Passive diffusion occurs without any transmembrane proteins being involved, the molecules cross the lipid bilayer following a concentration gradient (from the highest concentration to the lowest). Small uncharged molecules or hydrophobic ones cross this way (the best example is H2O).
Facilitated transport also involves a concentration gradient, however in this case the molecules cross the cell membrane through specific transmembrane proteins. These facilitate their passage, they are channels for the molecules (e.g. ions, glucose...).
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