On a beautiful Sunday afternoon, Charlie Sheen -- puffing away on a cigarette, despite his HIV-positive status -- hung out in Malibu at the exact same time we spotted Denise Richards out and about with the former couple's two kids, Sam and Lola. But yet their paths didn't cross and we're pretty sure that was intentional.

Back in January, Sheen reportedly cut off Denise and the kids and withdrew his offer to move them into a home he purchased for them in Mulholland Estates, where he lives. Denise was getting a reported $55K/month in child support and Charlie had been funneling tax-free cash to Richards over the years, but when something went wrong with these two right after the new year, Charlie decided to cut the cash and go off on a major rant against Denise and the girls.

Well apparently the two haven't repaired their relationship because when Sheen went on a rare outing to Malibu yesterday, he didn't even stop by Denise's beach rental to see the kids. He didn't meet up with them for lunch, take Sam and Lola shopping, give them a kiss on the cheek -- nothing!

Seems a guy in his state of health might want to make things right with his exes and his kids ... but maybe Charlie "That's Epic" Sheen doesn't give a sh*t. Too bad!

Before Denise stepped out with her daughters, we spotted the actress with a male companion, and she seemed to be in a way better mood. Could the ponytailed boho be a new romantic interest?