Rejection sampling methods have recently been proposed to improve the performance of discriminator-based generative models. However, these methods are only optimal under an unlimited sampling budget, and are usually applied to a generator trained independently of the rejection procedure. We first propose an Optimal Budgeted Rejection Sampling (OBRS) scheme that is provably optimal with respect to \textit{any} $f$-divergence between the true distribution and the post-rejection distribution, for a given sampling budget. Second, we propose an end-to-end method that incorporates the sampling scheme into the training procedure to further enhance the model's overall performance. Through experiments and supporting theory, we show that the proposed methods are effective in significantly improving the quality and diversity of the samples.

翻译：拒绝采样方法近来被提出用于提升基于判别器的生成模型的性能。然而，这些方法仅在无限采样预算下达到最优，且通常应用于独立于拒绝过程训练的生成器。我们首先提出一种最优预算拒绝采样方案，该方案在给定采样预算下，关于真实分布与拒绝后分布之间的任意$f$-散度具有可证明的最优性。其次，我们提出一种端到端方法，将采样方案融入训练过程，以进一步改善模型的整体性能。通过实验和理论支撑，我们证明了所提方法在显著提升样本质量与多样性方面的有效性。