abiotic stresses such as over-fertilization, high

soluble salts, lack of water. The plant may need repotting. When plants are pot bound, water tends to run down the sides of the interior of the pot and not get to the interior of the root ball.  Also check to make sure that the leaf with browning is not situated in a spot that gets drying breezes from a heat duct or air conditioning duct.  It can also be caused by being too close to a light fixture.  Yet another possibility is root damage.
 Diffenbachia drop their oldest leaves and this is normal for them. Lower leaf drop is increased by abioitic stresses as listed previously. Lower leaf drop also can be increased by insufficient light.   As diffenbachia ages and the lower leaves fall off people commonly cut off the top portion and repot. http://www.hort.purdue.edu/ext/ho-37web.html