New particles decaying to jet pairs, predicted by many theories of physics beyond the Standard Model, could be discovered at the Large Hadron Collider as resonances in the dijet invariant mass spectrum. Three searches for dijet resonances by the CMS Collaboration are presented, which employ several novel techniques to probe a wide range of resonance masses. The first search targets resonance masses above $1800\,\mathrm{GeV}$. A new background method using jet pairs with large pseudorapidity separation is described. The latter two searches target resonances below $450\,\mathrm{GeV}$, where trigger bandwidth limitation preclude the methods used at high masses. The resonances are required to be produced with high transverse momentum due to significant initial state radiation (ISR), and hence the resonance decay products are collimated into a single jet. The searches, which require either ISR jets or photons, probe resonance masses from $50$-$450\,\mathrm{GeV}$ and $10$-$125\,\mathrm{GeV}$, respectively.