# Improving Diffusion Models for ECG Imputation with an Augmented Template Prior

arXiv: https://arxiv.org/abs/2310.15742 · HTML: https://mlsanity.com/paper/2310.15742/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 27 of its 36 references that are in the map.
- First posted on arXiv 24 Oct 2023.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [It's Raw! Audio Generation with State-Space Models](https://mlsanity.com/paper/2202.09729/) (2022)
- [NAOMI: Non-Autoregressive Multiresolution Sequence Imputation](https://mlsanity.com/paper/1901.10946/) (2019)
- [BinauralGrad: A Two-Stage Conditional Diffusion Probabilistic Model for Binaural Audio Synthesis](https://mlsanity.com/paper/2205.14807/) (2022)
- [Missing Value Imputation on Multidimensional Time Series](https://mlsanity.com/paper/2103.01600/) (2021)
- [InferGrad: Improving Diffusion Models for Vocoder by Considering Inference in Training](https://mlsanity.com/paper/2202.03751/) (2022)
- [DeScoD-ECG: Deep Score-Based Diffusion Model for ECG Baseline Wander and Noise Removal](https://mlsanity.com/paper/2208.00542/) (2022)
- [ResGrad: Residual Denoising Diffusion Probabilistic Models for Text to Speech](https://mlsanity.com/paper/2212.14518/) (2022)
- [PulseImpute: A Novel Benchmark Task for Pulsative Physiological Signal Imputation](https://mlsanity.com/paper/2212.07514/) (2022)
- [A Deep Matched Filter For R-Peak Detection in Ear-ECG](https://mlsanity.com/paper/2305.14102/) (2023)

## Built on by (most cited first, 7 of 7)

- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Versatile Cardiovascular Signal Generation with a Unified Diffusion Transformer](https://mlsanity.com/paper/2505.22306/) (2025)
- [RespDiff: An End-to-End Multi-scale RNN Diffusion Model for Respiratory Waveform Estimation from PPG Signals](https://mlsanity.com/paper/2410.04366/) (2024)
- [Cyclostationary Phase Conditioning for Medical Time Series Diffusion](https://mlsanity.com/paper/2609.34965/) (2026)
- [A Laplace diffusion-based transformer model for heart rate forecasting within daily activity context](https://mlsanity.com/paper/2508.16655/) (2025)
- [Exploiting the Prior of Generative Time Series Imputation](https://mlsanity.com/paper/2512.23832/) (2025)
- [BeatFlow-ECG: Rectified Flow for ECG Reconstruction from Indirect Wearable Signals](https://mlsanity.com/paper/2610.09052/) (2026)

## Abstract (arXiv)

Pulsative signals such as the electrocardiogram (ECG) are extensively collected as part of routine clinical care. However, noisy and poor-quality recordings are a major issue for signals collected using mobile health systems, decreasing the signal quality, leading to missing values, and affecting automated downstream tasks. Recent studies have explored the imputation of missing values in ECG with probabilistic time-series models. Nevertheless, in comparison with the deterministic models, their performance is still limited, as the variations across subjects and heart-beat relationships are not explicitly considered in the training objective. In this work, to improve the imputation and forecasting accuracy for ECG with probabilistic models, we present a template-guided denoising diffusion probabilistic model (DDPM), PulseDiff, which is conditioned on an informative prior for a range of health conditions. Specifically, 1) we first extract a subject-level pulsative template from the observed values to use as an informative prior of the missing values, which personalises the prior; 2) we then add beat-level stochastic shift terms to augment the prior, which considers variations in the position and amplitude of the prior at each beat; 3) we finally design a confidence score to consider the health condition of the subject, which ensures our prior is provided safely. Experiments with the PTBXL dataset reveal that PulseDiff improves the performance of two strong DDPM baseline models, CSDI and SSSDS4, verifying that our method guides the generation of DDPMs while managing the uncertainty. When combined with SSSDS4, PulseDiff outperforms the leading deterministic model for short-interval missing data and is comparable for long-interval data loss.