There were unsubstantiated rumors that she and Ozu were lovers; he had spent most of his adult life — after returning from the second World War — looking after his mother.
There are also rumors, rather more substantiated, that Ozu was gay. (He was kicked out of school for writing a love letter to another boy. No Ozu scholars seem to deny the writing of the letter, although some dismiss it as a mere joke, and some gloss over its import in writings on Ozu, simply calling it a scandalous letter.) Setsuko Hara is rumored to have been a lesbian, although I'm not aware of any backup for this other than her never marrying.