The exposure to intense electromagnetic radiation can induce distortions and symmetry breaking in the crystal structure of solids, providing a route for the all-optical control of their properties. In this paper, we formulate a unified theoretical approach to describe the coherent lattice dynamics in presence of external driving fields, electron-phonon and phonon-phonon interactions, and quantum nuclear effects. The main mechanisms for the excitation of coherent phonons—including infrared absorption, displacive excitation, impulsive stimulated Raman scattering, and ionic Raman scattering—can be seamlessly accounted for. We apply this formalism to a model consisting of two coupled phonon modes, where we illustrate the influence of quantum nuclei on structural distortions induced by ionic Raman scattering. Besides validating the widely employed classical models for the coherent lattice dynamics, our paper provides a versatile approach to methodically explore the emergence of quantum nuclear effects in the structural response of crystal lattices to strong fields.