Echoes in the Noise: Posterior Samples of Faint Galaxy Surface Brightness Profiles with Score-Based Likelihoods and Priors

Examining the detailed structure of galaxies populations provides valuable insights into their formation and evolution mechanisms. Significant barriers to such analysis are the non-trivial noise properties of real astronomical images and the point spread function (PSF) which blurs structure. Here we present a framework which combines recent advances in score based likelihood characterization and diffusion model priors to perform a true Bayesian analysis of image deconvolution. Our technique, when applied to minimally processed Hubble Space Telescope (\emph{HST}) data, recovers structures which have otherwise only become visible in next generation James Webb Space Telescope (\emph{JWST}) imaging.