The unstable fluid–fluid displacement patterns in porous media with rough invasion fronts and trapping of the defending phase are often observed in drainage, i.e. when the solid is non-wetting to the invading phase. On the other hand, during imbibition, compact and faceted growth is expected in regular porous media with geometrically homogeneous pore structure. Here, we report the irregular growth of invading fluid during the imbibition process in two-dimensional regular porous media. The ramified invasion morphology associated with thin fingers is reminiscent of capillary fingering. Through examining the capillary pressure signals and the type of pore-scale invasion mechanisms, the fundamental differences between faceted growth and irregular invasion are revealed. By analysing the pore-scale invasion mechanisms, a phase diagram describing the dominance of different invasion events is proposed. Through conducting systematic quasi-static radial injection simulations across a wide range of porosity and wettability, excellent agreement is observed on the transition boundary from faceted and compact displacement patterns to irregular and dendritic invasion morphologies. This is reflected by the overlap of the transition boundaries from analytical prediction, type of pore-scale invasion events, and macroscopic morphology quantified by the fractal dimension. This work provides new insights on the role of geometrical features of solid structures during multiphase flow with emphasis on the porosity and wettability. The findings could assist in guiding the design of microfluidic devices to control deterministically the multiphase flow, transport and reaction processes.