  It is shown that the Di\'osi-Penrose criterion of gravity-induced quantum
collapse may be inconsistent with the discreteness of space-time, which is
generally considered as an indispensable element in a complete theory of
quantum gravity. Moreover, the analysis also suggests that the discreteness of
space-time may result in rapider collapse of the superposition of energy
eigenstates than required by the Di\'osi-Penrose criterion.
