# On the Geometry of Music Bandwidth Extension in Latent Spaces of Audio Codecs

arXiv: https://arxiv.org/abs/2608.03721 · HTML: https://mlsanity.com/paper/2608.03721/

## 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 33 of its 43 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [SoundStream: An End-to-End Neural Audio Codec](https://mlsanity.com/paper/2107.03312/) (2021)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [High Fidelity Neural Audio Compression](https://mlsanity.com/paper/2210.13438/) (2022)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [High-Fidelity Audio Compression with Improved RVQGAN](https://mlsanity.com/paper/2306.06546/) (2023)
- [Enabling Factorized Piano Music Modeling and Generation with the MAESTRO Dataset](https://mlsanity.com/paper/1810.12247/) (2018)
- [Speech Enhancement and Dereverberation with Diffusion-based Generative Models](https://mlsanity.com/paper/2208.05830/) (2022)
- [Stable Audio Open](https://mlsanity.com/paper/2407.14358/) (2024)
- [Diffusion Models for Image Restoration and Enhancement: A Comprehensive Survey](https://mlsanity.com/paper/2308.09388/) (2023)
- [Long-form music generation with latent diffusion](https://mlsanity.com/paper/2404.10301/) (2024)
- [AUDIT: Audio Editing by Following Instructions with Latent Diffusion Models](https://mlsanity.com/paper/2304.00830/) (2023)
- [ViSQOL v3: An Open Source Production Ready Objective Speech and Audio Metric](https://mlsanity.com/paper/2004.09584/) (2020)
- [Codec Does Matter: Exploring the Semantic Shortcoming of Codec for Audio Language Model](https://mlsanity.com/paper/2408.17175/) (2024)
- [Solving Audio Inverse Problems with a Diffusion Model](https://mlsanity.com/paper/2210.15228/) (2022)
- [VoiceFixer: Toward General Speech Restoration with Neural Vocoder](https://mlsanity.com/paper/2109.13731/) (2021)
- [AudioSR: Versatile Audio Super-resolution at Scale](https://mlsanity.com/paper/2309.07314/) (2023)
- [Music2Latent: Consistency Autoencoders for Latent Audio Compression](https://mlsanity.com/paper/2408.06500/) (2024)
- [Audio Super Resolution using Neural Networks](https://mlsanity.com/paper/1708.00853/) (2017)
- [Learning Disentangled Representations of Timbre and Pitch for Musical Instrument Sounds Using Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1906.08152/) (2019)
- [Blind Audio Bandwidth Extension: A Diffusion-Based Zero-Shot Approach](https://mlsanity.com/paper/2306.01433/) (2023)
- [FLowHigh: Towards Efficient and High-Quality Audio Super-Resolution with Single-Step Flow Matching](https://mlsanity.com/paper/2501.04926/) (2025)
- [ETTA: Elucidating the Design Space of Text-to-Audio Models](https://mlsanity.com/paper/2412.19351/) (2024)
- [A2SB: Audio-to-Audio Schrodinger Bridges](https://mlsanity.com/paper/2501.11311/) (2025)
- [High-Resolution Speech Restoration with Latent Diffusion Model](https://mlsanity.com/paper/2409.11145/) (2024)
- [CoDiCodec: Unifying Continuous and Discrete Compressed Representations of Audio](https://mlsanity.com/paper/2509.09836/) (2025)

## Abstract (arXiv)

Recent audio restoration increasingly relies on large-scale conditional latent generative modeling, including diffusion, Schrodinger Bridges, and Flow Matching variants, to invert degradations such as bandwidth limitation or noise. We present an analysis of the performance of various state-of-the-art methods compared to simple arithmetic transformations in the latent spaces of multiple neural codecs for musical bandwidth extension. We show that estimating a single transport vector between the clean and degraded latent centroids on a reference set, and adding it to degraded latents, can yield restoration performance competitive with large diffusion models. This suggests, first, that some neural codec latent spaces exhibit structure aligned with audio bandwidth; and second, that in such cases complex conditional models may offer only limited gains over a simple vector addition. We argue that these findings reveal an interesting avenue for future research whereby models could take advantage of the latent space structure in order to offer greater training and parameter efficiency, and overall better performance. Additionally, we propose to consider this simple arithmetic transformation as a baseline for music bandwidth extension research, as it allows an assessment of the contribution of learnable parameters towards restoration performance.