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

Music restoration seeks to recover a clean signal from an observed recording degraded by an unknown effect, distortion, or corruption. Existing systems often rely on paired training data and distortion-specific supervision, which limits their use when the forward process is not known in advance. We propose LOUDAR (Latent-space Optimization of Unknown Distortion for Audio Restoration) a general-purpose restoration method that operates in the latent space of a pretrained audio autoencoder and models the unknown distortion as a learnable latent operator. At inference time, LOUDAR alternates between estimating the clean latent variable and updating the latent operator parameters. An unconditional latent diffusion model provides a prior over clean audio and regularizes this inference by steering the latent estimate toward the manifold of clean recordings. Because the degradation model is adapted per input, the approach is broadly applicable across diverse restoration problems. We evaluate LOUDAR on singing voice effect removal and restoration, as well as guitar distortion removal, and show that it consistently improves over degraded inputs and is competitive with supervised and unsupervised baselines in waveform and latent domains.

Audio super-resolution (SR), also referred to as bandwidth extension (BWE), aims to reconstruct high-fidelity signals from low-resolution (LR) or band-limited (BL) observations, an inherently ill-posed task due to the ambiguity of missing high-frequency (HF) content. This survey provides a comprehensive overview of the field, with a particular focus on the paradigm shift from discriminative mapping to modern generative modeling. We first review early discriminative deep neural network (DNN) models, which formulate BWE/SR as a deterministic mapping problem and are prone to regression-to-the-mean effects and spectral over-smoothing. We then systematically review generative approaches, including autoregressive (AR) models, variational autoencoders (VAEs), generative adversarial networks (GANs), diffusion and score-based models, flow-based methods, and Schrödinger bridges. Across these approaches, we examine key design aspects, including representation domain, architecture, conditioning mechanisms, and trade-offs among reconstruction fidelity, perceptual quality, robustness, and computational efficiency. Furthermore, we discuss emerging directions involving large language models (LLMs) and multimodal foundation models, and highlight open challenges in perceptual evaluation, phase modeling, and real-world generalization. By providing a structured taxonomy and unified perspective, this survey establishes a comprehensive foundation and offers a practical roadmap for advancing BWE/SR from deterministic point estimation toward distribution-aware generative modeling.

Latent representations are at the heart of the majority of modern generative models. In the audio domain they are typically produced by a neural-audio-codec autoencoder. In this work we introduce SAME (Semantically-Aligned Music autoEncoder), an autoencoder for stereo music and general audio that reaches a 4096$\times$ temporal compression ratio while maintaining reconstruction quality and downstream generative performance. We achieve this by combining a tranformer-based backbone with set of semantic regularisation approaches, phase-aware reconstruction losses and improved discriminator designs. The architecture delivers substantial computational cost benefits, through both its high compression ratio and its reliance on well-optimised transformer primitives. Two variants (a large SAME-L and a CPU-deployable SAME-S) are released in open-weights form.