A variety of important cellular processes require, for functional purposes, the colocalization of multiple DNA loci at specific time points. In most cases, the physical mechanisms responsible for bringing them in close proximity are still elusive. Here we show that the interaction of DNA loci with a concentration of diffusing molecular factors can induce spontaneously their colocalization, through a mechanism based on a thermodynamic phase transition. We consider up to four DNA loci and different valencies for diffusing molecular factors. In particular, our analysis illustrates that a variety of nontrivial stable spatial configurations is allowed in the system, depending on the details of the molecular factor/DNA binding-sites interaction. Finally, we discuss as a case study an application of our model to the pairing of X chromosome at X inactivation, one of the best-known examples of DNA colocalization. We also speculate on the possible links between X colocalization and inactivation.