Log prismatic Dieudonné theory for log $p$-divisible groups over ${\mathcal{O}}_K$

Let ${\mathcal{O}}_K$ be a complete discrete valuation ring of mixed characteristic with perfect residue field, endowed with its canonical log-structure. We prove that log $p$-divisible groups over ${\mathcal{O}}_K$ correspond to Dieudonné crystals on the absolute log-prismatic site of ${\mathcal{O}}_K$ endowed with the Kummer log-flat topology. The proof uses log-descent to reduce the problem to the classical prismatic correspondence, recently established by Anschütz-Le Bras.