CAREER: Provable, Flexible, & Scalable Integration of Physical and Diffusion Models for Probabilistic Imaging

Computational imaging aims to recover meaningful visual information about an object or scene from measurements collected by an imaging system. In many important applications, however, those measurements are indirect, incomplete, and noisy, making it difficult to determine the true underlying image. For example, many three-dimensional microscopy applications would need to recover cellular structure from measurements acquired over only limited views. In such settings, the data may be consistent with many plausible images rather than a single unique solution. Yet existing methods typically produce only one reconstructed image and do not capture this ambiguity. As a result, they cannot indicate whether the image is trustworthy, where uncertainty is concentrated, or what other plausible images may also explain the measurements, all of which are important for scientific and clinical decision-making. Developing the next generation of computational imaging methods therefore requires a shift from single-answer reconstruction to probabilistic approaches that characterize the full range of plausible solutions. To address the need, this project will develop a novel provable, flexible, and scalable framework that combines physical forward models with generative diffusion models for computational imaging. The framework will recover the full distribution of image solutions consistent with the measured data, rather than only a single reconstruction, thereby enabling principled uncertainty characterization. The research will pursue three integrated directions: (i) developing a rigorous posterior sampling framework for imaging inverse problems with theoretical guarantees; (ii) designing flexible algorithms compatible with nonlinear and partially unknown forward models; and (iii) creating scalable methods for high-dimensional imaging. The project will draw on emerging connections between sampling and optimization to develop new reconstruction algorithms together with convergence analyses, while also producing practical methods based on gradient updates, proximal operators, and neural field representations. In collaboration with domain experts, the investigator will apply the developed methods to intensity diffraction tomography for three-dimensional live-cell imaging, optical coherence tomography for free-motion four-dimensional eye imaging, and quantitative magnetic resonance imaging for stroke diagnosis. The resulting theory and algorithms will advance probabilistic imaging and improve the reliability of computational imaging in scientific and biomedical applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2542022 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT,01002930DB NSF RESEARCH & RELATED ACTIVIT,01003031DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Yu Sun | Institution: Johns Hopkins University, BALTIMORE, MD | Award Amount: $441,528 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2542022 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2542022.html