We report a measurement of the diffraction dissociation differential cross section d2 sigma_SD/dM2 dt for p anti-p --> pbar X at sqrt s = 546 and 1800 GeV, M2/s < 0.2 and 0 \leq -t \leq 0.4 GeV2. Our results are compared to theoretical predictions and to extrapolations from experimental results at lower energies.