  We propose to jointly explain the electron/muon $g-2$ anomalies in the
framework of anomaly mediated SUSY breaking (AMSB) scenario. Two Yukawa
deflected AMSB models are proposed and discussed in depth: one with
lepton-specific interactions and the other one with messenger-matter
interactions. Both models are found to be able to jointly explain the anomalies
at $2 \sigma$ level by naturally realizing the preferred parameter space with
$\mu M_1,\mu M_2<0$ and very heavy left-handed smuon.
