# Bayesian Signal Component Decomposition via Diffusion-within-Gibbs Sampling

arXiv: https://arxiv.org/abs/2602.10792 · HTML: https://mlsanity.com/paper/2602.10792/

## Key facts

- Cited by 1 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 23 of its 57 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [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)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [TasNet: time-domain audio separation network for real-time, single-channel speech separation](https://mlsanity.com/paper/1711.00541/) (2017)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [Structured Logconcave Sampling with a Restricted Gaussian Oracle](https://mlsanity.com/paper/2010.03106/) (2020)
- [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024)
- [Multi-Source Diffusion Models for Simultaneous Music Generation and Separation](https://mlsanity.com/paper/2302.02257/) (2023)
- [Multilevel Wavelet Decomposition Network for Interpretable Time Series Analysis](https://mlsanity.com/paper/1806.08946/) (2018)
- [Split-and-augmented Gibbs sampler - Application to large-scale inference problems](https://mlsanity.com/paper/1804.05809/) (2018)
- [Deep Unfolded Robust PCA with Application to Clutter Suppression in Ultrasound](https://mlsanity.com/paper/1811.08252/) (2018)
- [Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inference](https://mlsanity.com/paper/2304.11134/) (2023)
- [Generative Plug and Play: Posterior Sampling for Inverse Problems](https://mlsanity.com/paper/2306.07233/) (2023)
- [Perturbation theory for Markov chains via Wasserstein distance](https://mlsanity.com/paper/1503.04123/) (2015)
- [IRGen: Generative Modeling for Image Retrieval](https://mlsanity.com/paper/2303.10126/) (2023)
- [An Overview of Algorithms for Contactless Cardiac Feature Extraction from Radar Signals: Advances and Challenges](https://mlsanity.com/paper/2508.02122/) (2025)
- [Bayesian Signal Separation via Plug-and-Play Diffusion-Within-Gibbs Sampling](https://mlsanity.com/paper/2509.12857/) (2025)

## Built on by (most cited first, 1 of 1)

- [Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding](https://mlsanity.com/paper/2609.30539/) (2026)

## Abstract (arXiv)

In signal processing, the data collected from sensing devices is often a noisy linear superposition of multiple components, and the estimation of components of interest constitutes a crucial pre-processing step. In this work, we develop a Bayesian framework for signal component decomposition, which combines Gibbs sampling with plug-and-play (PnP) diffusion priors to draw component samples from the posterior distribution. Unlike many existing methods, our framework supports incorporating component-wise model-driven and data-driven priors into diffusion models in a unified manner. Moreover, the proposed posterior sampler allows component priors to be learned separately and flexibly combined for different decomposition tasks at inference time. Under suitable assumptions, the proposed Diffusion-within-Gibbs (DiG) sampler provably produces samples from the posterior distribution. We also show that DiG can be interpreted as an extension of a class of recently proposed diffusion-based samplers, and that, for suitable classes of sensing operators, DiG better exploits the structure of the measurement model. Numerical experiments demonstrate the superior performance of our method over existing approaches.