  We consider Hermitian random band matrices $H$ in $d \geq 1 $ dimensions. The
matrix elements $H_{xy},$ indexed by $x, y \in \Lambda \subset \mathbb{Z}^d,$
are independent, uniformly distributed random variable if $|x-y| $ is less than
the band width $W,$ and zero otherwise. We update the previous results of the
converge of quantum diffusion in a random band matrix model from convergence of
the expectation to convergence in high probability. The result is uniformly in
the size $|\Lambda| $ of the matrix.
