Ammonia gas diffuses through air because the molecules are lighter than air.
The lighter (smaller) particles move more quickly than heavier (larger) ones at the same temperature.
For example, If we mix ammonia gas (NH₃) and hydrogen chloride gas (HCl), ammonia gas will travel faster because it is ligher, has smaller molar mass:
M(NH₃) = 17 g/mol.
M(HCl) = 36.45 g/mol.