Lady Gaga's Star-Studded Birthday Celebration

Lady Gaga stepped deeper into her dirty 30s by cleaning up real good -- dressing to the nines and looking chic for her 31st birthday bash.

Gaga headed to dinner at Gjelina in Venice Tuesday for the star-studded event.

Elton John and Johnny Depp joined in ... even if a little underdressed compared to the bday girl.