The 49-year-old actress was hospitalised last month after suffering a seizure and is rumoured to be seeking treatment for an "eating disorder and addiction issues", but Rumer Willis - Demi`s eldest daughter with ex-husband Bruce Willis - insists all the family "believe" she will get better.
She told German website tz-online: "Of course the situation weighs heavily on me.
"My mother is on the road to recovery. It`s slow going but we believe in her."
Zac Efron, a close friend of Rumer, 23, recently admitted while the `House Bunny` actress is finding her mother`s difficulties "tough", she is coping well with the situation.
He said: "It`s tough, but I think she`s all right.
"Me and Rumer have been friends for a long time. I know Demi is going through some personal stuff right now. I just wish her well. I hope she`s doing OK."
Demi - who split from husband Ashton Kutcher in November amid speculation he had cheated on her - is believed to be on "total lockdown" at a $1,000-a-night rehabilitation facility in Sundance, Utah, as she struggles to overcome her issues.
A source has previously said: "She`s on total lockdown and only talking to a small group of people."