# Diffusion-based Conditional ECG Generation with Structured State Space Models

arXiv: https://arxiv.org/abs/2301.08227 · HTML: https://mlsanity.com/paper/2301.08227/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 50 references that are in the map.
- First posted on arXiv 19 Jan 2023.

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [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)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Bag of Tricks for Image Classification with Convolutional Neural Networks](https://mlsanity.com/paper/1812.01187/) (2018)
- [See through Gradients: Image Batch Recovery via GradInversion](https://mlsanity.com/paper/2104.07586/) (2021)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [How Faithful is your Synthetic Data? Sample-level Metrics for Evaluating and Auditing Generative Models](https://mlsanity.com/paper/2102.08921/) (2021)
- [Modulating early visual processing by language](https://mlsanity.com/paper/1707.00683/) (2017)
- [Deep Learning for ECG Analysis: Benchmarks and Insights from PTB-XL](https://mlsanity.com/paper/2004.13701/) (2020)
- [Generating High Fidelity Data from Low-density Regions using Diffusion Models](https://mlsanity.com/paper/2203.17260/) (2022)
- [TTS-GAN: A Transformer-based Time-Series Generative Adversarial Network](https://mlsanity.com/paper/2202.02691/) (2022)
- [SimGANs: Simulator-Based Generative Adversarial Networks for ECG Synthesis to Improve Deep ECG Classification](https://mlsanity.com/paper/2006.15353/) (2020)
- [Synthesis of Realistic ECG using Generative Adversarial Networks](https://mlsanity.com/paper/1909.09150/) (2019)
- [Advancing the State-of-the-Art for ECG Analysis through Structured State Space Models](https://mlsanity.com/paper/2211.07579/) (2022)
- [Conditional Generative Data Augmentation for Clinical Audio Datasets](https://mlsanity.com/paper/2203.11570/) (2022)
- [Deepfake histological images for enhancing digital pathology](https://mlsanity.com/paper/2206.08308/) (2022)

## Built on by (most cited first, 30 of 36)

- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Time Weaver: A Conditional Time Series Generation Model](https://mlsanity.com/paper/2403.02682/) (2024)
- [Variational Diffusion Posterior Sampling with Midpoint Guidance](https://mlsanity.com/paper/2410.09945/) (2024)
- [Generative AI for Synthetic Data Across Multiple Medical Modalities: A Systematic Review of Recent Developments and Challenges](https://mlsanity.com/paper/2407.00116/) (2024)
- [Synthetic ECG Signal Generation using Probabilistic Diffusion Models](https://mlsanity.com/paper/2303.02475/) (2023)
- [T2S: High-resolution Time Series Generation with Text-to-Series Diffusion Models](https://mlsanity.com/paper/2505.02417/) (2025)
- [Region-Disentangled Diffusion Model for High-Fidelity PPG-to-ECG Translation](https://mlsanity.com/paper/2308.13568/) (2023)
- [Towards Generative Modeling of Urban Flow through Knowledge-enhanced Denoising Diffusion](https://mlsanity.com/paper/2309.10547/) (2023)
- [DiffuSETS: 12-lead ECG Generation Conditioned on Clinical Text Reports and Patient-Specific Information](https://mlsanity.com/paper/2501.05932/) (2025)
- [Adaptive Compressed Sensing with Diffusion-Based Posterior Sampling](https://mlsanity.com/paper/2407.08256/) (2024)
- [Generative AI-Driven Human Digital Twin in IoT-Healthcare: A Comprehensive Survey](https://mlsanity.com/paper/2401.13699/) (2024)
- [Transfer Learning for Diffusion Models](https://mlsanity.com/paper/2405.16876/) (2024)
- [A Review on Generative AI Models for Synthetic Medical Text, Time Series, and Longitudinal Data](https://mlsanity.com/paper/2411.12274/) (2024)
- [DiffECG: A Versatile Probabilistic Diffusion Model for ECG Signals Synthesis](https://mlsanity.com/paper/2306.01875/) (2023)
- [A Comprehensive Survey on Generative Diffusion Models for Structured Data](https://mlsanity.com/paper/2306.04139/) (2023)
- [Simulator and Experience Enhanced Diffusion Model for Comprehensive ECG Generation](https://mlsanity.com/paper/2511.09895/) (2025)
- [Deep Generative Models for Physiological Signals: A Systematic Literature Review](https://mlsanity.com/paper/2307.06162/) (2023)
- [Constrained Posterior Sampling: Time Series Generation with Hard Constraints](https://mlsanity.com/paper/2410.12652/) (2024)
- [A Survey of Transformer Enabled Time Series Synthesis](https://mlsanity.com/paper/2406.02322/) (2024)
- [Explaining Time Series Classification Predictions via Causal Attributions](https://mlsanity.com/paper/2405.15871/) (2024)
- [FlowECG: Using Flow Matching to Create a More Efficient ECG Signal Generator](https://mlsanity.com/paper/2509.10491/) (2025)
- [Bayesian ECG reconstruction using denoising diffusion generative models](https://mlsanity.com/paper/2401.05388/) (2023)
- [ECGTwin: Personalized ECG Generation Using Controllable Diffusion Model](https://mlsanity.com/paper/2508.02720/) (2025)
- [Prospects for AI-Enhanced ECG as a Unified Screening Tool for Cardiac and Non-Cardiac Conditions -- An Explorative Study in Emergency Care](https://mlsanity.com/paper/2312.11050/) (2023)
- [SSSD-ECG-nle: New Label Embeddings with Structured State-Space Models for ECG generation](https://mlsanity.com/paper/2407.11108/) (2024)
- [Conditional Electrocardiogram Generation Using Hierarchical Variational Autoencoders](https://mlsanity.com/paper/2503.13469/) (2025)
- [High-Fidelity Synthetic ECG Generation via Mel-Spectrogram Informed Diffusion Training](https://mlsanity.com/paper/2510.05492/) (2025)
- [TransConv-DDPM: Enhanced Diffusion Model for Generating Time-Series Data in Healthcare](https://mlsanity.com/paper/2602.07033/) (2026)
- [Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models](https://mlsanity.com/paper/2602.17830/) (2026)
- [ODE-Constrained Generative Modeling of Cardiac Dynamics for 12-Lead ECG Synthesis](https://mlsanity.com/paper/2409.17833/) (2024)

## Abstract (arXiv)

Synthetic data generation is a promising solution to address privacy issues with the distribution of sensitive health data. Recently, diffusion models have set new standards for generative models for different data modalities. Also very recently, structured state space models emerged as a powerful modeling paradigm to capture long-term dependencies in time series. We put forward SSSD-ECG, as the combination of these two technologies, for the generation of synthetic 12-lead electrocardiograms conditioned on more than 70 ECG statements. Due to a lack of reliable baselines, we also propose conditional variants of two state-of-the-art unconditional generative models. We thoroughly evaluate the quality of the generated samples, by evaluating pretrained classifiers on the generated data and by evaluating the performance of a classifier trained only on synthetic data, where SSSD-ECG clearly outperforms its GAN-based competitors. We demonstrate the soundness of our approach through further experiments, including conditional class interpolation and a clinical Turing test demonstrating the high quality of the SSSD-ECG samples across a wide range of conditions.