# Bayesian ECG reconstruction using denoising diffusion generative models

arXiv: https://arxiv.org/abs/2401.05388 · HTML: https://mlsanity.com/paper/2401.05388/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 29 of its 60 references that are in the map.
- First posted on arXiv 18 Dec 2023.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (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)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2001.06937/) (2020)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Automatic diagnosis of the 12-lead ECG using a deep neural network](https://mlsanity.com/paper/1904.01949/) (2019)
- [From Denoising Diffusions to Denoising Markov Models](https://mlsanity.com/paper/2211.03595/) (2022)
- [Diffusion-based Conditional ECG Generation with Structured State Space Models](https://mlsanity.com/paper/2301.08227/) (2023)
- [Deep Mean-Shift Priors for Image Restoration](https://mlsanity.com/paper/1709.03749/) (2017)
- [SimGANs: Simulator-Based Generative Adversarial Networks for ECG Synthesis to Improve Deep ECG Classification](https://mlsanity.com/paper/2006.15353/) (2020)
- [DeScoD-ECG: Deep Score-Based Diffusion Model for ECG Baseline Wander and Noise Removal](https://mlsanity.com/paper/2208.00542/) (2022)
- [Semi-supervised Invertible Neural Operators for Bayesian Inverse Problems](https://mlsanity.com/paper/2209.02772/) (2022)
- [Deep Unfolding with Normalizing Flow Priors for Inverse Problems](https://mlsanity.com/paper/2107.02848/) (2021)
- [Synthetic ECG Signal Generation using Probabilistic Diffusion Models](https://mlsanity.com/paper/2303.02475/) (2023)
- [A domain-decomposed VAE method for Bayesian inverse problems](https://mlsanity.com/paper/2301.05708/) (2023)
- [Utilizing variational autoencoders in the Bayesian inverse problem of photoacoustic tomography](https://mlsanity.com/paper/2204.06270/) (2022)
- [A Generative Modeling Approach to Limited Channel ECG Classification](https://mlsanity.com/paper/1802.06458/) (2018)

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

- [Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints](https://mlsanity.com/paper/2402.18012/) (2024)
- [Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance](https://mlsanity.com/paper/2501.02298/) (2025)

## Abstract (arXiv)

In this work, we propose a denoising diffusion generative model (DDGM) trained with healthy electrocardiogram (ECG) data that focuses on ECG morphology and inter-lead dependence. Our results show that this innovative generative model can successfully generate realistic ECG signals. Furthermore, we explore the application of recent breakthroughs in solving linear inverse Bayesian problems using DDGM. This approach enables the development of several important clinical tools. These include the calculation of corrected QT intervals (QTc), effective noise suppression of ECG signals, recovery of missing ECG leads, and identification of anomalous readings, enabling significant advances in cardiac health monitoring and diagnosis.