A general set-up is proposed to study stochastic volatility models. We consider here a two-dimensional diffusion process [math] and assume that only [math] is observed at [math] discrete times with regular sampling interval [math] . The unobserved coordinate [math] is an ergodic diffusion which rules the diffusion coefficient (or volatility) of [math] . The following asymptotic framework is used: the sampling interval tends to [math] , while the number of observations and the length of the observation time tend to infinity. We study the empirical distribution associated with the observed increments of [math] . We prove that it converges in probability to a variance mixture of Gaussian laws and obtain a central limit theorem. Examples of models widely used in finance, and included in this framework, are given.