  Anisotropic colloidal particles exhibit complex dynamics which play a crucial
role in their functionality, transport and phase behaviour. In this work, we
investigate the two-dimensional diffusion of smoothly curved colloidal rods --
also known as colloidal bananas -- as a function of their opening angle,
{\alpha}. We measure the translational and rotational diffusion coefficients of
the particles with opening angles ranging from 0{\deg} (straight rods) to
nearly 360{\deg}(closed rings). In particular, we find that the anisotropic
diffusion of the particles varies non-monotonically with their opening angle
and that the axis of fastest diffusion switches from the long to the short axis
of the particles when {\alpha}>180{\deg}.
  We also find that the rotational diffusion coefficient of nearly closed rings
is approximately an order of magnitude higher than that of straight rods of the
same length. Finally, we show that the experimental results are consistent with
Slender Body Theory, indicating that the dynamical behavior of the particles
arises primarily from their local drag anisotropy. These results highlight the
impact of curvature on the Brownian Motion of elongated colloidal particles,
which must be taken into account when seeking to understand the behaviour of
curved colloidal particles.
