Lepton $g-2$ and $W$-boson mass anomalies in the DFSZ axion model

With regard to the leptonic magnetic dipole moment anomaly as well as the $W$-boson mass excess, we study the DFSZ axion model. Considering theoretical and experimental constraints, we show that the muon and electron $g-2$ anomalies can be explained within the parameter space of the model for extra Higgs bosons with mass spectra around the electroweak scale and for an almost equivalent contribution of one- and two-loop diagrams. A negative electron $g-2$ could be achieved by introducing heavy neutrinos. Furthermore, the $W$ boson mass excess can be consistently addressed within the mass range of the matter content testable at collider experiments.