Nano, I am so sorry that we really can't help much with an identification without some pictures of the critters, or at the very least an improved, more detailed description of them.

Do they move? Have you seen any kind of damage that might be caused by their activity?

It's always a good idea to isolate new plants for a few days and to inspect them frequently. We never know what we're bringing home with the plants.

In the meantime, it would be a good idea to mix up a solution of one part plain rubbing alcohol (isopropyl) to three parts water and use it as a mist....to all parts of the plant, including the underside of the leaves and down into the little folds and rolls. Rubbing alcohol won't injure most plants, and not your dieffenbachia at all, but it will kill soft bodied pests such as aphids, spider mites, mealybugs, and immature scale insects called crawlers.

Spray it on every few days, keeping a watch for any new critter appearances. No need to wash it off, but don't put your plant in the full sun while using it. Not that you would do that to a dieffenbachia, anyway.