By biological diffusion, I believe you mean diffusion across a biological membrane. Diffusion is the movement of substances across a gradient, from lower concentration to higher concentration. An example of such biological diffusion is the transport of molecules across the cell membrane. The semi-permeable cell membrane allows the entry of only small or hydrophobic molecules through direct transport (or passive transport, which requires no energy input). Other molecules may enter the cell by diffusion but at the expense of energy from the cell (active transport). Another example of biological diffusion is the transport of oxygen in our body. The red blood cells in our blood receive oxygen, through diffusion, at alveoli and transport it throughout our body. It is also at alveoli that carbon dioxide, generated during cellular respiration, diffuses out.
Hope this helps.