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Understanding 4D scenes is a core challenge in visual intelligence, requiring models to jointly capture scene geometry, appearance, and dynamics from partial observations. However, existing approaches are subdivided into feedforward models for direct geometric prediction, and generative models for visual synthesis. We introduce UGG, a unified framework for 4D scene understanding that jointly models RGB video and geometric representations such as depth and camera pose. By assigning different noise levels across modalities and time, UGG formulates visual generation and geometric prediction as conditional completion within a single generative model. This flexible formulation enables the model to learn from diverse, heterogeneous datasets with different subsets of geometric and visual annotations. Furthermore, our generative formulation enables inference-time search over multiple plausible scene hypotheses, using geometric evidence extracted from observed RGB frames to improve geometric prediction without ground truth geometry. We demonstrate UGG's effectiveness over non-unified baselines across camera-controlled video generation, depth estimation, and camera pose prediction, including in challenging sparse observation settings. Code and visualizations are available at https://ugg-model.github.io/