Higher singularities for hypersurfaces

With an assumption on the codimension of the singular locus of a complex hypersurface $D$ in smooth variety $X$, we show that if ${\underset{‾}{\mathrm{\Omega }}}_D^m\cong {\mathrm{\Omega }}_D^m$, then ${\underset{‾}{\mathrm{\Omega }}}_D^i\cong {\mathrm{\Omega }}_D^i$ for all $0\le i\le m$. We also discuss an analogue of this statement in positive characteristic.