  The transition dynamics of two-state systems with time-dependent energy
levels, first considered by Landau, Zener, Majorana, and St\"uckelberg, is one
of the basic models in quantum physics and has been used to describe various
physical systems. We propose here a generalization of the Landau-Zener (LZ)
problem characterized by distinct paths of the instantaneous eigenstates as the
system evolves in time, while keeping the instantaneous eigenenergies exactly
as in the standard LZ model. We show that these paths play an essential role in
the transition probability $P$ between the two states, and can lead to
superadiabatic transitions, i.e., to a substantial reduction of $P$. As an
instructive extreme case, we identify an unconditionally adiabatic regime with
$P=0$ no matter how fast the system evolves in time and regardless of the
energy gap between the two levels at the anticrossing point. On the other hand,
large $P$ occur even in the absence of any anticrossing point. These phenomena
can be explained by observing the rotation of the instantaneous eigenvectors on
the Bloch sphere. The superadiabatic LZ model can describe valley transition
dynamics during charge and spin shuttling in semiconductor quantum dots.
