ΔE 27.7, loose: different enough that you should pick on purpose. Imperial Purple is noticeably lighter, much more saturated, warmer than Dioxazine Violet.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 28). Imperial Purple is noticeably lighter, much more saturated, warmer than Dioxazine Violet.
The same difference applies the other way round: Dioxazine Violet is noticeably darker, much more muted, cooler.
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 Imperial Purple on the colour wheel
All matches: Dioxazine Violet equivalents · Imperial Purple equivalents