We develop the theory of collective modes supported by a Fermi liquid of electrons in pristine graphene. Under reasonable assumptions regarding the electron-electron interaction, all the modes but the plasmon are overdamped. In addition to the SU(2)-symmetric spin mode, these include also the valley imbalance modes obeying a U(1) symmetry, and a U(2)-symmetric valley spin imbalance mode. We derive the interactions and diffusion constants characterizing the overdamped modes. The corresponding relaxation rates set fundamental constraints on graphene valley- and spintronics applications.