This paper shows that a learned generative prior can guide Richardson–Lucy (RL) deconvolution to give cleaner, more faithful images from low-light fluorescence microscopy. RL is an algorithm that tries to recover the original fluorescent signal that most likely produced the measured photon counts under a Poisson imaging model (a statistical model for counting photons). RL can sharpen contrast but, on its own, will often amplify noise and become unstable when photon counts are low.

The researchers integrated a score-based diffusion prior — a machine-learned model that knows what realistic biological images tend to look like — into a decoupled inverse-problem framework for deconvolution. In practice, the diffusion prior is used during the iterative RL optimization to nudge the solution toward biologically plausible structure, while the RL steps continue to enforce Poisson data consistency (they keep the reconstruction consistent with the measured photon counts). The team tested this approach across a range of biological samples and cellular shapes.

At a high level, the score-based diffusion model is a learned guide. It estimates how to change an image to make it look more like the training examples, which helps prevent the RL iterations from fitting random noise. The decoupled framework means the algorithm alternates between enforcing the physics of image formation (the RL/Poisson step) and applying the learned structural guidance (the diffusion step). This separation preserves the physical measurement model while adding structural information.

Why this matters: in low-photon imaging, researchers often face a trade-off between restoring detail and avoiding noise amplification. Simple regularizers such as total variation (TV) can stabilize RL but tend to oversmooth small, weak structures. According to the paper, adding the diffusion prior reduces RL’s noise amplification and better preserves weak filamentous and punctate (dot-like) features when photon counts are low. That could help researchers see faint biological structures without collecting more light, which can be slow or harmful to samples.