Diffusion is definitely not sufficient--natural convection is usually sufficient to do this on earth, but gravity is a requirement for most natural air convection.
Interestingly, a surprisingly large percentage of a spacecraft's power draw is spent just on air circulation (other conditioning adds as well).
I think it’s more about local pockets over temporally short periods of time. Gravity probably plays a role in kicking off the dispersion process by moving them from their initial place of production (where you exhale) so it doesn’t just cluster there.
Gravity definitely plays a role in convection, which is the main form of dispersion. The air one exhales has different composition — more CO2, more water — which means it has different buoyancy. Usually, this means the parcel of air rises here on Earth, but falling of your face is fine too. No gravity means no convection. Without wind to cause turbulence, mixing is really slow, leaving molecular diffusion as the only process. Remember, that’s random, and CO2 will still accumulate near the point source with a Gaussian distribution.