive a kinetic-optimal scheduler for prescribed scalar-parameterized probability paths, and instantiate it for MI-DFM as a training-free numerical schedule that traverses the path at constant Fisher-Rao speed. Second, we introduce a finite-step moment correction that adjusts the jump probability while preserving the CTMC jump destination distribution. We validate the resulting method, GibbsTTS, on codec-based zero-shot text-to-speech (TTS). Under controlled comparisons with a unified architecture and large-scale dataset, GibbsTTS achieves the best objective naturalness and is preferred in subjective evaluations over masked discrete generative baselines. Additionally, in comparison with the evaluated state-of-the-art TTS systems, GibbsTTS shows strong speaker similarity, achieving the highest similarity on three of four test sets and ranking second on the fourth. Project page: https://ydqmkkx.github.io/GibbsTTSProject