  We show that partially hyperbolic diffeomorphisms of $d$-dimensional tori
isotopic to an Anosov diffeomorphism, where the isotopy is contained in the set
of partially hyperbolic diffeomorphisms, are dynamically coherent. Moreover, we
show a \textit{global stability result}, i.e. every partially hyperbolic
diffeomorphism as above is \textit{leaf-conjugate} to the linear one. As a
consequence, we obtain intrinsic ergodicity and measure equivalence for
partially hyperbolic diffeomorphisms with one-dimensional center direction that
are isotopic to Anosov diffeomorphisms through such a path.
