Continuous visual world simulation requires coupling evolving scene geometry with temporally persistent appearance. We present UniWorld, a unified framework that integrates depth trajectories and reference appearance within a shared video generation model. The central design maintains visual and geometric histories on a common timeline. Noise-aligned overlapping continuation places generated history at the prescribed sampling noise level and commits only newly generated latents. Rolling depth latent state preserves the corresponding geometric controls, incrementally reads newly available geometry, and keeps the conditioning fixed within each sampling window. Together, these mechanisms ensure exact preservation of latent history while bounding the active depth state by the window size. We evaluate continuous generation, paired history interventions, and long-horizon behavior across diverse scene categories. The same generator supports estimated, native, and on-demand simulator depth, while cached and incremental execution paths produce bitwise-identical outputs. Appearance changes and geometric control branches operate through the same interface without modifying committed history. The measured steady-state DiT execution path achieves real-time generation throughput, demonstrating the efficiency of UniWorld for continuous visual world simulation. Project page: https://zephipage.github.io/UniWorld.

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