  We make the first steps towards diffusion models for unconditional generation
of multivariate and Arctic-wide sea-ice states. While targeting to reduce the
computational costs by diffusion in latent space, latent diffusion models also
offer the possibility to integrate physical knowledge into the generation
process. We tailor latent diffusion models to sea-ice physics with a censored
Gaussian distribution in data space to generate data that follows the physical
bounds of the modelled variables. Our latent diffusion models reach similar
scores as the diffusion model trained in data space, but they smooth the
generated fields as caused by the latent mapping. While enforcing physical
bounds cannot reduce the smoothing, it improves the representation of the
marginal ice zone. Therefore, for large-scale Earth system modelling, latent
diffusion models can have many advantages compared to diffusion in data space
if the significant barrier of smoothing can be resolved.
