Standard diffusion has no localization property, being in disagreement with quantum predictions. However, it turns out that it is based on approximation of the principle of maximum entropy, which says that the probability distribution which best represents the current state of knowledge is the one with largest entropy. This approximation is repaired in maximal entropy random walk, also repairing the disagreement: it turns out to lead to exactly the quantum ground state stationary probability distribution with its strong localization properties.