# Optimality of FSQ Tokens for Continuous Diffusion for Categorical Data with Application to Text-to-Speech

arXiv: https://arxiv.org/abs/2606.09962 · HTML: https://mlsanity.com/paper/2606.09962/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 51 of its 58 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 30 of 51)

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- [WavLM: Large-Scale Self-Supervised Pre-Training for Full Stack Speech Processing](https://mlsanity.com/paper/2110.13900/) (2021)
- [HiFi-GAN: Generative Adversarial Networks for Efficient and High Fidelity Speech Synthesis](https://mlsanity.com/paper/2010.05646/) (2020)
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- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
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- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Libri-Light: A Benchmark for ASR with Limited or No Supervision](https://mlsanity.com/paper/1912.07875/) (2019)
- [Finite Scalar Quantization: VQ-VAE Made Simple](https://mlsanity.com/paper/2309.15505/) (2023)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [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)
- [VideoFusion: Decomposed Diffusion Models for High-Quality Video Generation](https://mlsanity.com/paper/2303.08320/) (2023)
- [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)
- [NaturalSpeech 3: Zero-Shot Speech Synthesis with Factorized Codec and Diffusion Models](https://mlsanity.com/paper/2403.03100/) (2024)
- [Implicit Diffusion Models for Continuous Super-Resolution](https://mlsanity.com/paper/2303.16491/) (2023)
- [AnyGPT: Unified Multimodal LLM with Discrete Sequence Modeling](https://mlsanity.com/paper/2402.12226/) (2024)

## Abstract (arXiv)

Continuous diffusion for categorical data is a framework belonging to the diffusion family and aiming at generating discrete data. The scientific interest to such models has been constantly increasing these days because researchers try to achieve a challenging goal of finding reasonable alternatives to autoregressive large language models. In this paper, we study the properties of the structure of the latent space corresponding to discrete tokens expressed in terms of Kullback-Leibler divergence on diffusion path measures and accuracy of the correct token prediction by the optimally trained diffusion model. We find that FSQ tokenization scheme has the latent space structure with the properties that make it best suited for continuous diffusion for categorical data as verified through rigorous theoretical analysis and numerical experiments. To validate our findings in real-life scenario, we train several text-to-speech diffusion models having speech tokens as intermediate acoustic features, and show that the one based on FSQ tokens indeed performs the best, and, moreover, it outperforms its strong LLM-based counterpart, at the same time being significantly smaller and faster.