I think it depends to a degree on the DOC and nature of the habit.
After spending 2-3 years on methadone, my libido was fucking insane for about 12 months following cessation of all opioids. Both amazing and fucking horrible (more horrible, as I had a healthy sex drive while using opioids, but things got absolutely uncalled for after getting off).
I think I noticed my libido coming back with a vengeance around day 30-90 of abstinence and then continuing to be uncomfortably high for at least 6-9 more months.
It did balance out again eventually though. Over a year later and it's far more controllable/appropriate. YMMV with the timing. Like CH said, it just takes time.