Sources close to the couple tell TMZ ... it's NOT a coincidence Duff filed her docs a day after the Daily Mail reported Mike was drunkenly propositioning women at Mastro's steakhouse in Bev Hills.
Hilary -- who hired attorney Laura Wasser -- cites the usual irreconcilable differences as the reason for divorce. She lists the date of separation as January 2013.
In the docs, Hilary asks for primary physical custody of their son, Luca, who turns 3 next month. She wants Mike to have visitation, but sources connected with the couple say she's concerned that his partying and drinking could adversely affect their kid.
The couple has a prenup, but neither spouse is struggling in the money department. Hilary wants her earnings and other stuff to remain her stuff.
Hilary and her NHL star husband were married in 2010 and when they split Hilary's mom, Susan, said, "They're better friends than a married couple."
Since their split they have been seen together from time to time, but now it's pretty clearly over and out.