The Du Bois singularities and dense F-injective type conjecture

Let $R$ be a ring essentially of finite type over a field of characteristic zero. Du Bois–F-injective correspondence conjecture. The scheme $\operatorname{Spec} R$ has only Du Bois singularities if and only if $R$ is of dense $F$-injective type. One direction is known: dense $F$-injective type implies Du Bois singularities. The converse is stated to remain open even for two-dimensional normal local rings.