Abstract: Deep-learning-based methods have enabled significant breakthroughs in image super-resolution tasks. The key to their success is the requirement for significant amounts of paired low- and high-resolution images to train the super-resolution model. However， obtaining such significant numbers of one-to-one corresponding high/low-resolution real image pairs is challenging. Models trained on those synthetic image pairs tend to exhibit subpar performance when images with unexpected degradation are involved. This paper presents an approach for solving these problems by training a self-supervised diffusion model on a single image （SSDM-SR）. The proposed method learns the information distribution inside a single image based on the diffusion model and trains a small image-specific diffusion model for the image to be super-resolved. The training datasets are extracted solely from the image to be super-resolved such that the SSDM-SR can adapt to different input images. Additionally， coordinate information is incorporated to facilitate the construction of the overall image framework， which accelerates the model’s convergence. Experiments on standard benchmark datasets and datasets with unknown degradation kernels show that our SSDM-SR outperforms recent supervised and unsupervised image super-resolution methods in terms of image-restoration metrics and generates images with higher perceptual quality. On real-world LR images， it generates visually pleasing and artifact-free results.