  We train neural networks to perform likelihood-free inference from
$(25\,h^{-1}{\rm Mpc})^2$ 2D maps containing the total mass surface density
from thousands of hydrodynamic simulations of the CAMELS project. We show that
the networks can extract information beyond one-point functions and power
spectra from all resolved scales ($\gtrsim 100\,h^{-1}{\rm kpc}$) while
performing a robust marginalization over baryonic physics at the field level:
the model can infer the value of $\Omega_{\rm m} (\pm 4\%)$ and $\sigma_8 (\pm
2.5\%)$ from simulations completely different to the ones used to train it.
