Pixelated Posterior Sampling of Point-spread Functions in Astronomical Images

We introduce a novel framework for upsampled point-spread function (PSF) modeling using pixel-level Bayesian inference. Accurate PSF characterization is critical for precision measurements in many fields, including weak lensing, astrometry, and photometry. Our method defines the posterior distribution of the pixelized PSF model through the combination of an analytic Gaussian likelihood and a highly expressive generative diffusion model prior, trained on a library of Hubble Space Telescope effective PSF (ePSF) templates. Compared to traditional methods (parametric Moffat, ePSF template-based, and regularized likelihood), we demonstrate that our PSF models achieve orders-of-magnitude-higher likelihood and residuals consistent with noise, all while remaining visually realistic. Further, the method applies even for faint and heavily masked point sources, merely producing a broader posterior. By recovering a realistic, pixel-level posterior distribution, our technique enables the first meaningful propagation of detailed PSF morphological uncertainty in downstream analysis. An implementation of our posterior sampling procedure is available on GitHub.