That depends on the applied contraints and geometrical considerations.
Consider the formula one uses to determine the bending or torsional stresses or deflections in which the cross-sectional area is a factor. If the constraint is yield stress or maximum deflection, then one can solve for a particular cross-sectional area (and from that, diameter) based on a maximum stress less than or equal to yield stress, or maximum deflection based upon some limit (which could be limited by yield stress or interaction with some other structure).