Image super-resolution techniques exploiting the stochastic fluctuations of image intensities have become a powerful tool in fluorescence microscopy. Compared to other approaches, these techniques can be applied under standard acquisition settings and do not require special microscopes nor fluorophores. Most of these approaches can be mathematically modelled making use of second-order statistics possibly combined with a priori regularisation on the desired solution. In this work, we consider a different paradigm and formulate a physical-inspired data-driven approach based on generative learning. By simulating fluorescence and noise fluctuations by means of a suitable double Poisson-type process, the unknown distribution of the fluctuating sequence of lowresolution and noisy images is approximated via a GAN-type approach where both physical and network parameters are optimised. In this work, we provide theoretical insights on the choice of the corresponding cost functionals and gradient computations, and assess practical performance on simulated Argolight patterns.