  We present a (heuristic) theoretical derivation for the scaling of the
diffusion coefficient $D_f$ for fluctuating ``pulled'' fronts. In agreement
with earlier numerical simulations, we find that as $N\to\infty$, $D_f$
approaches zero as $1/\ln^3N$, where $N$ is the average number of particles per
correlation volume in the stable phase of the front. This behaviour of $D_f$
stems from the shape fluctuations at the very tip of the front, and is
independent of the microscopic model.
