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ABSTRACT The circum-galactic medium (CGM) can feasibly be mapped by multiwavelength surveys covering broad swaths of the sky. With multiple large data sets becoming available in the near future, we develop a likelihood-free Deep Learning technique using convolutional neural networks (CNNs) to infer broad-scale physical properties of a galaxy’s CGM and its halo mass for the first time. Using CAMELS (Cosmology and Astrophysics with MachinE Learning Simulations) data, including IllustrisTNG, SIMBA, and Astrid models, we train CNNs on Soft X-ray and 21-cm (H i) radio two-dimensional maps to trace hot and cool gas, respectively, around galaxies, groups, and clusters. Our CNNs offer the unique ability to train and test on ‘multifield’ data sets comprised of both H i and X-ray maps, providing complementary information about physical CGM properties and improved inferences. Applying eRASS:4 survey limits shows that X-ray is not powerful enough to infer individual haloes with masses log (Mhalo/M⊙) < 12.5. The multifield improves the inference for all halo masses. Generally, the CNN trained and tested on Astrid (SIMBA) can most (least) accurately infer CGM properties. Cross-simulation analysis – training on one galaxy formation model and testing on another – highlights the challenges of developing CNNs trained on a single model to marginalize over astrophysical uncertainties and perform robust inferences on real data. The next crucial step in improving the resulting inferences on the physical properties of CGM depends on our ability to interpret these deep-learning models.