# Fr'echet Distance Loss on Speech Representations for Text-to-Speech Synthesis

arXiv: https://arxiv.org/abs/2607.06027 · HTML: https://mlsanity.com/paper/2607.06027/

## 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 36 of its 40 references that are in the map.
- First posted on arXiv 7 Jul 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)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [HuBERT: Self-Supervised Speech Representation Learning by Masked Prediction of Hidden Units](https://mlsanity.com/paper/2106.07447/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [WavLM: Large-Scale Self-Supervised Pre-Training for Full Stack Speech Processing](https://mlsanity.com/paper/2110.13900/) (2021)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [Neural Codec Language Models are Zero-Shot Text to Speech Synthesizers](https://mlsanity.com/paper/2301.02111/) (2023)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [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)
- [Seed-TTS: A Family of High-Quality Versatile Speech Generation Models](https://mlsanity.com/paper/2406.02430/) (2024)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [NaturalSpeech 2: Latent Diffusion Models are Natural and Zero-Shot Speech and Singing Synthesizers](https://mlsanity.com/paper/2304.09116/) (2023)
- [NaturalSpeech 3: Zero-Shot Speech Synthesis with Factorized Codec and Diffusion Models](https://mlsanity.com/paper/2403.03100/) (2024)
- [DNSMOS P.835: A Non-Intrusive Perceptual Objective Speech Quality Metric to Evaluate Noise Suppressors](https://mlsanity.com/paper/2110.01763/) (2021)
- [E2 TTS: Embarrassingly Easy Fully Non-Autoregressive Zero-Shot TTS](https://mlsanity.com/paper/2406.18009/) (2024)
- [CosyVoice 3: Towards In-the-wild Speech Generation via Scaling-up and Post-training](https://mlsanity.com/paper/2505.17589/) (2025)
- [Matcha-TTS: A fast TTS architecture with conditional flow matching](https://mlsanity.com/paper/2309.03199/) (2023)
- [Qwen3-TTS Technical Report](https://mlsanity.com/paper/2601.15621/) (2026)
- [SoundStorm: Efficient Parallel Audio Generation](https://mlsanity.com/paper/2305.09636/) (2023)

## Abstract (arXiv)

Few-step diffusion and flow-matching text-to-speech (TTS) models are usually trained with local objectives, such as conditional flow matching, reconstruction, and stop prediction. These losses provide stable optimization, but they never ask whether sampled speech follows the distribution of high-quality speech. We propose Speech Representation Fr'echet Distance loss (SR-FD), a training-time distributional regularizer for tokenizer-free flow-matching autoregressive TTS. During fine-tuning, the model synthesizes speech with the same few-step sampler used at deployment, and SR-FD matches the mean and covariance of frozen Whisper and CTC features of this speech to reference statistics computed offline from three complementary content targets. The loss requires no discriminator and no inference-time computation. On Seed-TTS English, four-step SR-FD fine-tuning reduces WER from the original four-step VoxCPM2 baseline's 2.2279% to 1.4147%, a 36.5% relative reduction, and also surpasses the original ten-step baseline at 1.7366%; both gains are significant under an utterance-level paired bootstrap. Speaker similarity and objective quality proxies are preserved at the ten-step level, and an error analysis shows the gain comes from content substitutions across all prompt lengths. SR-FD is thus an intelligibility-improving distributional regularizer for few-step TTS.