Modern society increasingly relies on technologies that use waves to see inside complex environments that cannot be observed directly. Medical imaging, seismic exploration, remote sensing, and astronomical imaging all depend on interpreting how waves propagate through complicated materials in order to detect hidden structures or abnormalities. This project will develop new mathematical and artificial intelligence (AI) methodologies that will make such imaging technologies more accurate, reliable, and computationally efficient. A major focus will be on biomedical imaging, where the methods will help identify malignant tissue and improve early diagnosis of disease. The project will establish a rigorous mathematical foundation for emerging generative AI techniques used in imaging and uncertainty quantification, thereby improving confidence in AI-assisted scientific and medical decision making. The research will also strengthen connections between mathematics, physics, engineering, and data science, while training graduate and undergraduate students in interdisciplinary research areas of growing societal importance. The project will develop new mathematical theory for Bayesian inverse problems and generative modeling in infinite-dimensional settings arising from wave propagation in complex media. The research will analyze stochastic differential equations, their time reversal, and associated sampling dynamics in order to construct efficient algorithms that rapidly approach con