  Determining which parameters of a non-linear model best describe a set of
experimental data is a fundamental problem in science and it has gained much
traction lately with the rise of complex large-scale simulators. The likelihood
of such models is typically intractable, which is why classical MCMC methods
can not be used. Simulation-based inference (SBI) stands out in this context by
only requiring a dataset of simulations to train deep generative models capable
of approximating the posterior distribution that relates input parameters to a
given observation. In this work, we consider a tall data extension in which
multiple observations are available to better infer the parameters of the
model. The proposed method is built upon recent developments from the
flourishing score-based diffusion literature and allows to estimate the tall
data posterior distribution, while simply using information from a score
network trained for a single context observation. We compare our method to
recently proposed competing approaches on various numerical experiments and
demonstrate its superiority in terms of numerical stability and computational
cost.
