A Diffusion-Based Generative Equalizer for Music Restoration

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 significant improvements. This research broadens the concept of bandwidth extension to \emph{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 a marked 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.

Diffusion Models for Audio Restoration

With the development of audio playback devices and fast data transmission, the demand for high sound quality is rising, for both entertainment and communications. In this quest for better sound quality, challenges emerge from distortions and interferences originating at the recording side or caused by an imperfect transmission pipeline. To address this problem, audio restoration methods aim to recover clean sound signals from the corrupted input data. We present here audio restoration algorithms based on diffusion models, with a focus on speech enhancement and music restoration tasks. Traditional approaches, often grounded in handcrafted rules and statistical heuristics, have shaped our understanding of audio signals. In the past decades, there has been a notable shift towards data-driven methods that exploit the modeling capabilities of deep neural networks (DNNs). Deep generative models, and among them diffusion models, have emerged as powerful techniques for learning complex data distributions. However, relying solely on DNN-based learning approaches carries the risk of reducing interpretability, particularly when employing end-to-end models. Nonetheless, data-driven approaches allow more flexibility in comparison to statistical model-based frameworks whose performance depends on distributional and statistical assumptions that can be difficult to guarantee. Here, we aim to show that diffusion models can combine the best of both worlds and offer the opportunity to design audio restoration algorithms with a good degree of interpretability and a remarkable performance in terms of sound quality.

Noise Morphing for Audio Time Stretching

This letter introduces an innovative method to enhance the quality of audio time stretching by precisely decomposing a sound into sines, transients, and noise and by improving the processing of the latter component. While there are established methods for time-stretching sines and transients with high quality, the manipulation of noise or residual components has lacked robust solutions in prior research. The proposed method combines sound decomposition with previous techniques for audio spectral resynthesis. The time-stretched noise component is achieved by morphing its time-interpolated spectral magnitude with a white-noise excitation signal. This method stands out for its simplicity, efficiency, and audio quality. The results of a subjective experiment affirm the superiority of this approach over current state-of-the-art methods across all evaluated stretch factors. The proposed technique notably excels in extreme stretching scenarios, signifying a substantial elevation in performance. The proposed method holds promise for a wide range of applications in slow-motion media content, such as music or sports video production.

Zero-Shot Blind Audio Bandwidth Extension

Audio bandwidth extension involves the realistic reconstruction of high-frequency spectra from bandlimited observations. In cases where the lowpass degradation is unknown, such as in restoring historical audio recordings, this becomes a blind problem. This paper introduces a novel method called BABE (Blind Audio Bandwidth Extension) that addresses the blind problem in a zero-shot setting, leveraging the generative priors of a pre-trained unconditional diffusion model. During the inference process, BABE utilizes a generalized version of diffusion posterior sampling, where the degradation operator is unknown but parametrized and inferred iteratively. The performance of the proposed method is evaluated using objective and subjective metrics, and the results show that BABE surpasses state-of-the-art blind bandwidth extension baselines and achieves competitive performance compared to non-blind filter-informed methods when tested with synthetic data. Moreover, BABE exhibits robust generalization capabilities when enhancing real historical recordings, effectively reconstructing the missing high-frequency content while maintaining coherence with the original recording. Subjective preference tests confirm that BABE significantly improves the audio quality of historical music recordings. Examples of historical recordings restored with the proposed method are available on the companion webpage: (http://research.spa.aalto.fi/publications/papers/ieee-taslp-babe/)

Neural modeling of magnetic tape recorders

The sound of magnetic recording media, such as open-reel and cassette tape recorders, is still sought after by today's sound practitioners due to the imperfections embedded in the physics of the magnetic recording process. This paper proposes a method for digitally emulating this character using neural networks. The signal chain of the proposed system consists of three main components: the hysteretic nonlinearity and filtering jointly produced by the magnetic recording process as well as the record and playback amplifiers, the fluctuating delay originating from the tape transport, and the combined additive noise component from various electromagnetic origins. In our approach, the hysteretic nonlinear block is modeled using a recurrent neural network, while the delay trajectories and the noise component are generated using separate diffusion models, which employ U-net deep convolutional neural networks. According to the conducted objective evaluation, the proposed architecture faithfully captures the character of the magnetic tape recorder. The results of this study can be used to construct virtual replicas of vintage sound recording devices with applications in music production and audio antiquing tasks.

Diffusion-Based Audio Inpainting

Audio inpainting aims to reconstruct missing segments in corrupted recordings. Previous methods produce plausible reconstructions when the gap length is shorter than about 100\;ms, but the quality decreases for longer gaps. This paper explores recent advancements in deep learning and, particularly, diffusion models, for the task of audio inpainting. The proposed method uses an unconditionally trained generative model, which can be conditioned in a zero-shot fashion for audio inpainting, offering high flexibility to regenerate gaps of arbitrary length. An improved deep neural network architecture based on the constant-Q transform, which allows the model to exploit pitch-equivariant symmetries in audio, is also presented. The performance of the proposed algorithm is evaluated through objective and subjective metrics for the task of reconstructing short to mid-sized gaps. The results of a formal listening test show that the proposed method delivers a comparable performance against state-of-the-art for short gaps, while retaining a good audio quality and outperforming the baselines for the longest gap lengths tested, 150\;ms and 200\;ms. This work helps improve the restoration of sound recordings having fairly long local disturbances or dropouts, which must be reconstructed.

Solving Audio Inverse Problems with a Diffusion Model

This paper presents CQT-Diff, a data-driven generative audio model that can, once trained, be used for solving various different audio inverse problems in a problem-agnostic setting. CQT-Diff is a neural diffusion model with an architecture that is carefully constructed to exploit pitch-equivariant symmetries in music. This is achieved by preconditioning the model with an invertible Constant-Q Transform (CQT), whose logarithmically-spaced frequency axis represents pitch equivariance as translation equivariance. The proposed method is evaluated with objective and subjective metrics in three different and varied tasks: audio bandwidth extension, inpainting, and declipping. The results show that CQT-Diff outperforms the compared baselines and ablations in audio bandwidth extension and, without retraining, delivers competitive performance against modern baselines in audio inpainting and declipping. This work represents the first diffusion-based general framework for solving inverse problems in audio processing.

Realistic Gramophone Noise Synthesis using a Diffusion Model

This paper introduces a novel data-driven strategy for synthesizing gramophone noise textures. A diffusion probabilistic model is applied to generate highly realistic quasiperiodic noises. The proposed model is designed to generate samples of length equal to one disk revolution, but a method to generate plausible periodic variations between revolutions is also proposed. A guided approach is also applied as a conditioning method, where an audio signal generated with manually-tuned signal processing is refined via reverse diffusion to appear more realistically sounding. The method has been evaluated in a subjective listening test, in which the participants were often unable to recognize the synthesized signals from the real ones. The synthetic noises produced with the best proposed unconditional method are statistically indistinguishable from real noise recordings. This work shows the potential of diffusion models for highly realistic audio synthesis tasks.

BEHM-GAN: Bandwidth Extension of Historical Music using Generative Adversarial Networks

Audio bandwidth extension aims to expand the spectrum of narrow-band audio signals. Although this topic has been broadly studied during recent years, the particular problem of extending the bandwidth of historical music recordings remains an open challenge. This paper proposes BEHM-GAN, a model based on generative adversarial networks, as a practical solution to this problem. The proposed method works with the complex spectrogram representation of audio and, thanks to a dedicated regularization strategy, can effectively extend the bandwidth of out-of-distribution real historical recordings. The BEHM-GAN is designed to be applied as a second step after denoising the recording to suppress any additive disturbances, such as clicks and background noise. We train and evaluate the method using solo piano classical music. The proposed method outperforms the compared baselines in both objective and subjective experiments. The results of a formal blind listening test show that BEHM-GAN significantly increases the perceptual sound quality in early-20th-century gramophone recordings. For several items, there is a substantial improvement in the mean opinion score after enhancing historical recordings with the proposed bandwidth-extension algorithm. This study represents a relevant step toward data-driven music restoration in real-world scenarios.