His diary? Do you mean the jottings Willett finds in the room where the powder and instruments for using it are found within the circles? Unless I'm mistaken, those jottings are the responses given by whatever being it is which Curwen is questioning when he is "called away" to the asylum, not Curwen's own thoughts and experiences.
As to who it is that Curwen has raised (not what, in this case), Lovecraft doesn't specify, but as he and his cohorts had been raising the great thinkers and wizards of the ages, it is likely some famous long-dead mage that he was "grilling" (or at least threatening to torture) for information. Given that Lovecraft makes a sly mention of "Eliphas Levi", I'd say it's a safe bet he's hinting at said mage being Apollonius of Tyana, who has long had a reputation among occultists (and writers of occult literature or supernatural fiction) as a seer and sorcerer. As for why I think this is the case, consider the following, from his
Supernatural Horror in Literature, on the subject of Bulwer's
A Strange Story (1862):
-- The Annotated Supernatural Horror in Literature, p. 37
This would also jibe with the rather vague description muttered by Willett as he recovers, as well as the robes and such mentioned, and Lovecraft's choice of the Greek vessels for his description of sorcerous implements in the scene (even though in the novel their use was not restricted to this single case).