  Deep learning image processing models have had remarkable success in recent
years in generating high quality images. Particularly, the Improved Denoising
Diffusion Probabilistic Models (DDPM) have shown superiority in image quality
to the state-of-the-art generative models, which motivated us to investigate
their capability in the generation of the synthetic electrocardiogram (ECG)
signals. In this work, synthetic ECG signals are generated by the Improved DDPM
and by the Wasserstein GAN with Gradient Penalty (WGAN-GP) models and then
compared. To this end, we devise a pipeline to utilize DDPM in its original
$2D$ form. First, the $1D$ ECG time series data are embedded into the $2D$
space, for which we employed the Gramian Angular Summation/Difference Fields
(GASF/GADF) as well as Markov Transition Fields (MTF) to generate three $2D$
matrices from each ECG time series, which when put together, form a $3$-channel
$2D$ datum. Then $2D$ DDPM is used to generate $2D$ $3$-channel synthetic ECG
images. The $1D$ ECG signals are created by de-embedding the $2D$ generated
image files back into the $1D$ space. This work focuses on unconditional models
and the generation of \emph{Normal Sinus Beat} ECG signals exclusively, where
the Normal Sinus Beat class from the MIT-BIH Arrhythmia dataset is used in the
training phase. The \emph{quality}, \emph{distribution}, and the
\emph{authenticity} of the generated ECG signals by each model are
quantitatively evaluated and compared. Our results show that in the proposed
pipeline and in the particular setting of this paper, the WGAN-GP model is
consistently superior to DDPM in all the considered metrics.

Signal Processing;Machine Learning