  High-resolution (HR) simulations in cosmology, in particular when including
baryons, can take millions of CPU hours. On the other hand, low-resolution (LR)
dark matter simulations of the same cosmological volume use minimal computing
resources. We develop a denoising diffusion super-resolution emulator for large
cosmological simulation volumes. Our approach is based on the image-to-image
Palette diffusion model, which we modify to 3 dimensions. Our super-resolution
emulator is trained to perform outpainting, and can thus upgrade very large
cosmological volumes from LR to HR using an iterative outpainting procedure. As
an application, we generate a simulation box with 8 times the volume of the
Illustris TNG300 training data, constructed with over 9000 outpainting
iterations, and quantify its accuracy using various summary statistics.
