Testing QCD with CMS using jets and diffraction

Measurements of jet final states are presented, performed with the CMS experiment at the LHC at different centre-of-mass energies and down to very low $p_{\text{T}}$. The study of forward and/or low-$p_{\text{T}}$ jets is ideal to explore new kinematic domains in QCD, especially in the low-$x$ region. A measurement of the production of leading charged particles, and leading charged-particle jets, at small $p_{\text{T}}$ in proton-proton collisions at $\sqrt{s}$ = 8 TeV is presented, together with a first observation at the LHC of events with a large rapidity gap between the two leading jets at $\sqrt{s}$ = 7 TeV.