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：拒绝采样方法近期被提出用于提升基于判别器的生成模型的性能。然而，现有方法仅在无限采样预算条件下达到最优，且通常将采样方案独立于拒绝过程应用于已训练的生成器。我们首先提出一种最优预算拒绝采样（OBRS）方案，该方案在给定采样预算下，可证明相对于真实分布与拒绝后分布之间的任意 $f$ 散度达到最优。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提升模型的整体性能。通过实验与理论分析，我们证明所提方法能有效显著提升样本质量与多样性。