Magnetic Resonance Imaging (MRI) is a widely used, non-invasive imaging technology that plays a critical role in clinical diagnostics. Multi-modal MRI, which combines images from different modalities, enhances diagnostic accuracy by offering comprehensive tissue characterization. Meanwhile, multi-modal MRI enhances downstream tasks, like brain tumor segmentation and image reconstruction, by providing richer features. While recent advances in diffusion models (DMs) show potential for high-quality image translation, existing methods still struggle to preserve fine structural details and ensure accurate image synthesis in medical imaging. To address these challenges, we propose a Frequency-Aware Diffusion Model (FADM) for generating high-quality target modality MRI images from source modality images. The FADM incorporates a discrete wavelet transform within the diffusion model framework to extract both low- and high-frequency information from MRI images, enhancing the capture of tissue structural and textural features. Additionally, a wavelet downsampling layer and supervision module are incorporated to improve frequency awareness and optimize high-frequency detail extraction. Experimental results on the BraTS 2021 dataset and a 1.5T–3T MRI dataset demonstrate that the FADM outperforms existing generative models, particularly in preserving intricate brain structures and tumor regions while generating high-quality MRI images.