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We report on the recent CMS measurements of soft hadron-hadron production,including the measurements of inclusive single- and double-diffractive crosssections, as well as the measurement of pseudorapidity distributions, and ofthe leading charged particle and leading jet cross sections. We present thecross sections for low-pT forward jets production, and production of dijetswith large rapidity separation (central-forward, and forward-backward jets).Studies of double parton scattering using four-jet and W+2-jet events, and thecross sections for Drell-Yan with associated jet production are discussed aswell. The results, corresponding to the proton-proton center-of-mass energy of7 or 8 TeV, are compared to predictions of various Monte Carlo models.

Diffraction, forward physics and soft QCD results from CMS