  We introduce Sequential Neural Posterior Score Estimation (SNPSE), a
score-based method for Bayesian inference in simulator-based models. Our
method, inspired by the remarkable success of score-based methods in generative
modelling, leverages conditional score-based diffusion models to generate
samples from the posterior distribution of interest. The model is trained using
an objective function which directly estimates the score of the posterior. We
embed the model into a sequential training procedure, which guides simulations
using the current approximation of the posterior at the observation of
interest, thereby reducing the simulation cost. We also introduce several
alternative sequential approaches, and discuss their relative merits. We then
validate our method, as well as its amortised, non-sequential, variant on
several numerical examples, demonstrating comparable or superior performance to
existing state-of-the-art methods such as Sequential Neural Posterior
Estimation (SNPE).
