Neural simulation-based inference is an emergent field with significant advances in the recent past. In addition to (sequential) neural approximations to the posterior \citep{papamakarios2016fast,lueckmann2017flexible,greenberg2019automatic,deistler2022truncated,wildberger2023flow}, likelihood \citep{papamakarios2019sequential,glockler2022variational} or likelihood-ratio \citep{cranmer2015approximating,durkan2020contrastive,hermans2020likelihood,thomas2022likelihood,delaunoy2022towards,miller2022contrastive}, recent approaches have utilized flow matching and score-based models for posterior inference \citep{schmitt2023consistency,geffner2023compositional,wildberger2023flow}, albeit mainly in a non-sequential manner. Score-based NPE methods are a fruitful research direction which do not restrict the architecture of the neural network architecture. More recently, \citet{gruner2023pseudolikelihood} proposed a new method that is targeted at models in which the posterior is conditioned on multiple observations simultaneously. \citet{jia2024simulation} introduce a new family of methods, called \textit{neural quantile estimation}, which uses quantile regression to either approximate the intractable posterior or likelihood functions of a model. \citet{glaser2022maximum,pacchiardi2022score} propose approaches to SBI using energy-based models as density estimators. Finally, \citet{yao2023simulation} propose a method based on stacking to combine the results of multiple posterior inferences, i.e., when multiple posterior approximations from different methods are available. 

Related to our work, \citet{alsing2019nuisance,chen2021neural,chen2023learning} have developed methods for SBI to compute summary statistics which, however, requires learning an additional embedding network while our approach learns an embedding and computes likelihood approximations in a single step and without computational overhead. \citet{radev2023jana} discuss an approach that learns three networks for posterior approximations, likelihood approximations and summary statistic computation. \citet{beck2022efficient} discuss marginalization of data dimensions to see the influence of different covariates on the posterior distribution and propose an approach to find informative data dimensions.

In order to evaluate inferences of non-sequential procedures of models for which samples from the true posterior are not available, \citet{linhart2023lcst} have proposed a local procedure based on classifier tests. Similarly, \citet{yao2023discriminative} proposed a diagnostic related to, and with higher power than, simulation-based calibration (\citet{talts2018validating}; unfortunately, for neural likelihood methods we found them computationally infeasible to use, since they require either computing a vast number of permutation tests of which each requires learning a classifier or repeatedly sampling from the surrogate posterior for every model).
