Answer: The only disease problem associated with dieffenbachia is root rot, caused by over-watering. It is normal for the lower leaves to curl and die; as the plant matures, it will shed some of the older leaves in favor of new, young foliage. If the newer leaves are also exhibiting this problem, you may be over-watering, the plant is in a draft (from air conditioning vents), or the indoor air is too dry. Move the plant to a more protected place if necessary, and increase humidity by misting the plant each morning. The only other possibility is an insect problem. While insects aren't a constant problem, they do occasionally get mealy bugs and spider mites. Mealy bugs can be removed with a cotton swab dipped into rubbing alcohol and spider mites should be treated by spraying with insecticidal soap or pyrethrins.
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