There is a mistaken belief that Dionysus is a fat drunk. When, in fact, in all the original stories he was incredibly good looking and strong. He was so good looking in fact that a bunch of sailors thought he was royalty and tried to kidnap him for a ransom. Which he apparently found incredibly amusing right up until he drove them mad so that they all jumped into the ocean.
What people are probably thinking of is Silenus, who was a happy fat old man who rode a donkey around because he was too drunk to walk. He was Dionysus’ teacher.