The use of discriminators to train or fine-tune generative models has proven to be a rather successful framework. A notable example is Generative Adversarial Networks (GANs) that minimize a loss incurred by training discriminators along with other paradigms that boost generative models via discriminators that satisfy weak learner constraints. More recently, even diffusion models have shown advantages with some kind of discriminator guidance. In this work, we extend a strong-duality result related to $f$-divergences which gives rise to a discriminator-guided recipe that allows us to \textit{refine} any generative model. We then show that the refined generative models provably improve generalization, compared to its non-refined counterpart. In particular, our analysis reveals that the gap in generalization is improved based on the Rademacher complexity of the discriminator set used for refinement. Our recipe subsumes a recently introduced score-based diffusion approach (Kim et al., 2022) that has shown great empirical success, however allows us to shed light on the generalization guarantees of this method by virtue of our analysis. Thus, our work provides a theoretical validation for existing work, suggests avenues for new algorithms, and contributes to our understanding of generalization in generative models at large.

翻译：使用判别器训练或微调生成模型已被证明是一个相当成功的框架。一个显著的例子是生成对抗网络（GANs），它通过训练判别器来最小化损失，同时结合其他范式，借助满足弱学习器约束的判别器来提升生成模型。近期，甚至扩散模型也展现出在某种判别器引导下的优势。本文中，我们推广了一个与$f$-散度相关的强对偶结果，从而提出一种判别器引导的配方，使我们能够\textit{精炼}任意生成模型。接着，我们证明经精炼的生成模型相比于未精炼的对应模型在泛化性能上可验证地提升。特别地，我们的分析揭示，泛化差距的改进基于用于精炼的判别器集合的Rademacher复杂度。我们的配方涵盖了一种近期提出的基于得分的扩散方法（Kim et al., 2022），该方法虽取得了显著的实证成功，但通过我们的分析得以阐明该方法在泛化保证方面的特性。因此，本文为现有工作提供了理论验证，为新算法指明了方向，并整体上深化了我们对生成模型泛化性的理解。