<p>Diffusion Models (DMs) have recently emerged as a highly effective category of deep generative models, achieving exceptional results in various domains, including image synthesis, video generation, and molecule design. This survey provides a comprehensive analysis of the expanding body of research on this topic. The primary objective of this study is to investigate the architecture and requirements of generative artificial intelligence systems. Initially, an analysis of the prerequisites and frontier ideas for the implementation of generative AI systems is performed. To clarify the operational mechanisms of the methodology, the design choices of DMs are thoroughly examined, covering aspects such as refinement, parallel generation, editing, in-painting, and cross-domain generation. This study extensively reviews fundamental DMs and their diverse applications in fields such as computer vision (CV), natural language processing (NLP), image synthesis, and interdisciplinary applications (scene generation, 3D vision, video modeling, medical image diagnosis, time-series analysis, audio generation, 3D molecule generation etc.) in other scientific domains. A comparative study for all the works that use generative AI methods for various downstream tasks in each domain is performed. A comprehensive study on datasets is also carried out. Finally, it discusses the limitations of current methods, as well as the need for additional techniques and future directions in order to make meaningful progress in this area.</p>