# Score-based Source Separation with Applications to Digital Communication Signals

arXiv: https://arxiv.org/abs/2306.14411 · HTML: https://mlsanity.com/paper/2306.14411/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Sionna: An Open-Source Library for Next-Generation Physical Layer Research](https://mlsanity.com/paper/2203.11854/) (2022)
- ["Double-DIP": Unsupervised Image Decomposition via Coupled Deep-Image-Priors](https://mlsanity.com/paper/1812.00467/) (2018)
- [Learning to Detect](https://mlsanity.com/paper/1805.07631/) (2018)
- [Multi-Source Diffusion Models for Simultaneous Music Generation and Separation](https://mlsanity.com/paper/2302.02257/) (2023)
- [SinDDM: A Single Image Denoising Diffusion Model](https://mlsanity.com/paper/2211.16582/) (2022)
- [MIMO Channel Estimation using Score-Based Generative Models](https://mlsanity.com/paper/2204.07122/) (2022)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [Source Separation with Deep Generative Priors](https://mlsanity.com/paper/2002.07942/) (2020)
- [ViterbiNet: A Deep Learning Based Viterbi Algorithm for Symbol Detection](https://mlsanity.com/paper/1905.10750/) (2019)
- [Annealed Langevin Dynamics for Massive MIMO Detection](https://mlsanity.com/paper/2205.05776/) (2022)
- [Separate And Diffuse: Using a Pretrained Diffusion Model for Improving Source Separation](https://mlsanity.com/paper/2301.10752/) (2023)
- [Interference Suppression Using Deep Learning: Current Approaches and Open Challenges](https://mlsanity.com/paper/2112.08988/) (2021)
- [Exploiting Temporal Structures of Cyclostationary Signals for Data-Driven Single-Channel Source Separation](https://mlsanity.com/paper/2208.10325/) (2022)
- [Data-Driven Blind Synchronization and Interference Rejection for Digital Communication Signals](https://mlsanity.com/paper/2209.04871/) (2022)
- [Problems using deep generative models for probabilistic audio source separation](https://mlsanity.com/paper/2011.01761/) (2020)
- [Practical calibration of the temperature parameter in Gibbs posteriors](https://mlsanity.com/paper/2004.10522/) (2020)

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

- [Generating High Dimensional User-Specific Wireless Channels using Diffusion Models](https://mlsanity.com/paper/2409.03924/) (2024)
- [Diffusion Models for Wireless Communications](https://mlsanity.com/paper/2310.07312/) (2023)
- [RF Challenge: The Data-Driven Radio Frequency Signal Separation Challenge](https://mlsanity.com/paper/2409.08839/) (2024)
- [The Radio-Frequency Transformer for Signal Separation](https://mlsanity.com/paper/2603.09201/) (2026)
- [StrADiff: A Structured Source-Wise Adaptive Diffusion Framework for Linear and Nonlinear Blind Source Separation](https://mlsanity.com/paper/2604.04973/) (2026)
- [Advancing AI Challenges for the United States Department of the Air Force](https://mlsanity.com/paper/2511.00267/) (2025)
- [Conditional Denoising Diffusion Autoencoders for Wireless Semantic Communications](https://mlsanity.com/paper/2509.22282/) (2025)
- [FlowSep-RF: Rectified Flow Matching for Single-Channel Radio-Frequency Signal Separation](https://mlsanity.com/paper/2610.20269/) (2026)

## Abstract (arXiv)

We propose a new method for separating superimposed sources using diffusion-based generative models. Our method relies only on separately trained statistical priors of independent sources to establish a new objective function guided by maximum a posteriori estimation with an α-posterior, across multiple levels of Gaussian smoothing. Motivated by applications in radio-frequency (RF) systems, we are interested in sources with underlying discrete nature and the recovery of encoded bits from a signal of interest, as measured by the bit error rate (BER). Experimental results with RF mixtures demonstrate that our method results in a BER reduction of 95% over classical and existing learning-based methods. Our analysis demonstrates that our proposed method yields solutions that asymptotically approach the modes of an underlying discrete distribution. Furthermore, our method can be viewed as a multi-source extension to the recently proposed score distillation sampling scheme, shedding additional light on its use beyond conditional sampling. The project webpage is available at https://alpha-rgs.github.io