Kristen Stewart
is speaking publicly about her affair with married director Rupert Sanders -- and apologizing to boyfriend Robert Pattinson.

"I'm deeply sorry for the hurt and embarrassment I've caused to those close to me and everyone this has affected. This momentary indiscretion has jeopardized the most important thing in my life, the person I love and respect the most, Rob. I love him, I love him, I'm so sorry," Stewart told PEOPLE on Wednesday.

Rupert just released his own statement as well to the mag, saying "I am utterly distraught about the pain I have caused my family. My beautiful wife and heavenly children are all I have in this world. I love them with all my heart. I am praying that we can get through this together."

The statements come one day after photos surfaced of Stewart and Sanders in a romantic embrace.

People's source claims that the hookup between Kristen, 22, and Rupert, 41, happened only recently. Sanders has two children with wife Liberty Ross.

Stewart and Pattinson, 26, have reportedly been together since shooting the original "Twilight" flick, which came out in 2008, though have never fully gone on record acknowledging the coupling.

Now that Kristen's copped to the affair and apologized publicly, we gotta ask:

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