FlowECG: Using Flow Matching to Create a More Efficient ECG Signal Generator

Technical Summary: FlowECG

Problem Statement
Synthetic electrocardiogram (ECG) generation is critical for medical AI applications, particularly for privacy-preserving data sharing and training dataset augmentation. While current state-of-the-art methods, specifically diffusion-based models like SSSD-ECG, achieve high generation quality, they suffer from significant computational inefficiencies. The iterative denoising process inherent to diffusion models requires hundreds of neural network evaluations (forward passes) during sampling. This creates a computational bottleneck that limits the practical deployment of these models in clinical environments, especially for real-time generation or large-scale synthetic data creation.

Methodology
The authors propose FlowECG, a generative framework that adapts the established SSSD-ECG architecture but replaces the discrete, iterative diffusion process with continuous flow matching dynamics.

• Architecture: FlowECG retains the core structure of the SSSD-ECG baseline, utilizing 36 stacked residual layers with bidirectional Structured State Space (S4) components to capture long-range temporal dependencies. It conditions on 71 binary diagnostic labels derived from the PTB-XL dataset.
• Flow Matching Formulation: Unlike diffusion models that learn a reverse denoising process, FlowECG learns a time-dependent velocity field $u_t(x)$ to transport samples from a base Gaussian noise distribution ($p_0$) to the target data distribution ($p_1$).
  • Training: The model is trained to predict the vector field $v_t = x_1 - x_0$ (where $x_1$ is the target signal and $x_0$ is noise) via a linear interpolation path. The objective minimizes the mean-squared error between the predicted and target vector fields.
  • Sampling: Generation is achieved by solving an Ordinary Differential Equation (ODE) from $t=0$ to $t=1$ using the learned vector field. This allows for deterministic integration with significantly fewer steps compared to the discrete steps required by diffusion.
• Evaluation: The models were evaluated on the PTB-XL dataset (21,799 recordings) using four metrics: Dynamic Time Warping (DTW), Wasserstein distance, Maximum Mean Discrepancy (MMD), and a Spectral Similarity Score.

Key Contributions

1. Architectural Adaptation: The paper successfully adapts the SSSD-ECG architecture to a flow matching framework, demonstrating that the underlying state-space models are compatible with continuous flow dynamics.
2. Efficiency Demonstration: The primary contribution is the empirical demonstration that flow matching can achieve generation quality comparable to, or better than, state-of-the-art diffusion models while requiring substantially fewer sampling steps.
3. Robustness to Sampling Reduction: The study highlights that FlowECG maintains high fidelity even when the number of Neural Function Evaluations (NFE) is drastically reduced, whereas diffusion-based baselines suffer severe quality degradation under similar constraints.

Results
Experiments comparing FlowECG against a retrained SSSD-ECG baseline yielded the following findings:

• Performance at Standard Budget (200 NFE): At 200 neural function evaluations, FlowECG matched or exceeded the baseline performance. It achieved superior results on three of the four metrics:
  • MMD: 21.09 (FlowECG) vs. 80.70 (SSSD-ECG).
  • Wasserstein Distance: 0.62 (FlowECG) vs. 1.03 (SSSD-ECG).
  • Spectral Similarity: 0.37 (FlowECG) vs. 0.30 (SSSD-ECG).
  • DTW: FlowECG showed a modest increase (83.96 vs. 73.49), indicating slightly higher time-warping distance, but remained competitive.
• Performance at Reduced Budget (10–25 NFE): The most significant finding emerged when reducing sampling steps.
  • SSSD-ECG: Exhibited dramatic quality degradation. For instance, DTW distance increased to over 600 at just 2 NFE and remained over 200 at 25 NFE.
  • FlowECG: Demonstrated superior robustness, maintaining consistently high quality with only 10–25 NFE.
• Visual Quality: Generated ECGs exhibited physiologically plausible waveforms, consistent rhythm patterns, and realistic amplitude variations across all 12 leads, preserving inter-lead correlations.

Significance and Claims
The paper claims that FlowECG addresses the critical computational efficiency barrier limiting the deployment of generative models in clinical settings. By achieving comparable or superior results with 10–25 sampling steps instead of the 200 steps required by diffusion methods, FlowECG reduces computational requirements by an order of magnitude.

The authors posit that the continuous formulation of flow matching provides a more stable optimization landscape than discrete diffusion, allowing for accurate integration with fewer steps without the need for complex noise scheduling. This efficiency makes the approach viable for:

• Real-time ECG generation in resource-constrained clinical environments.
• Large-scale synthetic data creation for data augmentation.
• Privacy-preserving data sharing where rapid generation is necessary.

The work concludes that flow matching is a practical alternative to diffusion for medical time series synthesis, offering a pathway to deploy high-quality generative models in scenarios where computational resources are limited.