In order to sample from an unnormalized probability density function, we propose to combine continuous normalizing flows (CNFs) with rejection-resampling steps based on importance weights. We relate the iterative training of CNFs with regularized velocity fields to a JKO scheme and prove convergence of the involved velocity fields to the velocity field of the Wasserstein gradient flow (WGF). The alternation of local flow steps and non-local rejection-resampling steps allows to overcome local minima or slow convergence of the WGF for multimodal distributions. Since the proposal of the rejection step is generated by the model itself, they do not suffer from common drawbacks of classical rejection schemes. The arising model can be trained iteratively, reduces the reverse Kulback-Leibler (KL) loss function in each step, allows to generate iid samples and moreover allows for evaluations of the generated underlying density. Numerical examples show that our method yields accurate results on various test distributions including high-dimensional multimodal targets and outperforms the state of the art in almost all cases significantly.

翻译：为从未归一化的概率密度函数中采样，我们提出将连续归一化流（CNFs）与基于重要性权重的拒绝重采样步骤相结合。我们将具有正则化速度场的CNFs迭代训练与JKO方案相关联，并证明了所涉及速度场向Wasserstein梯度流（WGF）速度场的收敛。局部流步骤与非局部拒绝重采样步骤的交替，能够克服WGF对于多峰分布存在的局部极小值或收敛缓慢问题。由于拒绝步骤的提议由模型自身生成，因此避免了经典拒绝方案的常见缺陷。所提出的模型可以迭代训练，在每一步中减少反向Kullback-Leibler（KL）损失函数，能够生成独立同分布样本，并且允许对生成的基础密度进行评估。数值实验表明，我们的方法在各种测试分布（包括高维多峰目标分布）上均能获得精确结果，且在几乎所有情况下显著优于现有技术水平。