Another approach to simulate thermal diffusion and to calculate the Soret coefficient is based on the spontaneous fluctuations of the microscopic fluxes that are present in equilibrium molecular dynamics (EMD) simulations through the Green-Kubo formalism. Although the corresponding flux expressions for mixtures were thoroughly derived in the 1980s, 43;44 only a few molecular simulation studies on thermal diffusion employing EMD techniques can be found in the literature. Furthermore, EMD methods have been mostly used for validation purposes, that is, together with NEMD simulations. Presumably, this originates from the difficulties inherent to EMD simulations. First, cross-correlation functions are weaker and thus more challenging to sample than auto-correlation functions. Second, reliable information on the thermodynamic factor and the partial molar enthalpy is required to calculate the Soret coefficient. However, EMD simulations are valuable to gain insight into the sign and magnitude of the individual contributions to thermal diffusion processes, as recognized by Miller et al. In this work, the strengths of NEMD and EMD simulations were combined to reliably predict and understand the Soret coefficient of three different Lennard-Jones mixtures in the liquid state. Furthermore, a popular theoretical model, which mainly relies on thermodynamic input data, and a regression model to predict the Soret coefficient were tested, investigating their applicability limits. Our results and insights underscore that NEMD and EMD simulations in conjunction with theoretical models build a strong framework to foster understanding of thermodiffusion in liquid mixtures.