Two vortices of opposite sign in two dimensions merely move along parallel lines. We show that even a small buoyancy completely changes this dynamics. When the vortices are of different density from their surroundings, buoyancy produces a lateral drift by Kutta lift. This causes the density patches to merge, and the vortex dipole to collapse. This is followed by a rapid upward (for light vortices) ejection and creation of small-scale structures by baroclinic torque. Our simple analytical equation explains the trajectory of the vortices. We show that these events occur in viscous simulations of many buoyant vortices. © 2017 American Physical Society.