arXiv:2510.21615v3 Announce Type: replace Abstract: Video generation models have advanced significantly through the latent diffusion transformers trained with rectified flow techniques. Yet these models still struggle with geometric inconsistencies, unstable motion, and visual artifacts that break the illusion of realistic 3D scenes. 3D-consistent video generation could significantly impact numerous downstream applications in generation and reconstruction tasks. We explore how epipolar geometry constraints improve modern video diffusion models. Despite using massive training data, these models fail to capture fundamental geometric principles. We align diffusion models using pairwise epipolar geometry constraints via preference-based optimization, directly addressing unstable trajectories and geometric artifacts through mathematically principled geometric enforcement. Our approach efficiently enforces geometric principles without requiring end-to-end differentiability. Evaluation demonstrates that classical geometric constraints provide more reliable preference signals than the video-quality and geometry metrics based on foundational models. We construct preferences from static scenes with camera motion, where the epipolar metric is most reliable, while the aligned model generalizes to dynamic scenes. By bridging data-driven learning with classical computer vision, we reduce epipolar error by 31% and improve human-rated consistency from 54% to 72% without compromising visual quality.