My Dieffenbachia has white spots on the underside of leaves, which then yellow and drop. I have tried insecticidal soap and soapy water, with no success.
Certified GKH Gardening Expert
Spider Mites are a common pest on a Dieffenbachia, though this could also be Mealybug.
Neem Oil is a good treatment.
Here are some links with more information.