You might want to try using a paint scraper, dampen the area with soapy water, latex paint is a water based paint and should come off fairly easily. If you can maybe use a pressure washer to remove the real stubborn spots. Be very careful while using the pressure washer since some settings on the washer could chip the concrete
In the paint section, they have some stuff called oops. It is for cleaning up paint spills like this. Dab some on and you should be able to wipe it up a short time later and everything is better. If you are talking of a a large area, you may be able to power wash it, that is, if the base section of the wall is concrete
Have you tried using gasoline, that usually works but depends on what you want to get it off of. I don't suggest you put gas on carpet.
Use a low power pressure washer. 1500 to 2200 psi, with a fan tip. Be cautious and work in the least obvious area first to determine how close you need to bring the tip to the surface to lift the splatter without marking the concrete.