We present a numerical study on the dynamics of imbibition fronts in porous media using a pipe network model. This model quantitatively reproduces the anomalous scaling behavior found in imbibition experiments [Phys. Rev. E 52, 5166 (1995)]. Using simple scaling arguments, we derive a new identity among the scaling exponents in agreement with the experimental results. Typeset using REVT E X 1 Self-ane interfaces are found in a variety of phenomena such as two-phase ow in porous media, thin lm deposition, ame fronts, etc. . In particular, scaling properties of imbibition fronts have been the focus in many experimental studies [2-4]. Static scaling behavior has been suggested to be described by a directed depinning percolation model [2,5-7]. To explain dynamic properties, one need to go beyond local models and properly deal with the eects of long-range coupling through pressure. Much progress has been obtained using theoretical approaches including consideration of capilla..