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⊞υ⁰ＦＥΦθκ⁻ι§θκ≔⁺υ⁻ιυυＩΦυκ

Try it online! Link is to verbose version of code. Explanation: Adapted from both @Arnauld's and @loopywalt's answers.

⊞υ⁰

Start with a list of just 0.

ＦＥΦθκ⁻ι§θκ

Loop over the list of differences of the input array.

≔⁺υ⁻ιυυ

Subtract all of the elements of the output array from the current difference and then concatenate the result onto the output array.

ＩΦυκ

Output all but the first element of the output array.