Amber Heard denies affairs with Elon Musk, James Franco
But giving evidence she rejected the claims, in particular dismissing suggestions Musk visited her regularly at night from March 2015, not long after the couple wed.
"I wasn't even in communication with Elon until 2016," she told London's High Court on her second day on the witness stand.
Depp, star of "The Pirates of the Caribbean" franchise, is suing British tabloid The Sun and the author of a 2018 article that claimed he was a "wife-beater".
He maintains it severely damaged his reputation.
Depp's lawyer, Eleanor Laws, read out a 2016 text message sent by Musk offering protection against Depp after an alleged fight between the couple.
"The offer would stand, even if you never wanted to see me again... anyway, sorry for being an idiot," he wrote.
"The radio silence hurts a lot. It only matters because I really like you."
The text was sent the day after Heard claims the actor hit her in the face with a mobile phone during an argument, and while she was considering obtaining a restraining order.
"We were talking. He was saying to me 'Oh my god, what happened to you?'" she told the court.
Heard on Monday claimed that Depp threatened to kill her on a number of occasions, and subjected her to verbal and physical violence while under the influence of drink and drugs.
The couple met on the set of the 2011 film "The Rum Diary" and their relationship veered from "intensely affectionate, warm and charming" to "very intense and dark".
She said the actor blamed his actions on a "self-created third party" he sometimes named "the monster", and that she stayed in the relationship because she thought she could "fix" his well-documented problems.
The Sun's publisher, News Group Newspapers (NGN), argues it told the truth in its report, and that it has evidence to prove 14 alleged incidents of domestic violence.
The case is now in its third week and has lifted the lid on Depp's drunk-and-drug-fuelled lifestyle.
But he denies ever being violent to any woman, and has sought to portray his ex-wife as a calculating, dishonest and sociopathic narcissist intent on destroying his life.