We consider some general mixed-effects diffusion models, in which the observations are made at discrete time points and include measurement errors. In these models, the observed likelihood is generally not explicit, making maximum likelihood estimation of the parameters particularly complex. We propose a specific inference methodology for these models. In particular, we combine the SAEM algorithm with the extended Kalman filter to estimate the population parameters. We also provide some tools for estimating the individual parameters, for recovering the individual underlying diffusion trajectories and for evaluating the model. The methods are evaluated on simulations and applied to a pharmacokinetics example.