Would the word happen to be diffuse? I have tried imbibtion but that word is invalid because it isn't specific to osmosis.
This is not imbibition, as water molecules don't get absorbed in the semipermeable membranes commonly found in biological structures like Membrane around cells and cellular organelles (I took this example as you asked it in Biology forum). The water molecules pass through biological membranes via protein channels, that may be an active, secondarily active or passive process. Percolation and permeation are also inappropriate.
If the membrane doesn't hinder a particular solvent it can be said to be permeable to that solvent (e.g. Permeable to water etc.). "Osmosis" is also applicable. As osmosis is only a type of diffusion, you can use the term 'diffusion', but it would be too broad or generalized.
I am not quite sure what you are looking for but maybe the term
passive transport will satisfy your needs although it is not specific to water.
Passive Transport is a movement of biochemicals and other atomic or molecular substances across cell membranes without need of energy input. Unlike active transport, it does not require an input of cellular energy because it is instead driven by the tendency of the system to grow in entropy.