\dm_csml_event_details UCL ELLIS

Manifold-constrained diffusion models for inverse problems in imaging


Jong Chul Ye


Graduate School of Artificial Intelligence, KAIST, Daejeon, Korea


Friday, 03 February 2023




Function Space, UCL Centre for Artificial Intelligence, 1st Floor, 90 High Holborn, London WC1V 6BH



Event series

DeepMind/ELLIS CSML Seminar Series


Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce sub- optimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, 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. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Then, we extend diffusion solvers to efficiently handle general noisy (non)linear inverse problems via approximation of the posterior sampling. Interestingly, the resulting posterior sampling scheme is a blended version of diffusion sampling with the manifold constrained gradient without a strict measurement consistency projection step, yielding a more desirable generative path in noisy settings compared to the previous studies. Our method demonstrates that diffusion models can incorporate various measurement noise statistics such as Gaussian and Poisson, and also efficiently handle noisy nonlinear inverse problems such as Fourier phase retrieval and non-uniform deblurring.


Jong Chul Ye is a Professor of 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, and will be a program chair for IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 2024.