# A Diffusion-Based Generative Equalizer for Music Restoration

arXiv: https://arxiv.org/abs/2403.18636 · HTML: https://mlsanity.com/paper/2403.18636/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 23 of its 43 references that are in the map.
- First posted on arXiv 27 Mar 2024.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Large-scale Contrastive Language-Audio Pretraining with Feature Fusion and Keyword-to-Caption Augmentation](https://mlsanity.com/paper/2211.06687/) (2022)
- [High Fidelity Neural Audio Compression](https://mlsanity.com/paper/2210.13438/) (2022)
- [Enabling Factorized Piano Music Modeling and Generation with the MAESTRO Dataset](https://mlsanity.com/paper/1810.12247/) (2018)
- [Hybrid Transformers for Music Source Separation](https://mlsanity.com/paper/2211.08553/) (2022)
- [CADS: Unleashing the Diversity of Diffusion Models through Condition-Annealed Sampling](https://mlsanity.com/paper/2310.17347/) (2023)
- [Parallel Diffusion Models of Operator and Image for Blind Inverse Problems](https://mlsanity.com/paper/2211.10656/) (2022)
- [Adapting Frechet Audio Distance for Generative Music Evaluation](https://mlsanity.com/paper/2311.01616/) (2023)
- [Guidance with Spherical Gaussian Constraint for Conditional Diffusion](https://mlsanity.com/paper/2402.03201/) (2024)
- [Solving Audio Inverse Problems with a Diffusion Model](https://mlsanity.com/paper/2210.15228/) (2022)
- [Multi-Singer: Fast Multi-Singer Singing Voice Vocoder With A Large-Scale Corpus](https://mlsanity.com/paper/2112.10358/) (2021)
- [Opencpop: A High-Quality Open Source Chinese Popular Song Corpus for Singing Voice Synthesis](https://mlsanity.com/paper/2201.07429/) (2022)
- [Blind Audio Bandwidth Extension: A Diffusion-Based Zero-Shot Approach](https://mlsanity.com/paper/2306.01433/) (2023)
- [A Two-Stage U-Net for High-Fidelity Denoising of Historical Recordings](https://mlsanity.com/paper/2202.08702/) (2022)
- [BEHM-GAN: Bandwidth Extension of Historical Music using Generative Adversarial Networks](https://mlsanity.com/paper/2204.06478/) (2022)
- [Diffusion-Based Audio Inpainting](https://mlsanity.com/paper/2305.15266/) (2023)
- [Perceptual Loss Function for Neural Modelling of Audio Systems](https://mlsanity.com/paper/1911.08922/) (2019)
- [PJS: phoneme-balanced Japanese singing voice corpus](https://mlsanity.com/paper/2006.02959/) (2020)

## Built on by (most cited first, 12 of 12)

- [Audio Super-Resolution with Latent Bridge Models](https://mlsanity.com/paper/2509.17609/) (2025)
- [Unsupervised Estimation of Nonlinear Audio Effects: Comparing Diffusion-Based and Adversarial approaches](https://mlsanity.com/paper/2504.04751/) (2025)
- [Audio Decoding by Inverse Problem Solving](https://mlsanity.com/paper/2409.07858/) (2024)
- [Improving Music Source Separation with Diffusion and Consistency Refinement](https://mlsanity.com/paper/2412.06965/) (2024)
- [Noise-to-Notes: Diffusion-based Generation and Refinement for Automatic Drum Transcription](https://mlsanity.com/paper/2509.21739/) (2025)
- [Contrastive Diffusion Guidance for Spatial Inverse Problems](https://mlsanity.com/paper/2509.26489/) (2025)
- [SUBARU: A Practical Approach to Power Saving in Hearables Using SUB-Nyquist Audio Resolution Upsampling](https://mlsanity.com/paper/2506.22321/) (2025)
- [MusRec: Zero-Shot Text-to-Music Editing via Rectified Flow and Diffusion Transformers](https://mlsanity.com/paper/2511.04376/) (2025)
- [Latent Fourier Transform](https://mlsanity.com/paper/2604.17986/) (2026)
- [FlowSonic: Stable Zero-Shot Music Editing via High-Order Trajectory Integration](https://mlsanity.com/paper/2607.17526/) (2026)
- [Music Restoration via Latent Operator Optimization and Diffusion Model Priors](https://mlsanity.com/paper/2608.01972/) (2026)
- [End-to-End Historical Music Restoration in Latent Space](https://mlsanity.com/paper/2610.00607/) (2026)

## Abstract (arXiv)

This paper presents a novel approach to audio restoration, focusing on the enhancement of low-quality music recordings, and in particular historical ones. Building upon a previous algorithm called BABE, or Blind Audio Bandwidth Extension, we introduce BABE-2, which presents a series of improvements. This research broadens the concept of bandwidth extension to generative equalization, a novel task that, to the best of our knowledge, has not been explicitly addressed in previous studies. BABE-2 is built around an optimization algorithm utilizing priors from diffusion models, which are trained or fine-tuned using a curated set of high-quality music tracks. The algorithm simultaneously performs two critical tasks: estimation of the filter degradation magnitude response and hallucination of the restored audio. The proposed method is objectively evaluated on historical piano recordings, showing an enhancement over the prior version. The method yields similarly impressive results in rejuvenating the works of renowned vocalists Enrico Caruso and Nellie Melba. This research represents an advancement in the practical restoration of historical music.