A multiscale analysis of the spatially averaged velocity of an imbibition front Vl measured at scale l reveals that the slow front dynamics is intermittent: the distributions of increments ΔVl(τ) evolve continuously through time scales τ, from heavy-tailed to Gaussian¿reached at a time lag τc set by the extent of the medium heterogeneities. Intermittency results from capillary bursts triggered from the smallest scale of the disorder up to the scale lc at which viscous dissipation becomes dominant. The effective number of degrees of freedom of the front l/lc controls its intensity.