ΔE 17.0, loose: different enough that you should pick on purpose. Deep Sky is more saturated, cooler than Dioxazine Violet.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 17). Deep Sky is more saturated, cooler than Dioxazine Violet.
The same difference applies the other way round: Dioxazine Violet is more muted, warmer.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Dioxazine Violet on the colour wheel See Deep Sky on the colour wheel
All matches: Dioxazine Violet equivalents · Deep Sky equivalents