Recently, diffusion models (DM) have been applied in magnetic resonance imaging (MRI) super-resolution (SR) reconstruction, exhibiting impressive performance, especially with regard to detailed reconstruction. However, the current DM-based SR reconstruction methods still face the following issues: (1) They require a large number of iterations to reconstruct the final image, which is inefficient and consumes a significant amount of computational re-sources. (2) The results reconstructed by these methods are often misaligned with the real high-resolution images, leading to remarkable distortion in the reconstructed MR images. To address the aforementioned issues, we propose an efficient diffusion model for multi-contrast MRI SR, named as DiffMSR. Specifically, we apply DM in a highly compact low-dimensional latent space to generate prior knowledge with high-frequency detail information. The highly compact latent space ensures that DM requires only a few simple iterations to produce accurate prior knowledge. In addition, we design the Prior-Guide Large Window Trans-former (PLWformer) as the decoder for DM, which can ex-tend the receptive field while fully utilizing the prior knowledge generated by DM to ensure that the reconstructed MR image remains undistorted. Extensive experiments on public and clinical datasets demonstrate that our DiffMSR11Code: https://github.com/GuangYuanKK/DiffMSR outperforms state-of-the-art methods.