Pete Davidson drives Kate Beckinsale and her mom Judy Loe to dinner

Their relationship has been moving along quickly.

But things might have kicked up another gear for Pete Davidson, 25, and Kate Beckinsale, 45, with the Saturday Night Live funnyman seen driving the screen beauty and her mother, Judy Loe, to dinner at LA's exclusive Nobu restaurant on Tuesday.

They were joined by Kate's stepfather Roy Battersby, on what was the 40th anniversary of the passing of the actress' late father, Richard Beckinsale.  

Pearl Harbor star Kate was her usual radiant self for the outing, made up with nude lip and dark eyeliner.

Her wavy brunette tresses fell in glorious waves across her shoulders.

The man she has been linked with since February wore a colorful sweater for the dinner date with his girlfriend's mom. 

Kate Beckinsale has paid tribute to her late father Richard on the 40th anniversary of the Porridge star's death.

The actress posted a montage of childhood images to her Instagram page on Tuesday, leading an outpouring of remembrance for the talented actor, who passed away on March 19, 1979 at the age of just 31.

Kate, who was just five when she lost her father, wrote alongside the black and white shots: '40 years is a lot of missing. Thank you so much to everyone who has been kind. Lots of love xx #march19.'  

Richard Beckinsale was one of the stars of classic British sitcoms Porridge and Rising Damp, acting alongside comedy legends Ronnie Barker and Frances de la Tour.

He died in his sleep - survived by Kate, her mother Judy Loe and her older sister Samantha - from a heart attack, which was later revealed to be a congenital defect.

He reportedly complained of pains in his arms and chest the night before, but dismissed it.  

Fans of Kate's and her father's work replied to the post with fond words. One wrote: 'Your dad went far to early....i loved watching him on tv, he made me laugh so much,he would be very proud of you kate!! [sic]' 

Another echoed this sentiment: 'Couldn't imagine leaving my daughter at 5yrs old. Keep his memory alive and I'm sure he's proud of you [sic].'

Another wrote, 'Richard was brilliant taken too soon r.I.p. [sic],' as another penned, 'He’s a legend! One of the finest comic actors of the 1970’s [sic]'.

Director Stephen Frears told The Mirror: 'He was adorable - a wonderful actor and a very nice man. I was looking forward to directing him in future films. 

'I think he would have gone on to be a movie star. He was very good-looking. He had it all.'

Rising Damp co-star Don Warrington told The Express: 'He was a very fine actor who could turn his hand to anything. The trajectory of his career was upwards. He was a great loss.'