The clue is the word central. In central diabetes insipidus the posterior pituitary fails to release vasopressin, so a hormone analogue must be supplied externally. Desmopressin (1-deamino-8-D-arginine vasopressin) fits this requirement perfectly because it is a modified vasopressin molecule engineered for strong V2 receptor action and weak V1 action. Acting on V2 receptors in the collecting duct, it inserts aquaporin water channels and restores water reabsorption, abolishing the excessive dilute urine output. Its prolonged half-life allows convenient intranasal or oral dosing. Now ruling out the rest: Leuprolide is a gonadotropin-releasing hormone agonist with no role in water balance. Thiazide diuretics help only in the NEPHROGENIC form, where the kidney cannot respond to ADH, by reducing distal solute delivery and inducing mild volume contraction; they do nothing for the hormone deficiency of central DI. Insulin is purely a glucose-lowering agent for diabetes mellitus, a completely separate disorder despite the shared word diabetes. Therefore the hormone-replacement agent is the answer. \[\boxed{\text{Desmopressin}}\]