Rumer Willis has paid tribute to her father, actor Bruce Willis, as he continues to battle dementia.

The 68-year-old Die Hard star retired from the screen last year as his condition deteriorated further.

He was diagnosed with frontotemporal dementia – a rare and aggressive form of the cognitive disease which affects behaviour, personality, and language – in February this year.

Rumer, 35, took to Instagram today to post a photo of the pair together when she was a baby.

“Really missing my papa today,” the caption read.

In the photo, a shirtless Bruce can be seen smiling as he gazes lovingly at his young daughter.

Glenn Gordon Caron, the creator of Moonlighting – the 1980s comedy drama which helped launch Bruce’s career – last month told the New York Post the actor is “not totally verbal”.

“All those language skills are no longer available to him, and yet he’s still Bruce.”