Heat transport in quasi-two-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi mathvariant="normal">C</mml:mi> <mml:msub> <mml:mi mathvariant="normal">u</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi

Low-dimensional crystalline materials exhibiting large atomic fluctuations enable low thermal conductivity for many applications, yet the critical interplay between thermal anisotropy and lattice anharmonicity remains elusive. Here, we combine first-principles calculations with unified thermal transport theory to uncover the unconventional thermal transport anisotropy correlated with the striking quartic anharmonicity in a quasi-two-dimensional compound $\mathrm{C}{\mathrm{u}}_{2}{\mathrm{P}}_{2}{\mathrm{O}}_{7}$. We find that the unique quasiplanar atomic network and hierarchical bonding create a permissive environment for intense oscillations of interlayered O atoms, triggering giant quartic anharmonicity. This, combined with small phonon interbranch spacing, renders wavelike coherences the dominant mechanism for heat transport, resulting in a nonmonotonic temperature dependence of lattice thermal conductivity and a reversal of its anisotropy between in-plane and out-of-plane directions. Our findings yield fundamental insights into the coherence-driven thermal transport anomaly in highly anharmonic low-dimensional crystals, which would guide the rational design of advanced thermal materials.