## 1 Introduction  
Electrocardiogram (ECG) signals represent the electrical activity of the heart and serve as a cornerstone in modern cardiac diagnostics. These signals, typically ranging from 0.05 to 100 Hz in frequency, contain critical morphological features including P waves, QRS complexes, and T waves [1, 2], each reflecting specific cardiac events. However, in real-world clinical settings, ECG recordings are invariably contaminated by noise, particularly electromyogram (EMG) artifacts. These EMG artifacts, generated by skeletal muscle contractions [3, 4], manifest as high-frequency components ranging from 20 Hz to 500 Hz and can exhibit amplitudes comparable to or even exceeding the ECG signal itself. This interference poses a significant challenge as it can mask subtle ECG features [5, 6], distort important diagnostic markers like ST segments, and potentially lead to false interpretations of arrhythmias or other cardiac abnormalities. The denoising of electrocardiogram signals constitutes a pivotal area of research, tackling the complexities introduced by noise interference within clinical diagnostic frameworks. Conventional filtering methodologies, as elaborated in [7], emphasize the utilization of reference datasets such as SimEMG to assess the efficacy of denoising performance. Although these methodologies demonstrate efficacy in mitigating noise [8], residual artifacts frequently endure, thereby impacting diagnostic precision. Adaptive filtering methodologies, exemplified in [9], offer an effective approach for the real-time removal of cardiogenic oscillations from esophageal pressure signals. This methodology illustrates a substantial attenuation of noise levels, achieved without the necessity for supplementary apparatus, thereby rendering it appropriate for clinical application. The iterative regeneration method (IRM) presented in [10] exemplifies innovative techniques that provide significant enhancements compared to conventional wavelet and FIR filters. IRM demonstrates a proficient equilibrium between the attenuation of noise and the preservation of signal morphology, while also exhibiting computational efficiency, thereby rendering it particularly suitable for both mobile and conventional ECG devices. In a comparable manner, hierarchical adaptive filtering, illustrated by the hierarchical Kalman filter (HKF) in [11], utilizes patient-specific dynamics to attain enhanced denoising efficacy. The adaptive methodologies highlighted herein emphasize the critical necessity of customizing noise suppression strategies to align with particular clinical scenarios. The advent of machine learning and deep learning methodologies has significantly revolutionized the domain, providing effective solutions for the denoising of electrocardiogram signals. Ref. [12] presents an adversarial deep learning framework aimed at the denoising of fetal ECG signals, which results in a notable enhancement of the signal-to-noise ratio (SNR) and an increase in the accuracy of QRS complex detection. Methods based on autoencoders, such as the denoising convolutional autoencoder (DCAE) referenced in [13], significantly improve ECG signals derived from in-ear recordings, demonstrating exceptional accuracy in R-peak detection and producing clinically viable waveform reconstructions. Fully convolutional networks (FCNs), as examined in [14], demonstrate superior performance compared to conventional techniques in the reconstruction of single-channel ECG signals that have been compromised by noise, thereby highlighting the capabilities of deep learning across various applications. Emerging generative models present a compelling avenue for exploration. Refs. [15; 16] investigate the utilization of diffusion models in the context of time series data, emphasizing score-based denoising techniques specifically applied to ECG and sEMG signals. These models demonstrate exceptional capability in preserving signal fidelity while effectively mitigating noise, thereby establishing an innovative framework for generative denoising. Furthermore, ref.