The current paradigm of self-propelled motion of liquid droplets on surfaces with chemical or topographical wetting gradients is always mono-directional. In contrast, here, we demonstrate bidirectional droplet motion, which we realize using liquid infused surfaces with topographical gradients. The deposited droplet can move either toward the denser or the sparser solid fraction area. We rigorously validate the bidirectional phenomenon using various combinations of droplets and lubricants, and different forms of structural/topographical gradients, by employing both lattice Boltzmann simulations and experiments. We also present a simple and physically intuitive analytical theory that explains the origin of the bidirectional motion. The key factor determining the direction of motion is the wettability difference of the droplet on the solid surface and on the lubricant film.