We have recently studied the QCD pomeron loop evolution equations in zero transverse dimensions [Shoshi:2005pf]. Using the techniques developed in [Shoshi:2005pf] together with the AGK cutting rules, we present a calculation of single, double and central diffractive cross sections (for large diffractive masses and large rapidity gaps) in zero transverse dimensions in which all dominant pomeron loop graphs are consistently summed. We find that the diffractive cross sections unitarise at asymptotic energies and that they are suppressed by powers of alpha_s. Our calculation is expected to expose some of the diffractive physics in hadron-hadron collisions at high energy.
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