As Kate Middleton continues to deal with the fallout from her photo scandal -- Prince William is just ... well, being a Royal and doing Royal things.

The Prince of Wales was out and about Monday at Frameless London -- a multi-sensory experience tourist attraction with a bunch of cool art exhibitions -- where he was hobnobbing with folks for something called Earthshot Prize Launchpad ... a climate change initiative.

PW spoke during the event ... and he was seen chopping it up with environmentalists. Photos of his outing here were posted to his and Kate's official Royal social media account too.

The problem ... everybody around the world is only focused on one thing as it pertains to William and Kate -- and that would be this edited photo they posted over the weekend, which has now been revealed to be altered ... something Kate herself took the blame for.

There's a fresh round of conspiracy theories all over social media ... and despite this frenzy over her whereabouts and condition, Bill's out here just carrying on like nothing's happening.

Even before his climate event, William showed up for a Commonwealth service alongside Queen Camilla -- and there, too, he looked like nothing was amiss ... just business as usual.

As William was arriving at the latter event ... he and Kate were actually snapped in the car heading on over from Windsor, but Kate was turned to the side -- looking out a window.

Of course, with her admitting that she edited her Mother's Day photo ... there's more speculation and intrigue than ever before ... this after she's been out of the public eye for months now, with mounting concern over her well-being.

Kensington Palace has refused to comment further on what exactly Kate altered in the picture, and how -- but a lot of people have taken educated guesses on what she did.