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.

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