UGA-GAN: Unified Geometry-Aware GAN for Enhanced Training and Generation of High-Dimensional Data

Generative Adversarial Networks (GANs) have shown impressive performance in generating realistic data across various domains. However, they suffer from key challenges such as mode collapse, latent space disorganization, and geometric inconsistency, which hinder the generation of high-fidelity and diverse samples in complex, high-dimensional datasets. In this paper, we introduce a novel framework, the Unified Geometry-Aware Generative Adversarial Network (UGA-GAN), which integrates manifold learning, latent space regularization, and geometry-aware discrimination to address these challenges. We propose a unified architecture that enhances GAN performance by aligning generated samples with the underlying data manifold, promoting smooth and interpretable latent space representations, and ensuring global geometric consistency. Our experimental evaluation on the CIFAR-10 dataset demonstrates that UGA-GAN outperforms several baseline models, including DCGAN, WGAN, and LSGAN, achieving a 37.97% reduction in Fréchet Inception Distance (FID) score, indicating superior sample quality and diversity. Furthermore, t-SNE visualizations confirm that UGA-GAN generates more coherent and diverse samples with better mode coverage. These results highlight the potential of UGA-GAN to significantly improve high-dimensional data generation tasks in domains such as medical imaging, video generation, and 3D object synthesis. While UGA-GAN presents state-of-the-art performance, future work will focus on optimizing its computational efficiency, scaling it to larger datasets, and integrating it with emerging models such as diffusion networks and reinforcement learning for further performance enhancement.