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Katy Perry is apparently kind of, sort of dating rapper Riff Raff (according to him).

The two did the whole shebang... Sushi. Bowling. Drinks.

He's totally smitten, and she "regrammed" his Instagram post of the "date"-- But can you honestly picture these two together?

Here's what Riff Raff had to say... (only watch if you're cool with him caressing that chick's butt...


Post by TMZ.

We'd LOVE to hear Katy's side of this whole thing.