Charlie and Denise -- Love Is a Crazy Thing

It's the modern day version of, "She loves me, she loves me not" ...

One day, Charlie Sheen and Denise Richards hate each other ... the next day they're arm in arm and dining together ... like last night, when they hit Da Tommaso in NYC.

As we have reported over time, Denise has gone through periods where she couldn't stand Charlie's guts, feeling he was compromising their kids and making her life a living hell.

Charlie says he's a changed man ... and judging by the HUGE smiles on their faces, it seems, Denise believes him ... for now.

11:45 AM PST: A source close to the couple tells TMZ ... Charlie and Denise didn't plan to be in NY together ... but both happened to be in town on business ... and figured they'd get a bite to eat while there.

Denise flew in to shoot a guest spot on “30 Rock,” and Charlie is out pitching his new show “Anger Management.”