VE-cGAN: Improved Generalization Analysis of Conditional Generative Adversarial Networks Using Vicinal Estimation

Abstract

Abstract Conditional Generative Adversarial Networks (cGANs) provide a flexible framework for learning conditional distributions, but they suffer from two fundamental challenges: the scarcity of conditional samples and the curse of dimensionality in the image space. In this work, we address both issues by introducing Vicinal Estimation (VE) into the cGAN framework and analyzing it through Barron-space discriminators. VE alleviates the lack of conditional samples by coupling nearby labels via an auxiliary sampling distribution, effectively transforming the problem into a collection of unconditional GANs in the vicinal label space. Meanwhile, the Barron-space analysis yields a dimension-independent generalization bound that holds irrespective of the image dimension, and we show how this bound transfers from VE conditionals back to the original conditional distributions. We develop VE-cGAN , a practical instantiation of this idea, and demonstrate through experiments on benchmark datasets that it achieves improved perceptual quality and label consistency compared with baselines. Our theoretical and empirical findings together highlight VE as a principled and effective approach to overcoming the lack of conditional samples and the curse of dimensionality in conditional generative modeling.