  We present two infinite families of coherent quantum speed limits (QSLs) for
general unitary dynamics by employing the H\"older's inequality for matrix
norms. Our approach clearly highlights the contribution of the coherence of the
evolved states, and provides novel QSL bounds characterized by coherence
measures based on Schatten $p$-norm or Hellinger distance. We illustrate our
findings with relevant models, demonstrating our bounds are much tighter than
the established ones and asymptotically saturable in the adiabatic limit. Our
results show that rapid quantum dynamics requires coherent superpositions of
energy eigenstates, singling out coherence as a key resource for the evolution
of quantum systems.
