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