We present OctWorld, a video diffusion framework with persistent 3D memory for generating explorable, world-consistent, and high-fidelity visual scenes. Given a single image, OctWorld performs stable autoregressive world generation along user-specified camera trajectories. We focus on long-range generation, characterized by extended camera paths and wide viewpoint coverage, where preserving spatial consistency is particularly challenging when previously generated regions are revisited. To address this problem, we introduce OctMap, an extensible and spatially adaptive 3D memory that progressively fuses generated visual observations and their corresponding depth maps into a global representation. OctMap employs TSDF fusion within a dynamic sparse octree whose spatial resolution adapts to image evidence. This design preserves geometric and appearance details across diverse scene scales while maintaining low memory overhead. Experiments demonstrate that OctWorld generates long-range, spatially consistent videos and outperforms prior methods on both existing benchmarks and challenging long-range generation settings. OctMap also provides clear advantages over point-based caches and fixed-resolution TSDF volumes. Project page: https://maxtirerror.github.io/octworldpage/
Generating high-quality triangle meshes is essential for film, gaming, and interactive 3D applications. Mainstream methods rely on mesh serialization and autoregressive processes, which stuggles in effective inference and is sensitive to error accumulation. In this paper, we present Nexus, a diffusion method that achieves holistic mesh generation via decoupled vertex and topology generation. First, we view mesh vertices as sparse voxels organized as an octree and adopt a diffusion model to generate the vertices in a coarse-to-fine manner. Second, for topology modeling, we propose Spacetime Interval, as an extension of Spacetime Distance to encode arbitrary edge and face topology into continuous per-vertex embeddings. It allows for a global and efficient recovery of complex topology. We then employ a diffusion model to generate the continuous embeddings on the generated vertices. Extensive experiments on the Objaverse and Toys4K datasets and in-the-wild images demonstrate that our method outperforms state-of-the-art autoregressive and two-stage baselines, effectively circumventing the inherent limitations of sequential mesh modeling. A blind user study from 3D practitioners confirms strong perceptual preference for our results.