  We study the phase diagrams of the bifundamental QCD (QCD(BF)) of different
ranks, which is the $4$d $SU(N_1) \times SU(N_2)$ gauge theory coupled with a
bifundamental Dirac fermion. After discussing the anomaly constraints on
possible vacuum structures, we apply a novel semiclassical approach on
$\mathbb{R}^2\times T^2$ with the baryon-'t Hooft flux to obtain the concrete
dynamics. The $2$d effective theory is derived by the dilute gas approximation
of center vortices, and it serves as the basis for determining the phase
diagram of the model under the assumption of adiabatic continuity. As an
application, we justify the non-supersymmetric duality cascade between
different QCD(BF), which has been conjectured in the large-${N}$ argument.
Combined with the semiclassics and the large-$N_{1,2}$ limit, we construct the
explicit duality map from the parent theory, $SU(N_1) \times SU(N_2)$ QCD(BF),
to the daughter theory, $SU(N_1) \times SU(N_2-N_1)$ QCD(BF), including the
correspondence of the coupling constants. We numerically examine the validity
of the duality also for finite $N_{1,2}$ within our semiclassics, finding a
remarkable agreement of the phase diagrams between the parent and daughter
sides.
