Realistic galaxy image simulation via score-based generative models

We show that a Denoising Diffusion Probabalistic Model (DDPM), a class of score-based generative model, can be used to produce realistic mock images that mimic observations of galaxies. Our method is tested with Dark Energy Spectroscopic Instrument (DESI) grz imaging of galaxies from the Photometry and Rotation curve OBservations from Extragalactic Surveys (PROBES) sample and galaxies selected from the Sloan Digital Sky Survey. Subjectively, the generated galaxies are highly realistic when compared with samples from the real dataset. We quantify the similarity by borrowing from the deep generative learning literature, using the `Fr\'echet Inception Distance' to test for subjective and morphological similarity. We also introduce the `Synthetic Galaxy Distance' metric to compare the emergent physical properties (such as total magnitude, colour and half light radius) of a ground truth parent and synthesised child dataset. We argue that the DDPM approach produces sharper and more realistic images than other generative methods such as Adversarial Networks (with the downside of more costly inference), and could be used to produce large samples of synthetic observations tailored to a specific imaging survey. We demonstrate two potential uses of the DDPM: (1) accurate in-painting of occluded data, such as satellite trails, and (2) domain transfer, where new input images can be processed to mimic the properties of the DDPM training set. Here we `DESI-fy' cartoon images as a proof of concept for domain transfer. Finally, we suggest potential applications for score-based approaches that could motivate further research on this topic within the astronomical community.