The displacement of fluids through porous rocks is fundamental for the recharge of geothermal and hydrocarbon reservoirs <Grant et al., 1982; Lake, 1989>, for contaminant dispersal through the groundwater <Bear, 1972> and in controlling mineral reactions in permeable rocks <Phillips, 1991>. In many cases, the buoyancy force associated with density differences between the formation fluid and the displacing fluid controls the rate and pattern of flow through the permeable rock <Phillips, 1991; Barenblatt, 1996; Turcotte and Schubert, 2002>. Here, using new laboratory experiments, we establish that a striking range of different flow patterns may develop depending on whether this density contrast is associated with differences in temperature and/or composition between the two fluids. Owing to the effects of thermal inertia in a porous rock, thermal fronts lag behind compositional fronts <Woods and Fitzgerald, 1993; Turcotte and Schubert, 2002>, so that two zones of different density develop in the region flooded with injected fluid. This can lead to increasing, decreasing or even reversing buoyancy in the injected liquid; in the latter case it may then form a double-flood front, spreading along both the upper and lower boundary of the rock. Recognition of these different flow regimes is key for predicting sweep efficiency and dispersal patterns in natural and engineered flows, and offers new opportunities for the enhanced recovery of natural resources in porous rocks.