This research project explores the statistical aspects of diffusion models, an emerging class of generative modeling techniques that are transforming current practices in image and video synthesis, scientific simulation, inverse problems, and offline reinforcement learning. The project will apply information theory methods to explain when and why diffusion models succeed under certain statistical assumptions and when they do not. The results of the research are expected to advance the understanding of diffusion-based generative models and inform how they can be improved in terms of generation quality, computational efficiency, and user privacy preservation. The project provides research topics for training undergraduate and graduate students in modern statistical and machine learning techniques. Specifically, the project aims to address three technical questions: (1) What are the statistical limits of diffusion models in the minimax sense, especially the effect of low probability regions that may explain hallucination behaviors of generative models? (2) What is the optimal query complexity for sampling in diffusion models? The investigator will provide a systematic approach for the optimal query complexity by establishing connections with information-theoretic techniques previously used for analyzing the channel capacity. Accelerated diffusion methods will be constructed that nearly achieve this optimal complexity. (3) What is the fundamental trade-off between accuracy and