There are no visible watermarks, but model makers can use steganographic codes to identify outputs from their own models.

Text-to-Image Models Leave Identifiable Signatures: Implications for Leaderboard Security

https://arxiv.org/pdf/2510.06525

This is true, however LMArena does employ some methods to mitigate attempts to manipulate the leaderboard, see https://openreview.net/forum?id=zf9zwCRKyP

They also control for style https://news.lmarena.ai/sentiment-control/