  Galaxy cluster mass functions are a function of cosmology, but mass is not a
direct observable, and systematic errors abound in all its observable proxies.
Mass-free inference can bypass this challenge, but it requires large suites of
simulations spanning a range of cosmologies and models for directly observable
quantities. In this work, we devise a U-net - an image-to-image machine
learning algorithm - to ``paint'' the IllustrisTNG model of baryons onto
dark-matter-only simulations of galaxy clusters. Using 761 galaxy clusters with
$M_{200c} \gtrsim 10^{14}M_\odot$ from the TNG-300 simulation at $z<1$, we
train the algorithm to read in maps of projected dark matter mass and output
maps of projected gas density, temperature, and X-ray flux. The models train in
under an hour on two GPUs, and then predict baryonic images for $\sim2700$ dark
matter maps drawn from the TNG-300 dark-matter-only (DMO) simulation in under
two minutes. Despite being trained on individual images, the model reproduces
the true scaling relation and scatter for the $M_{DM}-L_X$, as well as the
distribution functions of the cluster X-ray luminosity and gas mass. For just
one decade in cluster mass, the model reproduces three orders of magnitude in
$L_X$. The model is biased slightly high when using dark matter maps from the
DMO simulation. The model performs well on inputs from TNG-300-2, whose mass
resolution is 8 times coarser; further degrading the resolution biases the
predicted luminosity function high. We conclude that U-net-based baryon
painting is a promising technique to build large simulated cluster catalogs
which can be used to improve cluster cosmology by combining existing
full-physics and large $N$-body simulations.
