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Abstract Models of physics beyond the Standard Model often contain a large number of parameters. These form a high-dimensional space that is computationally intractable to fully explore. Experimental results project onto a subspace of parameters that are consistent with those observations, but mapping these constraints to the underlying parameters is also typically intractable. Instead, physicists often resort to scanning small subsets of the full parameter space and testing for experimental consistency. We propose an alternative approach that uses generative models to significantly improve the computational efficiency of sampling high-dimensional parameter spaces. To demonstrate this, we sample the constrained and phenomenological Minimal Supersymmetric Standard Models subject to the requirement that the sampled points are consistent with the measured Higgs boson mass. Our method achieves orders of magnitude improvements in sampling efficiency compared to a brute force search.