of, pertaining to, or characteristic of a prophet.
"Yeeeeessss, YEEEESSSS!" cried Professor Trelawney. "Mr. Potter has indeed a most vatic glow about his face; see how his eyes glaze over when staring into the crystal ball.... Mr. Weasley, what ARE you sniggering at?"
1. very sheer and light; almost completely transparent or translucent.
2. delicately hazy.
As it happened, Mr. Potter was actually steadily drifting to sleep as he stared blankly into his diaphanous crystal ball. Needless to say, this is what so amused Mr. Weasley and what ultimately caused Professor Trelawney to give them both detention.