Pete Davidson and Kim Kardashian really aren't hiding their new romance anymore. The Daily Mail ran photos last night of the two out together on Sunday, with what appears to be a hickey very visible on Davidson's neck. Kardashian, meanwhile, wore a turtleneck, so it's unclear whether she had her own or if Davidson was the only recipient. The two had dinner together at Giorgio Baldi in Santa Monica.

Kardashian and Davidson's surprise new relationship was confirmed last week. Davidson is the first person Kardashian had publicly dated since she filed for divorce from Kanye West in February.

A source told E! of their dynamic, “They are really happy and seeing where it goes. Pete has told her he doesn't want to see anyone else. She is telling some people they aren't super serious but she isn't seeing anyone else... She's trying to not make a big deal about it but is super into him. Kim is smitten over him and it's very exciting to her.”

The energy between her and Davidson is light, and Kardashian is “giddy” around him, E!'s source added: “He makes her laugh the entire time they are together and she is completely enthralled by him.”

The two are taking turns seeing each other, as Kardashian lives in California and Davidson lives in New York. “They are making the distance work and have plans to continue seeing each other,” the source said.

Page Six was told by its own source that Kardashian and Davidson really want to keep their relationship more private—for Kardashian standards, anyway—days before the hickey paparazzi photo surfaced.

“[They] want to keep it as private and low-key as possible,” Page Six's source said. “They’re still getting to know each other, and want as little pressure as possible. They’re trying to keep it under wraps.”

Davidson and Kardashian haven't labeled their relationship either: “They’re dating. There’s no formal title,” Page Six's source said. “They’re dating and getting to know each other—still figuring it out.”