  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.
