A dish treating appliance for treating dishes according to an automatic cycle of operation and including a tub at least partially defining a treating chamber receiving dishes for treatment according to the automatic cycle of operation, multiple sprayers emitting a liquid into the treating chamber, and a diverter valve having a manifold defining a plenum with an inlet and multiple outlets and a membrane movably mounted within the plenum and having at least one through opening, which is sequentially aligned with the multiple outlets upon movement of the membrane.