[Paper Review] Geometry-Free Conditional Diffusion Modeling for Solving the Inverse Electrocardiography Problem

Ramiro Valdes Jara, Adam Meyers|arXiv (Cornell University)|Jan 26, 2026

Cardiac electrophysiology and arrhythmias0 citations

TL;DR

This paper develops a geometry-free, data-driven conditional diffusion model to estimate heart-surface potentials from body-surface measurements, providing probabilistic reconstructions for the ECGI inverse problem and outperforming deterministic baselines.

ABSTRACT

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.

Motivation & Objective

• Motivate noninvasive ECGI and address the ill-posed inverse problem.
• Propose a geometry-free, data-driven conditional diffusion framework.
• Enable probabilistic sampling of multiple plausible heart-surface reconstructions.
• Assess performance against deterministic baselines on real ECGI-like data.

Proposed method

• Use a forward diffusion process to progressively corrupt cardiac signals and a learnable conditional reverse process guided by body-surface measurements.
• Implement the conditional denoising function as a transformer-based network that predicts noise given x_t, t, and y.
• Train with a conditional diffusion objective that minimizes the MSE between true noise and predicted noise.
• No explicit physics-based forward operator or patient-specific geometry is required; learning is data-driven and geometry-free.
• During inference, sample from p_theta(x_0|y) via the conditional reverse process to obtain multiple plausible reconstructions.

Experimental results

Research questions

• RQ1 Can a geometry-free conditional diffusion model accurately reconstruct epicardial potentials from torso measurements?
• RQ2 Does conditioning diffusion denoising on body-surface data improve reconstruction quality over deterministic baselines?
• RQ3 What is the model’s ability to capture temporal morphology and amplitude of epicardial signals in ECGI?
• RQ4 Can the approach provide uncertainty-aware, probabilistic reconstructions for the ECGI inverse problem?

Key findings

• The diffusion model achieves the highest temporal correlation (0.78) and lowest MSE (32.83) and MAE (3.42) among tested methods.
• Compared baselines (1D-CNN, LSTM, Transformer), the diffusion model consistently improves reconstruction accuracy.
• Deterministic baselines showed comparable performance (1D-CNN and Transformer) while LSTM performed worse in temporal correlation and errors.
• The conditional diffusion approach yields more accurate recovery of waveform morphology and amplitude than baselines.
• Empirical uncertainty in reconstructions is modest in the reported setting but may broaden with more diverse noise and forward-model perturbations.