  We establish strong ballistic transport for a family of discrete
quasiperiodic Schr\"odinger operators as a consequence of exponential dynamical
localization for the dual family. The latter has been, essentially, shown by
Jitomirskaya and Kr\"uger in the one-frequency setting and by Ge--You--Zhou in
the multi-frequency case. In both regimes, we obtain strong convergence of
$\frac{1}{T}X(T)$ to the asymptotic velocity operator $Q$, which improves
recent perturbative results by Zhao and provides the strongest known form of
ballistic motion. In the one-frequency setting, this approach allows to treat
Diophantine frequencies non-perturbatively and also consider the weakly
Liouville case.
