January Jones Lake Hollywood dog park pregnant hat
January Jones Lake Hollywood dog park pregnant hat

After rumors surfaced that X-Men director Matthew Vaughn (husband to supermodel Claudia Schiffer), could be the daddy of January Jones' baby, Vaughn denied the allegations, according to a Daily Mirror report.

"These rumors are categorically not true. Everything is fine with my marriage but these allegations are deeply hurtful," Vaughn reportedly told a friend.

Meanwhile, Jones is weathering the controversy well ... she hung out with her dog at Hollywood Lake park Saturday, just enjoying the sunny LA weather. She's good at keeping a secret, this woman!

Just watch how she has ABSOLUTELY no problem keeping her mouth shut when we ask about the baby daddy ...