  In this paper, we show that one-dimensional discrete multi-frequency
quasiperiodic Schr\"odinger operators with smooth potentials demonstrate
ballistic motion on the set of energies on which the corresponding
Schr\"odinger cocycles are smoothly reducible to constant rotations. The proof
is performed by establishing a local version of strong ballistic transport on
an exhausting sequence of subsets on which reducibility can be achieved by a
conjugation uniformly bounded in the $\mathrm{C}^{\ell}$-norm. We also
establish global strong ballistic transport under an additional integral
condition on the norms of conjugation matrices. The latter condition is quite
mild and is satisfied in many known examples.
