This should be contrasted to the displacement of a free particle with initial velocity $v_0$. In that case the distance from the initial position after a time $t$ is $x(t) = vt$ whereas for a diffusion process the root mean square value is $\sqrt{\langle x^2\rangle-\langle x\rangle^2} \propto \sqrt{t}$. Since diffusion is strongly linked with random walks, we could say that a random walker escapes much more slowly from the starting point than would a free particle.