Biomedical signals such as electrocardiograms (ECG) are distorted by diverse types of noise such as baseline wander, undermining diagnostic accuracy. Current denoising methods struggle to balance noise reduction and preservation of critical waveforms such as P/QRS/T waves. For this purpose, this study proposes a Fast Fourier Transform Diffusion (FFT Diffusion) framework. FFT Diffusion implements Fourier transform to decompose ECG into multiscale frequency subbands, enabling adaptive noise reduction while retaining frequency-specific biological features. A U-shaped architecture based on Transformers captures local waveform details and models long-term dependencies. This study also uses a composite loss function to train the U-shaped model. By combining adaptive frequency decomposition and transformer architecture, FFT Diffusion outperforms state-of-the-art methods and provides a robust solution for ECG denoising and effective preservation of diagnostic information from complex noise.