It is generally believed that collisions of particles reduce the self-diffusion coefficient. In this work we show that in odd-diffusive systems, which are characterized by diffusion tensors with antisymmetric elements, collisions surprisingly can enhance the self-diffusion. In these systems, due to an inherent curving effect, the motion of particles is facilitated, instead of hindered by collisions leading to a mutual rolling effect. Using a geometric model, we analytically predict the enhancement of the self-diffusion coefficient with increasing density. The physical interpretation is quantitatively supported by the force-autocorrelation function, which turns negative with increasing odd-diffusivity. We validate our findings by many body Brownian dynamics simulations in dilute systems.