Beyond the Remembered World: Predictive 4D Belief for Persistent Navigation in Evolving Worlds

Recent embodied navigation systems increasingly use persistent spatial memories and vision–language models to act across repeated visits to familiar environments. Persistent maps make prior observations available for subsequent decisions and reduce the need to reconstruct familiar scenes for every task. However, remembered observations need not describe the current world: objects may move outside the agent's view, even while it travels toward a predicted destination. Despite advances in memory retrieval and state prediction, existing methods do not jointly account for continued hidden world evolution during navigation and visibility-conditioned belief revision. We study navigation under hidden world evolution, where an agent must infer the latent current state from irregular histories and revise its decisions as time and evidence accumulate. We present $\text{EvolvingNav}$, an embodied agent that turns timestamped 3D entity histories into a structured belief over whether the last observed state persists or the target has relocated. A frozen, zero-shot vision–language controller acts on this belief, while an event-driven filter forecasts states at candidate arrival times, incorporates newly informative, visibility-aware RGB-D evidence, and replans as the world evolves. We further introduce $\text{EvoWorld-Bench}$, a human-trace-grounded benchmark with $\text{54}$ scenes and $\text{803.68k}$ tasks for evaluating state prediction and embodied decisions under controlled changes before and during navigation. Across simulation benchmarks and physical robot trials, $\text{EvolvingNav}$ improves navigation success and search efficiency relative to evaluated baselines. Paired controls show that temporal prediction is most useful when changes exhibit learnable regularity; ablations demonstrate the value of preserving uncertainty and updating beliefs from visual evidence.