What is the difference between fusion, diffusion and osmosis?

Fusion has nothing to do with the processes of diffusion and osmosis.

Explanation:

Let's go with diffusion and osmosis.

Diffusion is the net movement of a substance from a region of higher concentration to a region of lower concentration down a concentration gradient. Diffusion can occur with and without a membrane.

Osmosis is the net movement of water $\left({H}_{2} O\right)$ molecules from a region of less negative water potential to a region of more negative water potential down a water potential gradient through a membrane.

Fusion may refer to a lot of things. Here are the more common things that fusion refers to.
Fusion may refer to two similarly structured items bonding together under certain circumstances, or may refer to interactions between atoms under the influence of the four fundamental forces. It may also refer to nuclear fusion.