Please correct any misunderstandings I may have in the following:
* Vacuum has no mass (gravitational attraction).
* Normal matter has mass.
* Vacuum is composed of matter and antimatter.
* Therefore, antimatter has negative mass (negative gravitational attraction).
Its tricky to answer, as I am limited to browsing wikipedia pages on these topics and no more knowledgeable than you are on the topic :-). One obvious alternative to your line of thinking is that the matter+anti-matter that is created in a vacuum is not 'normal' (using your position on normal matter), and has no mass.
It seems to have something to do with normally existing only for a very short time, and affecting the universe only on a very short range that these virtual particles get away with appearing to not having a mass from the point of view of the rest of the universe.
http://en.wikipedia.org/wiki/Virtual_particles
* Vacuum has no mass (gravitational attraction). * Normal matter has mass. * Vacuum is composed of matter and antimatter. * Therefore, antimatter has negative mass (negative gravitational attraction).