The deformation conjecture for Du Bois singularities

Let $D\subset X$ be a reduced Cartier divisor, and let $x\in D$. Assume that $D$ has only Du Bois singularities in a neighborhood of $x$.

Deformation conjecture for Du Bois singularities. Then $X$ has only Du Bois singularities in a neighborhood of $x$.

This conjecture asks whether Du Bois singularities deform from a reduced Cartier divisor to the ambient variety. The source states that it was settled by Kovács and Schwede, so the conjecture is no longer open.