  We discuss bounds for nonadiabatic transitions from the viewpoints of the
adiabatic perturbation theory and the quantum speed limit. We show that the
amount of nonadiabatic transitions from the $n$th level to the $m$th level is
bounded by a function of the quantum geometric tensor for the $m$th level. We
analyze this bound from the viewpoint of the adiabatic perturbation theory. In
addition, this bound and the viewpoint of the quantum speed limit suggest
nontrivial relationship between the dynamical transformation and the adiabatic
transformation. We also derive a universal bound for any nonadiabatic
transition. This bound is written in terms of the counterdiabatic Hamiltonian.
