Measurements of diffractive dissociation cross sections in pp collisions at s=7  TeV are presented in kinematic regions defined by the masses MX and MY of the two final-state hadronic systems separated by the largest rapidity gap in the event. Differential cross sections are measured as a function of ξX=MX2/s in the region -5.53, log10MX>1.1, and log10MY>1.1, a region dominated by DD. The cross sections integrated over these regions are found to be, respectively, 2.99±0.02(stat)-0.29+0.32(syst)  mb, 1.18±0.02(stat)±0.13(syst)  mb, and 0.58±0.01(stat)-0.11+0.13(syst)  mb, and are used to extract extrapolated total SD and DD cross sections. In addition, the inclusive differential cross section, dσ/dΔηF, for events with a pseudorapidity gap adjacent to the edge of the detector, is measured over ΔηF=8.4 units of pseudorapidity. The results are compared to those of other experiments and to theoretical predictions and found compatible with slowly rising diffractive cross sections as a function of center-of-mass energy.