# Efficient Speech Language Modeling via Energy Distance in Continuous Latent Space

arXiv: https://arxiv.org/abs/2505.13181 · HTML: https://mlsanity.com/paper/2505.13181/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 82 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 30 of 61)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [HuBERT: Self-Supervised Speech Representation Learning by Masked Prediction of Hidden Units](https://mlsanity.com/paper/2106.07447/) (2021)
- [Conformer: Convolution-augmented Transformer for Speech Recognition](https://mlsanity.com/paper/2005.08100/) (2020)
- [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)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [Autoregressive Image Generation without Vector Quantization](https://mlsanity.com/paper/2406.11838/) (2024)
- [Moshi: a speech-text foundation model for real-time dialogue](https://mlsanity.com/paper/2410.00037/) (2024)
- [SpeechGPT: Empowering Large Language Models with Intrinsic Cross-Modal Conversational Abilities](https://mlsanity.com/paper/2305.11000/) (2023)
- [High-Fidelity Audio Compression with Improved RVQGAN](https://mlsanity.com/paper/2306.06546/) (2023)
- [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)
- [Generative Spoken Language Modeling from Raw Audio](https://mlsanity.com/paper/2102.01192/) (2021)
- [CosyVoice: A Scalable Multilingual Zero-shot Text-to-speech Synthesizer based on Supervised Semantic Tokens](https://mlsanity.com/paper/2407.05407/) (2024)
- [Speech Resynthesis from Discrete Disentangled Self-Supervised Representations](https://mlsanity.com/paper/2104.00355/) (2021)
- [DNSMOS: A Non-Intrusive Perceptual Objective Speech Quality metric to evaluate Noise Suppressors](https://mlsanity.com/paper/2010.15258/) (2020)
- [DNSMOS P.835: A Non-Intrusive Perceptual Objective Speech Quality Metric to Evaluate Noise Suppressors](https://mlsanity.com/paper/2110.01763/) (2021)
- [MaskGCT: Zero-Shot Text-to-Speech with Masked Generative Codec Transformer](https://mlsanity.com/paper/2409.00750/) (2024)

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

- [Continuous Autoregressive Language Models](https://mlsanity.com/paper/2510.27688/) (2025)

## Abstract (arXiv)

We introduce SLED, an alternative approach to speech language modeling by encoding speech waveforms into sequences of continuous latent representations and modeling them autoregressively using an energy distance objective. The energy distance offers an analytical measure of the distributional gap by contrasting simulated and target samples, enabling efficient training to capture the underlying continuous autoregressive distribution. By bypassing reliance on residual vector quantization, SLED avoids discretization errors and eliminates the need for the complicated hierarchical architectures common in existing speech language models. It simplifies the overall modeling pipeline while preserving the richness of speech information and maintaining inference efficiency. Empirical results demonstrate that SLED achieves strong performance in both zero-shot and streaming speech synthesis, showing its potential for broader applications in general-purpose speech language models.