Diffeomoprhism-Informed 3D Gaussian Splattings via Screen-Space Optimal Transport (OT)

3D Gaussian Splatting (3DGS) has emerged as an effective solution for real-time novel view synthesis (NVS) with high rendering quality, but training memory scales with image resolution, making downsampled supervision common and leading to loss of sharp, high-frequency details and degraded perceptual quality. Moreover, uniform supervision assigns equal weight to all pixels, resulting in weak emphasis on detail-rich regions such as edges and thin structures. We propose \textbf{OT-3DGS}, which leverages optimal transport in screen space to reparameterize the image domain prior to downsampling, inducing importance-based non-uniform supervision that redistributes pixel budget toward geometry-critical regions and strengthens supervision on high-frequency content. Our method remains fully compatible with the original 3DGS pipeline, requiring no modification to loss functions, rendering settings, or pruning, cloning, and splitting strategies. Experiments across diverse datasets show that OT-3DGS produces sharper structures, clearer reflectance, and reduced over-smoothing; while PSNR and SSIM may slightly decrease due to deviation from downsampled references, reference-free metrics including BRISQUE, NIQE, and Laplacian Variance (LV) improve significantly, better reflecting perceptual quality and high-frequency detail. These results demonstrate that OT-3DGS aligns with the fundamental goal of NVS: generating perceptually realistic, high-quality unseen views.