Diabetic hospitalized for cellulitus. how long before an improvement?

Hospitalized patient: There are so many factors involved in this. Depends on how severe the infection is, other medical problems, blood sugar control, where the infection is and how good the blood supply is to that area. Also since the person is hospitalized best perso to ask is the attending physician.

Hard to say: Varies with severity, and with individual. Often will see slight improvement in a day or two, but usually the order of week or more for resolution, assuming there is no deeper component of abscess etc, and assuming appropriate antibiotics etc.

What's the cause: Cellulitis is basically a visible inflammation (itis) of the skin and soft tissues (red, hot, swollen and tender) . It can be caused by many things including sunburn (radiation), trauma (sprained ankle) or poor vein circulation (stasis dermatitis). It need not be caused by bacteria. If you have repeated episodes of this, get to a wound care or vascular specialist, the diagnoses you have is wrong.