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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper introduces a new approach to sampling from continuous probability distributions. The method extends prior work on using a combination of Gumbel perturbations and optimization to the continuous case. This is technically challenging, and they devise several interesting ideas to deal with continuous spaces, e.g. to produce an exponentially large or even infinite number of random variables (one per point of the continuous/discrete space) with the right distribution in an implicit way. Finally, they highlight an interesting connection with adaptive rejection sampling.