  Neural Posterior Estimation methods for simulation-based inference can be
ill-suited for dealing with posterior distributions obtained by conditioning on
multiple observations, as they tend to require a large number of simulator
calls to learn accurate approximations. In contrast, Neural Likelihood
Estimation methods can handle multiple observations at inference time after
learning from individual observations, but they rely on standard inference
methods, such as MCMC or variational inference, which come with certain
performance drawbacks. We introduce a new method based on conditional score
modeling that enjoys the benefits of both approaches. We model the scores of
the (diffused) posterior distributions induced by individual observations, and
introduce a way of combining the learned scores to approximately sample from
the target posterior distribution. Our approach is sample-efficient, can
naturally aggregate multiple observations at inference time, and avoids the
drawbacks of standard inference methods.
