Diffusion models have achieved impressive performance on various image generation tasks, including image super-resolution. Despite their impressive performance, diffusion models suffer from high computational costs due to the large number of denoising steps. In this paper, we proposed a novel accelerated diffusion model, termed Partial Diffusion Models (PDMs), for magnetic resonance imaging (MRI) super-resolution. We observed that the latents of diffusing a pair of low- and high-resolution images gradually converge and become indistinguishable after a certain noise level. This inspires us to use certain low-resolution latent to approximate corresponding high-resolution latent. With the approximation, we can skip part of the diffusion and denoising steps, reducing the computation in training and inference. To mitigate the approximation error, we further introduced 'latent alignment' that gradually interpolates and approaches the high-resolution latents from the low-resolution latents. Partial diffusion models, in conjunction with latent alignment, essentially establish a new trajectory where the latents, unlike those in original diffusion models, gradually transition from low-resolution to high-resolution images. Experiments on three MRI datasets demonstrate that partial diffusion models achieve competetive super-resolution quality with significantly fewer denoising steps than original diffusion models. In addition, they can be incorporated with recent accelerated diffusion models to further enhance the efficiency.