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This paper introduces a novel approach to reducing statistical errors in generative models, with a specific focus on generative adversarial networks (GANs). Inspired by the error analysis of GANs, we find that statistical errors mainly arise from random sampling, leading to significant uncertainties in GANs. To address this issue, we propose a selective sampling mechanism called space‐filling sampling. Our method aims to increase the sampling probability in areas with insufficient data, thereby improving the learning performance of the generator. Theoretical analysis confirms the effectiveness of our approach in reducing statistical errors and accelerating convergence in GANs. This research represents a pioneering effort in targeting the reduction of statistical errors in GANs, and it demonstrates the potential for enhancing the training of other generative models. [ABSTRACT FROM AUTHOR]