Not knowing a whole lot about paint formulations, I offer the following: paint is a suspension, not a simple solution. Typically it is a suspension of various inorganic colorants in either an organic or aqueous-based binding matrix (a binder dissolved in a solvent that evaporates after you slather it onto a wall or canvas). It also includes a whole bunch of other substances, like stabilizers, UV protectants, biocidal agents, and etc. The pigments themselves are typically granular solids that are insoluble in the host solvent. As such, they do settle to the bottom of the paint can over time. However this doesn't necessarily mean that you can easily decant the rest of the paint components off of the solid pigments, because other chemicals in the paint may also co-settle or otherwise be irreversibly bound to the inorganic colorants that settle off. Also, white is also an inorganic pigment, so you couldn't remake "white paint" by this procedure anyway. You'd be left with some kind of semi-transparent goop that probably wouldn't function well as a paint even if you added new pigments to them.
You haven't specified WHY you want to do this, but speculating that you maybe intend to recolor your paint, it's probably far easier and less expensive just to buy new paint.