Video customization has gained significant interest, yet achieving temporal and geometric consistency remains challenging. To address this, we propose a novel framework that leverages neural representations to model dynamic 3D scenes in videos, distilling their knowledge into rendering consistency to regularize diffusion models. Our method conceptualizes dynamic scenes as 4D volumes, employing grid-based dynamic geometry representations to enhance geometric consistency and cross-view appearance representations to improve visual coherence across frames. To seamlessly integrate these representations into diffusion models, we propose a latent neural rendering strategy that aligns geometry and appearance in a unified manner. Comprehensive evaluations across tasks such as local object editing and composite customization reveal consistent and significant performance gains, demonstrating the effectiveness and robustness of our proposed method.