<ul data-eligibleForWebStory="true">Neural likelihood estimation methods for simulation-based inference face issues with high-dimensional data.A new method called Surjective Sequential Neural Likelihood (SSNL) estimation is introduced for simulation-based inference.SSNL utilizes a dimensionality-reducing surjective normalizing flow model as a surrogate likelihood function.It enables computational inference via Markov chain Monte Carlo or variational Bayes methods.SSNL eliminates the need for manual crafting of summary statistics for high-dimensional data inference.The method is evaluated on various experiments and surpasses or matches state-of-the-art techniques.SSNL proves to be a promising option for simulation-based inference on high-dimensional data sets.