Mark Zuckerberg and his new baby, Maxima, are getting along just swimmingly.

The Facebook founder and CEO posted a new photo of his two month old baby girl serenely floating in what appears to be a lake as her billionaire daddy holds her lightly behind her head and looks adoringly into her eyes.

He captioned the photo 'Max's first swim. She loves it!'

Prodigy? Just like dad, it appears that baby Max will be a fast learner and early starter - she's already learning to swim at two months old.

The post has so received almost a million likes and over 21,000 comments.

Pretty little Max is wearing a green striped onesie bathing suit with a red rose on the front. Her hair seems a little longer and her features a bit more defined than in previous photos the proud dad has shared. Baby Max is growing up!

It's unclear if this was truly Max's first swim lesson - as many babies can be taught how to swim very young, although most experts don't recommend it this young - or was just a little floating around safe in dad's hands.

Since Maxima was born, Zuckerberg and his wife, Dr. Priscilla Chan, haven't been shy about sharing pictures of the little girl on - where else? - Facebook.

Zuck has just returned to work after a two month parental leave to spend time with Max - all Facebook employees receive four months paid parental leave.

On January 8, Mark took Max for her first vaccines -proving that he is not going to be an 'anti-vaxx' dad.

He has posted pictures of her getting her first vaccines, celebrating her first New Year's Eve in her daddy's arms, and posing with Star Wars merchandise, including a baby light saber.

There is absolutely no doubt that Zuck is besotted with his little girl - so much so that he and Priscilla vowed to give away 99 percent of their $46billion (in stock) fortune in her honor to charity.

Before her birth, the couple made a time capsule video promising to try to make the world a better place for her and all children. 

'The Force is strong with this one' Zuck captioned this photo of his baby Jedi Max.