Pixellated Posterior Sampling of Point Spread Functions in Astronomical Images

TL;DR

This paper presents a new Bayesian framework for pixel-level PSF modeling in astronomical images, improving accuracy and uncertainty quantification over traditional methods, with applications in weak lensing, astrometry, and photometry.

Contribution

It introduces a novel posterior sampling method combining Gaussian likelihood with a diffusion model prior for detailed PSF uncertainty estimation.

Findings

Achieves higher likelihood and lower residuals than traditional methods

Effective even for faint and masked sources, providing broader posterior distributions

Enables propagation of PSF morphological uncertainty in analysis

Abstract

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 HST 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.