This survey provides a comprehensive overview of Diffusion Models (DMs) in the context of image Super-Resolution (SR), highlighting their unique characteristics, methodologies, and challenges. The paper discusses the theoretical foundations of DMs, their application in SR, and their relationship with other generative models like GANs, VAEs, and Flow-based methods. It also explores various improvements for DMs, including efficient sampling techniques and enhanced likelihood estimation, which are crucial for effective SR. The survey covers key aspects of image SR, such as datasets, models, and image quality assessment metrics. It emphasizes the importance of DMs in generating high-quality SR images that align with human perceptual preferences, while also addressing challenges like computational demands, color shifts, and lack of explainability. The paper concludes with a discussion on emerging trends and future research directions in the field of DMs and image SR.This survey provides a comprehensive overview of Diffusion Models (DMs) in the context of image Super-Resolution (SR), highlighting their unique characteristics, methodologies, and challenges. The paper discusses the theoretical foundations of DMs, their application in SR, and their relationship with other generative models like GANs, VAEs, and Flow-based methods. It also explores various improvements for DMs, including efficient sampling techniques and enhanced likelihood estimation, which are crucial for effective SR. The survey covers key aspects of image SR, such as datasets, models, and image quality assessment metrics. It emphasizes the importance of DMs in generating high-quality SR images that align with human perceptual preferences, while also addressing challenges like computational demands, color shifts, and lack of explainability. The paper concludes with a discussion on emerging trends and future research directions in the field of DMs and image SR.