# Bayesian Signal Separation via Plug-and-Play Diffusion-Within-Gibbs Sampling

arXiv: https://arxiv.org/abs/2509.12857 · HTML: https://mlsanity.com/paper/2509.12857/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 10 of 10)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [TasNet: time-domain audio separation network for real-time, single-channel speech separation](https://mlsanity.com/paper/1711.00541/) (2017)
- [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024)
- [TF-GridNet: Integrating Full- and Sub-Band Modeling for Speech Separation](https://mlsanity.com/paper/2211.12433/) (2022)
- [Multi-Source Diffusion Models for Simultaneous Music Generation and Separation](https://mlsanity.com/paper/2302.02257/) (2023)
- [Diffusion-based Generative Speech Source Separation](https://mlsanity.com/paper/2210.17327/) (2022)
- [EDSep: An Effective Diffusion-Based Method for Speech Source Separation](https://mlsanity.com/paper/2501.15965/) (2025)

## Built on by (most cited first, 3 of 3)

- [Bayesian Signal Component Decomposition via Diffusion-within-Gibbs Sampling](https://mlsanity.com/paper/2602.10792/) (2026)
- [Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding](https://mlsanity.com/paper/2609.30539/) (2026)
- [FlowSep-RF: Rectified Flow Matching for Single-Channel Radio-Frequency Signal Separation](https://mlsanity.com/paper/2610.20269/) (2026)

## Abstract (arXiv)

We propose a posterior sampling algorithm for the problem of estimating multiple independent source signals from their noisy superposition. The proposed algorithm is a combination of Gibbs sampling method and plug-and-play (PnP) diffusion priors. Unlike most existing diffusion-model-based approaches for signal separation, our method allows source priors to be learned separately and flexibly combined without retraining. Moreover, under the assumption of perfect diffusion model training, the proposed method provably produces samples from the posterior distribution. Experiments on the task of heartbeat extraction from mixtures with synthetic motion artifacts demonstrate the superior performance of our method over existing approaches.