The Kullback-Leibler divergence is the only Bregman divergence whose gradient flow with respect to many popular metrics does not require the normalizing constant of the target distribution π.
URL http://www.jstor.org/stable/2310775
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A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flows
The Kullback-Leibler divergence is the only Bregman divergence whose gradient flow with respect to many popular metrics does not require the normalizing constant of the target distribution π.