Did Adam descend to Earth naked?

It appears that Adam and Eve, peace be upon them, after eating from the tree, covered their private parts with the leaves of the Garden's trees, and descended to Earth in that state. The verse, "So when they tasted the tree, their private parts became apparent to them, and they began to fasten over themselves from the leaves of Paradise," indicates this. Commentators have mentioned that their clothing was light that covered their private parts, and when they ate from the tree, their private parts became apparent, so they began to fasten over themselves with the leaves of Paradise like a garment. Some also said that the light that covered them diminished, so they took fig leaves to cover themselves with. In the verse, there is evidence of the ugliness of exposing one's private parts and the obligation to cover them.