A diagnostic subroutine was a type of subroutine.
In 2372, while downloading data for a subspace tensor matrix into the main computer of the USS Defiant, a problem with the diagnostic subroutines caused a calibration drift in the backup navigation program. (DS9: "Rejoined")
In the 2378 holonovel set aboard the fictional USS Vortex, Kymble worried that deleting non-essential subroutines of the EMH could accidentally delete some of his diagnostic subroutines as well. (VOY: "Author, Author")