# Improving Source Separation by Explicitly Modeling Dependencies Between Sources

arXiv: https://arxiv.org/abs/2203.15140 · HTML: https://mlsanity.com/paper/2203.15140/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2022.

## Built on by (most cited first, 8 of 8)

- [Multi-Source Diffusion Models for Simultaneous Music Generation and Separation](https://mlsanity.com/paper/2302.02257/) (2023)
- [Generalized Multi-Source Inference for Text Conditioned Music Diffusion Models](https://mlsanity.com/paper/2403.11706/) (2024)
- [Simultaneous Music Separation and Generation Using Multi-Track Latent Diffusion Models](https://mlsanity.com/paper/2409.12346/) (2024)
- [Unleashing the Denoising Capability of Diffusion Prior for Solving Inverse Problems](https://mlsanity.com/paper/2406.06959/) (2024)
- [Improving Music Source Separation with Diffusion and Consistency Refinement](https://mlsanity.com/paper/2412.06965/) (2024)
- [Training-Free Multi-Step Audio Source Separation](https://mlsanity.com/paper/2505.19534/) (2025)
- [Source Separation of Multi-source Raw Music using a Residual Quantized Variational Autoencoder](https://mlsanity.com/paper/2408.07020/) (2024)
- [The Perception of Phase Intercept Distortion and its Application in Data Augmentation](https://mlsanity.com/paper/2506.14571/) (2025)

## Abstract (arXiv)

We propose a new method for training a supervised source separation system that aims to learn the interdependent relationships between all combinations of sources in a mixture. Rather than independently estimating each source from a mix, we reframe the source separation problem as an Orderless Neural Autoregressive Density Estimator (NADE), and estimate each source from both the mix and a random subset of the other sources. We adapt a standard source separation architecture, Demucs, with additional inputs for each individual source, in addition to the input mixture. We randomly mask these input sources during training so that the network learns the conditional dependencies between the sources. By pairing this training method with a block Gibbs sampling procedure at inference time, we demonstrate that the network can iteratively improve its separation performance by conditioning a source estimate on its earlier source estimates. Experiments on two source separation datasets show that training a Demucs model with an Orderless NADE approach and using Gibbs sampling (up to 512 steps) at inference time strongly outperforms a Demucs baseline that uses a standard regression loss and direct (one step) estimation of sources.