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Fig. 2.

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Example of annealing on the two moons distribution. The distribution is convolved with a multivariate Gaussian of variance σ. This variance decreases over the sampling procedure so that the MCMC is always over high-density regions, i.e., σ4 > σ3 > σ2 > σ1. The chain is initialized from a wide multivariate Gaussian, as in the top left panel, and converges to the data distribution, as in the bottom right panel. In blue is the density of the convolved distribution and the arrows represent its score function.

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