Exploring diffusion models: theory, applications and beyond

This dissertation describes a general study on diffusion model and its diverse applications across various domains. Diffusion models, including Denoising diffusion probabilistic models (DDPMs), Score-based generative models (SGMs), and stochas- tic differential equations (SDEs), serve as the foundational probabilistic generative models underpinning this exploration. We delve into the core concepts of diffusion models and its essential roles in denoising and probabilistic modeling. Additionally, we examine the intricate relationships between diffusion models and other generatice models, such as Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and flow-based models. The interplay and com- monalities between these models are thoroughly explored, unveiling their potential applications in a wide range of tasks. In terms of practical applications, we emphasize the technical utility of diffusion models in computer vision, natural language processing, and multi-modal generation. These applications encompass image generation, language modeling, image denoising, and the synthesis of multi-modal data, highlighting the advantages of diffusion models in handling complex data distributions and generating high-quality samples. Lastly, we spotlight the application of diffusion models in the field of weather forecasting. Leveraging diffusion model techniques, researchers have made significant strides in enhancing accuracy and computational efficiency in weather and climate prediction. This application underscores the importance and potential of diffusion models in addressing real-world challenges.