# Unsupervised Source Separation via Bayesian Inference in the Latent Domain

arXiv: https://arxiv.org/abs/2110.05313 · HTML: https://mlsanity.com/paper/2110.05313/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 11 Oct 2021.

## Builds on (most cited first, 15 of 15)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Jukebox: A Generative Model for Music](https://mlsanity.com/paper/2005.00341/) (2020)
- [Music Source Separation in the Waveform Domain](https://mlsanity.com/paper/1911.13254/) (2019)
- [Cutting Music Source Separation Some Slakh: A Dataset to Study the Impact of Training Data Quality and Quantity](https://mlsanity.com/paper/1909.08494/) (2019)
- [The 2018 Signal Separation Evaluation Campaign](https://mlsanity.com/paper/1804.06267/) (2018)
- [Source Separation with Deep Generative Priors](https://mlsanity.com/paper/2002.07942/) (2020)
- [Conditioned-U-Net: Introducing a Control Mechanism in the U-Net for Multiple Source Separations](https://mlsanity.com/paper/1907.01277/) (2019)
- [D3Net: Densely connected multidilated DenseNet for music source separation](https://mlsanity.com/paper/2010.01733/) (2020)
- [MMDenseLSTM: An efficient combination of convolutional and recurrent neural networks for audio source separation](https://mlsanity.com/paper/1805.02410/) (2018)
- [Parallel and Flexible Sampling from Autoregressive Models via Langevin Dynamics](https://mlsanity.com/paper/2105.08164/) (2021)
- [Unsupervised Audio Source Separation using Generative Priors](https://mlsanity.com/paper/2005.13769/) (2020)
- [LaSAFT: Latent Source Attentive Frequency Transformation for Conditioned Source Separation](https://mlsanity.com/paper/2010.11631/) (2020)
- [Denoising Auto-encoder with Recurrent Skip Connections and Residual Regression for Music Source Separation](https://mlsanity.com/paper/1807.01898/) (2018)

## Built on by (most cited first, 2 of 2)

- [Efficient and Fast Generative-Based Singing Voice Separation using a Latent Diffusion Model](https://mlsanity.com/paper/2511.20470/) (2025)
- [Learning Linearity in Audio Consistency Autoencoders via Implicit Regularization](https://mlsanity.com/paper/2510.23530/) (2025)

## Abstract (arXiv)

State of the art audio source separation models rely on supervised data-driven approaches, which can be expensive in terms of labeling resources. On the other hand, approaches for training these models without any direct supervision are typically high-demanding in terms of memory and time requirements, and remain impractical to be used at inference time. We aim to tackle these limitations by proposing a simple yet effective unsupervised separation algorithm, which operates directly on a latent representation of time-domain signals. Our algorithm relies on deep Bayesian priors in the form of pre-trained autoregressive networks to model the probability distributions of each source. We leverage the low cardinality of the discrete latent space, trained with a novel loss term imposing a precise arithmetic structure on it, to perform exact Bayesian inference without relying on an approximation strategy. We validate our approach on the Slakh dataset arXiv:1909.08494, demonstrating results in line with state of the art supervised approaches while requiring fewer resources with respect to other unsupervised methods.