All these are processes that allow cells to transport materials into and out of the cell's internal environment. Diffusion is thought of as a natural process that distributes concentrations of a substance equally throughout the containment area, in this case, within the cell membrane. The best example of this is the process of osmosis, which is diffusion by water. Water will diffuse out of the cell, if the environment outside the cell is not equal to the environment inside the cell. The reverse will occur if the conditions are reversed.
Passive transport is a process that allows larger molecules to go across the cell membrane, usually larger molecules than water molecules. Again, the word "passive" implies no energy is needed to get this process to go, so the molecules will go from a greater concentration to a lesser concentration, in an attempt to equalize the concentrations. Passive transport is the same thing as facilitated diffusion.
Active transport, as the name implies, requires energy. It is going against the norm, moving molecules from a lower concentration to a higher concentration. These molecules are generally larger than water molecules, and pass through special "doorway" portals within the cell membrane.