The photodesorption of a diatomic from a metal surface, following absorption of visible or UV light, involves electronic transitions of the desorbing species coupled to the lattice vibrations and electron-hole excitations of the substrate. We present a general treatment of these phenomena, based on the Liouville-Von Neuman equation for the density operator, and a stochastic theory of localized perturbations in an extended system. The Hamiltonian of the extended molecular system is divided into a term for the localized primary degrees of freedom (DFs) affected by the desorption, coupled to secondary DFs that acts as a time-evolving bath. A self-consistent field treatment gives an effective (non-Hermitian) Hamiltonian for the primary DFs that accounts for energy fluctuation and dissipation in terms of the properties of adsorbate and substrate. A diabatic electronic representation is used to eliminate momentum couplings between adsorbate electronic states. The bath dynamics is studied for lattice vibrations and for electronic excitations. Electron-hole excitations of the substrate are considered for intraband and interband transitions. The assumption of Brownian motion leads to expressions for the dissipative potentials in terms of the time-correlation functions of lattice displacements and of electron density fluctuations. The dissipation depends on time, allowing for time-dependent substrate temperatures and generalizing the Langevin description. Dissipation contributes to the time evolution of both ground and excited electronic states of the desorbing species. The model is discussed for the special case of Ni(001)(ads)CO.