The state consensus problem among groups of linear parameter-varying (LPV) systems is addressed. The systems are assumed to have an identical LPV structure. We consider both homogeneous groups, where the time-varying parameters are identical, and heterogeneous groups, where the parameters can be different for all agents. Motivated by relative sensing we assume static, possibly parameter-varying, diffusive couplings between neighboring agents. We provide necessary and sufficient conditions for state consensus and, in the homogeneous case, present design procedures for the coupling gains based on linear matrix inequalities.