  We report an experimental and theoretical study of the phase diffusion in
small Josephson junctions under microwave irradiation. A peculiar enhancement
of the phase diffusion by microwaves is observed. The enhancement manifests
itself by a pronounced current peak in the current-voltage characteristics. The
voltage position $V_{\rm top}$ of the peak increases with the power $P$ of
microwave radiation as $V_{\rm top}\propto\sqrt P$, while its current amplitude
weakly decreases with $P$. As the microwave frequency increases, the peak
feature evolves into Shapiro steps with finite slope. Our theoretical analysis
taking into account the enhancement of incoherent superconducting current by
multi-photon absorption is in good agreement with experimental data.
