Uncertainty-aware localization microscopy by variational diffusion

Fast extraction of physically relevant information from images using deep neural networks has led to significant advances in fluorescence microscopy and its application to the study of biological systems. For example, the application of deep networks for kernel density (KD) estimation in single-molecule localization microscopy (SMLM) has accelerated super-resolution imaging of densely labeled structures in the cell. However, localization of fluorescent molecules in dense images is a difficult inverse problem with potentially multiple solutions. To model a probability distribution of solutions to this problem, we propose a generative modeling framework for KD estimation in SMLM based on a conditional variational diffusion model (CVDM). In this framework, CVDM is trained to perform localization tasks on low-resolution measurements by modeling a distribution of high-resolution KD estimates. This approach allows us to probe the structure of the distribution on KD estimates and express uncertainty, which is not currently offered by existing deep models for localization microscopy. We demonstrate that this model permits high-fidelity super-resolution, enables the uncertainty estimation of regressed KD estimates, and has important implications for image restoration in single-molecule and super resolution microscopy.