We generalize the result of block-wise convergence of the Brownian motion on the unitary group $U(nm)$ towards a quantum Lévy process on the unitary dual group $U\langle n\rangle$ when $m\rightarrow\infty$, obtained by the author in a previous paper, by showing that the Brownian motions on the orthogonal group $O(nm)$ and the symplectic group $Sp(nm)$ also converge block-wise to this same quantum Lévy process.