Kardashian and Davidson enjoyed pizza at Jon & Vinny's Fairfax, then went to Rite Aid to pick up some Thrifty's ice cream and head home. The release of the photos is interestingly timed, though: One night later, Kardashian's ex Kanye West was photographed kissing his new love interest Julia Fox by paparazzi in Los Angeles, too.

A source close to Kardashian and West told Peoplelast week that West hasn't given up on his dream of reconciling with Kardashian. “He's still telling people that he wants to have Kim back and he is willing to make appropriate changes to do so,” that source said.

Kardashian isn't interested, though. A source told Entertainment Tonighton Jan. 10 that Kardashian is actually very, very into her new boyfriend. “Kim has such a great time with Pete. He makes her laugh, plays around and has a sense of humor,” the source said.

“It is nice for Kim to be around that,” the source added. “Pete knows how to talk to Kim. He is the most confident guy, but not cocky. It is why it works with them. Kim thinks Pete is super sexy and likes how he knows so much about comedy, since that is a world she doesn't know as much about.”