Embodied World Models (EWMs) have emerged as a scalable and risk-free paradigm for advancing embodied intelligence, enabling the safety-critical evaluation of Vision-Language-Action systems. However, their reliability as evaluation benchmarks and foundational simulators is often hindered by the representation gap between low-dimensional actions and high-dimensional video synthesis. This gap results in a lack of geometric correspondence, manifesting as accumulated trajectory drift and inconsistent robot-object interactions during long-horizon rollouts. To bridge this gap, we propose ViPSim, a framework that achieves consistent long-horizon generation through the synergistic collaboration of Visual and Parameter Spaces. We define the Visual Space as a domain of explicit spatial priors, integrating pixel-aligned projections of end-effector pose, camera perspectives, depth-informed scene geometry, and robotic morphological masks to provide dense structural grounding. Concurrently, the Parameter Space serves as a domain of numerical drivers, injecting raw action sequences and camera matrices to provide precise motion guidance. By unifying these two spaces, ViPSim ensures that the generated states are simultaneously anchored by geometric boundaries and steered by numerical commands. Extensive experiments demonstrate that ViPSim is backbone-agnostic and significantly enhances trajectory consistency. Notably, our approach exhibits emergent capabilities in generating complex interactions with deformable objects (e.g., cloth folding) and maintains robust performance in out-of-distribution and cross-embodiment scenarios, providing a high-fidelity foundation for the automated evaluation and predictive control of embodied agents.

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