Natural and synthetic materials based on,associating polymers possess diverse mechanical behavior, transport properties and responsiveness to external stimuli. Although much is known about their dynamics on the molecular and macroscopic level, knowledge of self-diffusive dynamics of the network-forming constituents remains limited. Using forced Rayleigh scattering, anomalous self-diffusion is observed in model associating protein hydrogels originating from the interconversion between species that diffuse in both the molecular and associated state. The diffusion can be quantitatively modeled using a two-state model for polymers in the gel, where diffusivity in the associated state is critical to the super diffusive behavior. The dissociation time from bulk rheology measurements was 2-3 orders of magnitude smaller than the one measured by diffusion, because the former characterizes submolecular dissociation dynamics, whereas the latter depicts single protein molecules completely disengaging froth the network. Rheological data also show a sticky Rouse-like relaxation at long times due to collective relaxation of large groups of proteins, suggesting mobility of associated molecules. This study experimentally demonstrates a hierarchy of relaxation processes in associating polymer networks, and it is anticipated that the results can be generalized to other associative systems to better understand the relationship of dynamics among sticky bonds, single molecules, and the entire network.