Jean-Marc Vallée's Sons Say Late Director Was a 'Generous Man' and 'Wanted to Live a Long Life'

Jean-Marc Vallée's family is remembering the filmmaker one week after his untimely death.

The 58-year-old director — known for movies like Dallas Buyers Club and Wild plus television series like Big Little Lies and Sharp Objects — died on Christmas Day, Dec. 25, at his cabin outside Quebec City.

His sons Alex and Émile said in a statement, obtained by PEOPLE Friday, that their dad "wanted to live a long life."

"Our father was a generous man, deeply human and who lived life to its fullest. He wanted to live a long life and was working on major projects. He was a source of inspiration for many and leaves wonderful memories for those who had the privilege to work with him, to love him and to appreciate his craft," his family said.

"We wish to thank everyone who took the time to express their sadness and compassion," they added. "We are very grateful by the outpouring of support received from around the world."

Vallée's family also shared that a preliminary coroner's report did not fully find a cause of death, though they did determine his death "was not caused by the intervention of another party, a voluntary act or a known disease." (A rep for the filmmaker told the Los Angeles Times on Monday that he died from a heart attack.)

The Vallée family asked that everyone respect their need to mourn their loss in private and said additional details of a ceremony to celebrate his life will be provided at a later date.

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Emmy winner Vallée had been developing a TV adaptation of Laura Lippman's book Lady in the Lake starring Natalie Portman and Lupita Nyong'o.

Portman, 40, honored him on her Instagram Story earlier this week, writing, "Devastating to lose this great man. I've been lucky enough to work with him as a producer these past months and was constantly moved by his kindness, thoughtfulness and soul. A rare human. A massive loss. My thoughts are with his family and loved ones."

His longtime producing partner Nathan Ross said in a statement to PEOPLE this week, "Jean-Marc stood for creativity, authenticity and trying things differently. He was a true artist and a generous, loving guy. Everyone who worked with him couldn't help but see the talent and vision he possessed."

"He was a friend, creative partner and an older brother to me," Ross continued. "The maestro will sorely be missed but it comforts knowing his beautiful style and impactful work he shared with the world will live on."