# Geometry-Free Conditional Diffusion Modeling for Solving the Inverse Electrocardiography Problem

arXiv: https://arxiv.org/abs/2601.18615 · HTML: https://mlsanity.com/paper/2601.18615/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Placed in

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

## Builds on (most cited first, 4 of 4)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Solving the Inverse Problem of Electrocardiography for Cardiac Digital Twins: A Survey](https://mlsanity.com/paper/2406.11445/) (2024)
- [Graph convolutional regression of cardiac depolarization from sparse endocardial maps](https://mlsanity.com/paper/2009.14068/) (2020)
- [Reducing Line-of-block Artifacts in Cardiac Activation Maps Estimated Using ECG Imaging: A Comparison of Source Models and Estimation Methods](https://mlsanity.com/paper/2108.06602/) (2021)

## Abstract (arXiv)

This paper proposes a data-driven model for solving the inverse problem of electrocardiography, the mathematical problem that forms the basis of electrocardiographic imaging (ECGI). We present a conditional diffusion framework that learns a probabilistic mapping from noisy body surface signals to heart surface electric potentials. The proposed approach leverages the generative nature of diffusion models to capture the non-unique and underdetermined nature of the ECGI inverse problem, enabling probabilistic sampling of multiple reconstructions rather than a single deterministic estimate. Unlike traditional methods, the proposed framework is geometry-free and purely data-driven, alleviating the need for patient-specific mesh construction. We evaluate the method on a real ECGI dataset and compare it against strong deterministic baselines, including a convolutional neural network, long short-term memory network, and transformer-based model. The results demonstrate that the proposed diffusion approach achieves improved reconstruction accuracy, highlighting the potential of diffusion models as a robust tool for noninvasive cardiac electrophysiology imaging.