How did Kant distinguish free beauty from beauty that depends on a concept of an object?

In his Critique of Judgment (1790), Immanuel Kant distinguished between two types of beauty based on their relationship to concepts and purpose:

• Free Beauty (pulchritudo vaga): This is "pure" beauty, where the judgment of taste is not based on any concept of what the object is or what it is intended to be. Kant famously cited a flower as an example, noting that even a botanist, who understands the flower's reproductive function, ignores this "natural purpose" when judging its beauty through taste.1
• Dependent Beauty (pulchritudo adhaerens): This beauty depends on a concept of the object’s purpose (Zweck) or design (Absicht). Kant classified architecture as a form of dependent beauty, arguing that in such objects, regularity and symmetry must express the unity of the intuition that accompanies the concept of the object's function.1

For Kant, the distinction hinges on whether the aesthetic experience is entirely free from conceptual constraints or if it is mediated by the understanding of an object's intended use or nature.1