Synaptic conductances are influenced markedly by the geometry of the space surrounding the synapse since the transient glutamate concentration in the synaptic cleft is determined by this geometry. Our paper is an attempt to understand the reasons for slow glutamate diffusion in the cerebellar glomerulus, a structure situated around the enlarged mossy fiber terminal in the cerebellum and surrounded by a glial sheath. For this purpose, analytical expressions for glutamate diffusion in the glomerulus were considered in models with two-, three-, and fractional two-three-dimensional (2D-3D) geometry with an absorbing boundary. The time course of average glutamate concentration in the synaptic cleft of the mossy fiber-granule cell connection was calculated for both direct release of glutamate from the same synaptic unit, and for cumulative spillover of glutamate from neighboring release sites. Several kinetic schemes were examined, and the parameters of the diffusion models were estimated by identifying theoretical activation of AMPA receptors with direct release and spillover components of published experimental AMPA receptor-mediated EPSCs. For model selection, the correspondence of simulated paired-pulse ratio and EPSC increase after prevention of desensitization to experimental values were also taken into consideration. Our results suggest at least a 7- to 10-fold lower apparent diffusion coefficient of glutamate in the porous medium of the glomerulus than in water. The modeling of glutamate diffusion in the 2D-3D geometry gives the best fit of experimental EPSCs. We show that it could be only partly explained by normal diffusion of glutamate in the complex geometry of the glomerulus. We assume that anomalous diffusion of glutamate occurs in the glomerulus. A good match of experimental estimations and theoretical parameters, obtained in the simulations that use an approximation of anomalous diffusion by a solution for fractional Brownian motion, confirms our assumption.