This work presents an algorithm to sample from the Wasserstein barycenter of absolutely continuous measures. Our method is based on the gradient flow of the multimarginal formulation of the Wasserstein barycenter, with an additive penalization to account for the marginal constraints. We prove that the minimum of this penalized multimarginal formulation is achieved for a coupling that is close to the Wasserstein barycenter. The performances of the algorithm are showcased in several settings.

翻译：这项工作提供了从瓦塞斯坦温温热点采样的绝对连续措施的算法。 我们的方法基于瓦塞斯特温热点多边际配方的梯度流,加加惩罚以说明边际限制。 我们证明,在靠近瓦塞斯坦温热点的结合中,最起码实现了这种受罚的多边际配方。 算法的性能在若干环境中展示。