Video diffusion models have become a powerful technique for generating and modifying high-quality, coherent video content. This survey provides a systematic overview of key aspects of video diffusion models, including their applications, architectural choices, and modeling of temporal dynamics. Recent advancements in the field are summarized and grouped into development trends. The survey concludes with an overview of remaining challenges and an outlook on the future of the field. The survey discusses various applications of video diffusion models, including text-conditioned generation, image-conditioned video generation, video completion, audio-conditioned video generation, video editing, and intelligent decision-making. Each application is analyzed in terms of its specific challenges and potential solutions. The mathematical formulation of diffusion generative models is reviewed, focusing on the denoising process and the training of the model. The survey also discusses the architecture of video diffusion models, including UNets and transformers, and how they can be adapted for video generation. The survey explores the modeling of temporal dynamics in video diffusion models, including spatio-temporal attention mechanisms and temporal upsampling techniques. It also discusses the training and evaluation of video diffusion models, including the use of various benchmark datasets and evaluation metrics. The survey concludes with a discussion of the current state of video diffusion models and their potential future developments. It highlights the challenges that remain in the field and the opportunities for further research and innovation.Video diffusion models have become a powerful technique for generating and modifying high-quality, coherent video content. This survey provides a systematic overview of key aspects of video diffusion models, including their applications, architectural choices, and modeling of temporal dynamics. Recent advancements in the field are summarized and grouped into development trends. The survey concludes with an overview of remaining challenges and an outlook on the future of the field. The survey discusses various applications of video diffusion models, including text-conditioned generation, image-conditioned video generation, video completion, audio-conditioned video generation, video editing, and intelligent decision-making. Each application is analyzed in terms of its specific challenges and potential solutions. The mathematical formulation of diffusion generative models is reviewed, focusing on the denoising process and the training of the model. The survey also discusses the architecture of video diffusion models, including UNets and transformers, and how they can be adapted for video generation. The survey explores the modeling of temporal dynamics in video diffusion models, including spatio-temporal attention mechanisms and temporal upsampling techniques. It also discusses the training and evaluation of video diffusion models, including the use of various benchmark datasets and evaluation metrics. The survey concludes with a discussion of the current state of video diffusion models and their potential future developments. It highlights the challenges that remain in the field and the opportunities for further research and innovation.