{"ID":2897861,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.04330","arxiv_id":"2507.04330","title":"A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flows","abstract":"We consider the problem of sampling from a probability distribution $π$ which admits a density w.r.t. a dominating measure. It is well known that this can be written as an optimisation problem over the space of probability distributions in which we aim to minimise a divergence from $π$. The optimisation problem is normally solved through gradient flows in the space of probability distributions with an appropriate metric. We show that the Kullback--Leibler divergence is the only divergence in the family of Bregman divergences whose gradient flow w.r.t. many popular metrics does not require knowledge of the normalising constant of $π$.","short_abstract":"We consider the problem of sampling from a probability distribution $π$ which admits a density w.r.t. a dominating measure. It is well known that this can be written as an optimisation problem over the space of probability distributions in which we aim to minimise a divergence from $π$. The optimisation problem is norm...","url_abs":"https://arxiv.org/abs/2507.04330","url_pdf":"https://arxiv.org/pdf/2507.04330v2","authors":"[\"Francesca Romana Crucinio\"]","published":"2025-07-06T10:34:38Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"cs.LG\",\"math.ST\",\"stat.CO\"]","methods":"[]","has_code":false}