Generative AI models have revolutionized various fields by enabling the creation of realistic and diverse data samples. Among these models, diffusion models have emerged as a powerful approach for generating high-quality images, text, and audio. This survey paper provides a comprehensive overview of generative AI diffusion and legacy models, focusing on their underlying techniques, applications across different domains, and their challenges. We delve into the theoretical foundations of diffusion models, including concepts such as denoising diffusion probabilistic models (DDPM) and score-based generative modeling. Furthermore, we explore the diverse applications of these models in text-to-image, image inpainting, and image super-resolution, along with others, showcasing their potential in creative tasks and data augmentation. By synthesizing existing research and highlighting critical advancements in this field, this survey aims to provide researchers and practitioners with a comprehensive understanding of generative AI diffusion and legacy models and inspire future innovations in this exciting area of artificial intelligence.