We present calculations of the intrinsic vacancy and interstitial diffusivities, D-V and D-I, in silicon using order(N) tight-binding molecular dynamics simulations. Vacancy diffusion was found to occur rapidly, with a diffusivity of around 10(-4) cm(2)/s in the temperature range 900-1200 degrees C. Interstitial diffusion was found to be a factor of 10-100 times slower than vacancy diffusion, being on the order of 10(-5) cm(2)/s for the same temperature range. These diffusivities have the same order of magnitude as previous molecular dynamics calculations performed with both classical and Car-Parrinello models. The interstitial diffusion was found to occur via two different paths, one involving motion of a single interstitial down the open (110) channels in the lattice, and another involving an intermediate [110] split interstitial which facilitates the interstitial crossing from one (110) channel to another. Within the tight-binding model we use, the split interstitial path is more important than drift of a single interstitial at higher temperatures (here, above around 1000 degrees C). The reverse is true below this temperature, with few, if any, formations of split interstitials and a diffusion dominated by traversal down the open channels of the lattice. New LDA data shows that the energetic advantage of the split interstitial over the tetrahedral interstitial is smaller than previously calculated, lending credence to the tight-binding results. The split interstitials were found to be relatively long-lived (in some cases, lifetimes in excess of 15 ps), even in a potential that favors tetrahedral interstitial formation. In order to perform these calculations, we developed a constant N-elec version of the forces in the Goedecker and Colombo O(N) tight-binding algorithm originally written for systems with a constant chemical potential. Omission of this correction can lead to errors approaching 40% in the forces.