Generalization for Discriminator-Guided Diffusion Models via Strong Duality

Hisham Husain, Richard Nock

Keywords: f-divergences, diffusion, integral probability metrics

TL;DR: We characterize the convergence of discriminator guided diffusion models with their connections to strong duality and expose the generalization abilities, ultimately advocating for the use of these methods.

Abstract: In the past few years, score-based generative models (SGMs) and diffusion models have proven to be efficient methods for learning distributions and have been of great practical significance. However, only a few lines of work are attempting to understand the theoretical guarantees of such models, and only one recent work (Oko et al., 2023) focuses on the generalization abilities. In this work, we extend the study of generalization in SGMs and look to answer how model complexity emerges as a key player in the success of these models. For example, in other deep generative models, such as Generative Adversarial Networks (GANs), it has been revealed that the complexity of the discriminator set plays a crucial role in generalization. We prove that when diffusion models are further refined by discriminators (Kim et al., 2022a), the Integral Probability Metric (IPM) can be exactly represented through strong duality. Our findings advocate for discriminator refinement of deep generative models and, more specifically, unveil the generalization effect of using regularized discriminators in this setting. This result validates existing work on discriminator refinement to a great deal of generality. Therefore, our work provides theoretical validation for existing practices, provides a notion of regularization for SGMs, and contributes to the understanding of efficient distributional learning at large.

Primary Area: generative models

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Submission Number: 3564