Bruce Willis' Family 'Closer Than Ever' amid FTD Diagnosis: They're Making 'Positive Memories' (Source)

The bond in Bruce Willis' brood continues to strengthen after his diagnosis of frontotemporal dementia.

A source tells PEOPLE that the Sixth Sense actor's family "is all closer than ever" amid news of his FTD diagnosis, which they announced on Thursday.

And Bruce's wife of 13 years, Emma Heming Willis, "has the biggest support system" that "she couldn't be more grateful" for, adds the source.

Part of that system includes all the women closest to Bruce: Emma, 44, his ex-wife Demi Moore and their children: Mabel, 10, and Evelyn, 8, whom he shares with Emma, plus his three daughters with Moore, 60: Rumer Willis, 34, Scout Willis, 31, and Tallulah Willis, 29.

"She is trying to make as many positive memories for them as she can," the source says of Emma's efforts with Mabel and Evelyn. "She wants them to remember Bruce as an amazing, fun dad. She wants them to have the best memories of him."

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In the family's statement on Thursday, they wrote in part about Bruce, 67, "Since we announced Bruce's diagnosis of aphasia in spring 2022, Bruce's condition has progressed and we now have a more specific diagnosis: frontotemporal dementia (known as FTD)."

"Unfortunately, challenges with communication are just one symptom of the disease Bruce faces. While this is painful, it is a relief to finally have a clear diagnosis," they continued.

The family added in their full statement, "Bruce always believed in using his voice in the world to help others, and to raise awareness about important issues both publicly and privately. We know in our hearts that – if he could today — he would want to respond by bringing global attention and a connectedness with those who are also dealing with this debilitating disease and how it impacts so many individuals and their families."

Demi Moore/instagram Bruce Willis and family

"Bruce has always found joy in life — and has helped everyone he knows to do the same," they continued. "It has meant the world to see that sense of care echoed back to him and to all of us. We have been so moved by the love you have all shared for our dear husband, father, and friend during this difficult time."

"Your continued compassion, understanding, and respect will enable us to help Bruce live as full a life as possible," they concluded, singing off, "Emma, Demi, Rumer, Scout, Tallulah, Mabel and Evelyn."

Bruce's blended family has been tight-knit over the years, and open about their support for the actor since revealing his original diagnosis and subsequent decision to retire from acting.

And the Die Hard star will soon become a grandparent for the first time, as his oldest daughter Rumer is expecting her first baby with boyfriend Derek Richard Thomas.

A source close to the family told PEOPLE in December that Bruce is "happy" about his impending new role. "He is happy about becoming a grandpa," the insider said. "He loves having a big family. They are all spending Christmas together."

"Bruce is enjoying not working and having more family time. He likes being around his girls more," added the source.