We prove its consistency and show that the asymptotic variance ofitssolution canattaintheequality oftheefficiencybound undermild regularity conditions.

Examples of such models arise naturally in modelling images [27, 39], natural language [54], Markov random fields [61] and nonparametric density estimation [63, 69].

Wealsoproposeawayto regularize this MMD flow, based on an injection of noise in the gradient. This algorithmic fix comes with theoretical and empirical evidence.

Thefamily of f-divergences includes Kullback-Leibler divergence [23] and Total Variation distance.

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Many approaches are available to reliably model univariate distributions of real-valued variables.