Plumes and gravity currents are primarily-vertical and primarily-horizontal flows, respectively, driven due to buoyancy/density differences between two fluids. In porous media, such flows occur at various instances like during carbon sequestration, geothermal energy recovery etc. While in general the density-driven flows result in mixing between the fluids due to molecular diffusion, in porous media, especially at high Peclet number regimes, the mixing gets enhanced by mechanical dispersion, which in turn is caused due to tortuous paths. We examine the effects of mechanical dispersion on the porous media plumes and gravity currents. We derive new similarity solutions and show that the differences in mixing are quite significant compared to that of molecular diffusion models or with no-mixing models. The results are also verified using laboratory experiments.