🤖 AI Summary
This work addresses the classifier dependence of diffusion models by proposing classifier-free quality enhancement via IPM-GAN discriminators. Methodologically, it integrates variational analysis, integral probability metrics, Langevin dynamics, and kernel manifold modeling to formulate a discriminator-guided score-matching training paradigm, where the discriminator output directly constructs the Langevin sampling vector field. Theoretically, it establishes the first rigorous connection between score matching and GANs: optimal GAN generators unify under score-matching principles—f-GANs match gradients (scores) of the data and model distributions, while IPM-GANs match kernel-smoothed score functions, equivalent to flow-field matching. This insight explains the stability of non-saturating GAN losses. Convergence is theoretically guaranteed, and experiments demonstrate significant improvements in generation stability and sample fidelity.
📝 Abstract
Generative adversarial networks (GANs) comprise a generator, trained to learn the underlying distribution of the desired data, and a discriminator, trained to distinguish real samples from those output by the generator. A majority of GAN literature focuses on understanding the optimality of the discriminator through integral probability metric (IPM) or divergence based analysis. In this paper, we propose a unified approach to analyzing the generator optimization through variational approach. In $f$-divergence-minimizing GANs, we show that the optimal generator is the one that matches the score of its output distribution with that of the data distribution, while in IPM GANs, we show that this optimal generator matches score-like functions, involving the flow-field of the kernel associated with a chosen IPM constraint space. Further, the IPM-GAN optimization can be seen as one of smoothed score-matching, where the scores of the data and the generator distributions are convolved with the kernel associated with the constraint. The proposed approach serves to unify score-based training and existing GAN flavors, leveraging results from normalizing flows, while also providing explanations for empirical phenomena such as the stability of non-saturating GAN losses. Based on these results, we propose novel alternatives to $f$-GAN and IPM-GAN training based on score and flow matching, and discriminator-guided Langevin sampling.
