  Recent measurements of the Higgs-muon coupling are directly probing muon mass
generation for the first time. We classify minimal models with a one-loop
radiative mass mechanism and show that benchmark models are consistent with
current experimental results. We find that these models are best probed by
measurements of $(g-2)_\mu$, even when taking into account the precision of
Higgs measurements expected at future colliders. The current $(g-2)_\mu$
anomaly, if confirmed, could therefore be a first hint that the muon mass has a
radiative origin.
