HyperbolicDiffusion：双曲平面上的清晰且可扩展的平铺生成
HyperbolicDiffusion: Sharp & Scalable Tiled Generation on the Hyperbolic Plane
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中文总结 AI 辅助
该研究提出无需训练的HyperbolicDiffusion方法，通过Hyperbolic Blooming Cover与几何修复阶段，在双曲平面H²上生成清晰、可重投影且跨视点一致的视觉场，为埃舍尔《圆极限》系列提供生成对应物。
中文摘要 AI 辅助
平面平铺扩散对矩形画布的重叠窗口进行去噪，而双曲平面不存在此类画布，其面积随半径呈指数增长。我们提出HyperbolicDiffusion，一种无需训练的方法，用于直接在双曲平面H²上生成有限视觉场。我们的Hyperbolic Blooming Cover将窗口放置简化为紧凑的动态规划，运行仅需数秒且提供强理论保证。永久表面ID构成共享潜在画布：标准扩散模型对局部窗口去噪，其预测被融合回H²。由于曲率导致多窗口交界处存在残差不一致和模糊，基于几何的第二阶段会重新加噪并精确修复这些区域。生成的视觉场清晰、可重投影且跨视点一致，为埃舍尔《圆极限》系列提供了提示驱动的生成对应物。
英文摘要
Planar tiled diffusion denoises overlapping windows of one rectangular canvas. The hyperbolic plane has no such canvas, and its area grows exponentially with radius. We introduce HyperbolicDiffusion, a training-free method for generating finite visual fields directly on the hyperbolic plane H2. Our Hyperbolic Blooming Cover reduces window placement to a compact dynamic program that runs in seconds while providing strong theoretical guarantees. Permanent surface IDs form a shared latent canvas: a standard diffusion model denoises local windows, whose predictions are fused back onto H2. Because curvature causes residual disagreement and blur at multi-window junctions, a geometry-derived second stage re-noises and repairs precisely those regions. The resulting fields are sharp, reprojectable, and consistent across viewpoints, providing a prompt-driven generative counterpart to Escher's Circle Limit series.
