Why does oxygen diffusion from the alveolus to the alveolar capillary occur?

Diffusion (of anything) occurs because of a concentration gradient meaning there is more oxygen in one place than another.

Alveolus when you inhale will have a higher concentration of oxygen that that of the alveolar capillary resulting in a concentration gradient, this causing diffusion to occur until equilibrium is met.

This means more oxygen in alveolus so oxygen travels into the alveolar capillary until a balanced amount of oxygen is in both places, but then of course the oxygen is transported and you exhale and inhale so the process repeats.