  The CDF collaboration at Fermilab has recently reported a new precision
measurement of the $W$~boson mass showing a substantial $7\sigma$ deviation
from the Standard Model prediction. Moreover, Fermilab has recently confirmed
the longstanding tension in the $(g-2)_\mu$ measurement. We propose a unified
solution to these deviations within the simplest radiative neutrino mass model:
the Zee model. Our analysis establishes non-trivial links between the origin of
neutrino mass, the $(g-2)_\mu$ anomaly, and the $W$~boson mass shift while
being consistent with lepton flavor violation and all other experimental
constraints. We find that the mass spectrum of the physical scalars must be
hierarchical to be consistent with the $W$~boson mass shift; remarkably, this
is also the key to resolving the $(g-2)_\mu$ tension. Furthermore, this mass
splitting offers a unique same-sign dimuon signal through which our model can
be tested at the LHC.
