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Diffusion is the passive movement of substances down their concentration gradients, requiring no expenditure of cellular energy. The rate to cross the membrane depends mostly on the molecule's relative hydrophobicity. The more lipid soluble and non-polar the molecules are, the more readily they will diffuse.
This includes small gases, oxygen and carbon dioxide, as well as larger substances like vitamins. Other uncharged but polar molecules, such as water, and larger ones, like glucose, will pass through, although at a much slower rate. In contrast, charged ions, no matter their size, and non-lipid soluble proteins are repelled by the lipid bilayer and require other mechanisms to cross. 
Following diffusion, particles will continue to move from one side to the other due to random motion but at a constant exchange rate with no net movement to achieve dynamic equilibrium.