Recently, diffusion models have been used to solve various inverse problems for medical imaging applications in an unsupervised manner. However, the current solvers, which recursively apply a reverse diffusion step followed by a measurement consistency step, often produce sub-optimal results. By studying the generative sampling path, we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. Furthermore, diffusion models are inherently slow to sample from, needing few thousand steps of iteration to generate images from pure Gaussian noise. In this talk, we show that starting from Gaussian noise is unnecessary. Instead, starting from a single forward diffusion with better initialization significantly reduces the number of sampling steps in the reverse conditional diffusion. This phenomenon is formally explained by the contraction theory of the stochastic difference equations like our conditional diffusion strategy - the alternating applications of reverse diffusion followed by a non-expansive data consistency step. Furthermore, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. Experimental results with image inpainting, and compressed sensing MRI and sparse-view CT demonstrate that our method can achieve state-of-the-art reconstruction performance at significantly reduced sampling steps.
Jong Chul Ye is a Professor of the Kim Jaechul Graduate School of Artificial Intelligence (AI) of Korea Advanced Institute of Science and Technology (KAIST), Korea. He received the B.Sc. and M.Sc. degrees from Seoul National University, Korea, and the Ph.D. from Purdue University, West Lafayette. Before joining KAIST, he worked at Philips Research and GE Global Research in New York. He has served as an associate editor of IEEE Trans. on Image Processing, and an editorial board member for Magnetic Resonance in Medicine. He is currently an associate editor for IEEE Trans. on Medical Imaging, and a Senior Editor of IEEE Signal Processing Magazine. He is an IEEE Fellow, was the Chair of IEEE SPS Computational Imaging TC, and IEEE EMBS Distinguished Lecturer. He was a General Cochair (with Mathews Jacob) for IEEE Symp. On Biomedical Imaging (ISBI) 2020. His research interest is in machine learning for biomedical imaging and computer vision.