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. Some experimental results are provided and show the promise of the approach. 

This paper introduces a sampling algorithm based on the Gumbel-max trick and A* search for continuous spaces. The Gumbel-Max trick adds perturbations to an energy function and after applying argmax, results in exact samples from the Gibbs distribution. While this applies to discrete spaces, this paper extends this idea to continuous spaces using the upper bounds on the infinitely many perturbation values.