In this study, we use rational-quadratic neural spline flows, a sophisticated parametrization of normalizing flows, for inferring posterior probability distributions in scenarios where direct evaluation of the likelihood is challenging at inference time. We exemplify this approach using the T2K near detector as a working example, focusing on learning the posterior probability distribution of neutrino flux binned in neutrino energy. The predictions of the trained model are conditioned at inference time by the momentum and angle of the outgoing muons released after neutrino-nuclei interaction. This conditioning allows for the generation of personalized posterior distributions, tailored to the muon observables, all without necessitating a full retraining of the model for each new dataset. The performances of the model are studied for different shapes of the posterior distributions.