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Recording of Prof. Yong Chul Ye's talk on Jan. 30, 2025, at the EPFL Seminar Series in Imaging. Abstract: The recent emergence of diffusion models has driven significant advancements in solving inverse problems by leveraging these models as powerful generative priors. However, challenges persist due to the ill-posed nature of such problems, including extending solutions to 3D and temporal domains and addressing inherent ambiguities in measurements. In this talk, we present strategies developed by our lab at KAIST to tackle these challenges. First, we explore the manifold geometry of diffusion models, which has become a foundational concept for designing constrained diffusion models. Building on this, we introduce the Diffusion Posterior Sampling (DPS) algorithm, which enables manifold-constrained measurement guidance during the reverse sampling process. Additionally, we present its accelerated implementation, the Decomposed Diffusion Sampling (DDS) method, tailored for high-dimensional imaging problems in biomedical applications. Finally, we discuss several extensions, including text-driven reconstruction, CFG++, and applications to video and 3D domains.