Diffusion models have gained significant popularity in the field of image-to-image translation. Previous efforts applying diffusion models to image super-resolution (SR) have demonstrated that iteratively refining pure Gaussian noise using a U-Net architecture trained on denoising at various noise levels can yield satisfactory high-resolution images from low-resolution inputs. However, this iterative refinement process comes with the drawback of low inference speed, which strongly limits its applications. To speed up inference and further enhance the performance, our research revisits diffusion models in image super-resolution and proposes a straightforward yet significant diffusion model-based super-resolution method called ACDMSR (accelerated conditional diffusion model for image super-resolution). Specifically, our method adapts the standard diffusion model to perform super-resolution through a deterministic iterative denoising process. Our study also highlights the effectiveness of using a pre-trained SR model to provide the conditional image of the given low-resolution (LR) image to achieve superior high-resolution results. We demonstrate that our method surpasses previous attempts in qualitative and quantitative results through extensive experiments conducted on benchmark datasets such as Set5, Set14, Urban100, BSD100, and Manga109. Moreover, our approach generates more visually realistic counterparts for low-resolution images, emphasizing its effectiveness in practical scenarios.