Titus suggested they marry, Domitian declined .... then they lived together after Titus' death.
Domitian's love life was, to say the least, messy. Dio 67.3:
He planned to put his wife, Domitia, to death on the ground of adultery, but having been dissuaded by Ursus, he divorced her, after murdering Paris, the actor, in the middle of the street because of her. And when many persons paid honour to that spot with flowers and ointments, he ordered that they, too, should be slain. 2 After this he lived with his own niece (Julia, that is to say) as husband with wife, making little effort at concealment. Then upon the demands of the people he became reconciled with Domitia, but continued his relations with Julia none the less.Julia seems to have died as a result of a pregnancy (AD 91), after which she was deified, and her ashes placed in the temple of the deified Flavians. Domitian was later buried with her. Suetonius, Domitian 17.3:
but his ashes she secretly carried to the temple of the Flavian family and mingled them with those of Julia, daughter of Titus, whom she had also reared.I wanted to post this amazing image of her to remind people that sometimes portraits survive in mediums other than busts and coins. [BNF, source]. For busts and statues of her, see here.