  Climate change is causing the intensification of rainfall extremes.
Precipitation projections with high spatial resolution are important for
society to prepare for these changes, e.g. to model flooding impacts.
Physics-based simulations for creating such projections are very
computationally expensive. This work demonstrates the effectiveness of
diffusion models, a form of deep generative models, for generating much more
cheaply realistic high resolution rainfall samples for the UK conditioned on
data from a low resolution simulation. We show for the first time a machine
learning model that is able to produce realistic samples of high-resolution
rainfall based on a physical model that resolves atmospheric convection, a key
process behind extreme rainfall. By adding self-learnt, location-specific
information to low resolution relative vorticity, quantiles and time-mean of
the samples match well their counterparts from the high-resolution simulation.
