I. Introduction  
II. Image Super-Resolution  
A. Datasets  
C. Image Quality Assessment (IQA)  
III. Diffusion Models Basics  
A. Denoising Diffusion Probabilistic Models (DDPMs)  
B. Score-based Generative Models (SGMs)  
D. Relation between Diffusion Models  
E. Relation to other Image SR Generative Models  
IV. Improvements for Diffusion Models  
B. Improved Likelihood  
V. Diffusion Models for Image SR  
VI. Diffusion-Based Zero-Shot SR  
VII. Domain-Specific Applications  
A. Medical Imaging  
B. Blind Face Restoration  
C. Atmospheric Turbulence in Face SR  
D. Remote Sensing  
VIII. Discussion and Future Work  
A. Color Shifting  
B. Computational Costs  
C. Efficient Sampling  
D. Corruption Spaces  
E. Comparability  
F. Image Manipulation  
G. Cascaded Image Generation  
IX. Conclusion