在双曲平面上直接生成高清图像，支持多视角一致的视觉场。
HyperbolicDiffusion: Sharp & Scalable Tiled Generation on the Hyperbolic Plane
- 基于双曲几何动态规划放置图像窗口，快速生成
- 修复多窗口拼接处的模糊与不一致，保持图像清晰
- 无需训练，适合艺术创作与高维视觉生成
平面拼贴扩散通过重叠窗口对矩形画布进行去噪。双曲平面无固定画布，其面积随半径指数增长。我们提出HyperbolicDiffusion，一种无需训练的方法，可直接在双曲平面H2上生成有限视觉域。我们的双曲绽放覆盖将窗口布局简化为紧凑的动态规划，仅需数秒即可完成，并提供强理论保障。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，预测结果回传至H2。由于曲率导致多窗口交界处残差分歧与模糊，第二阶段基于几何特性重新去噪并精准修复这些区域。最终生成的视觉域清晰、可重投影且视角间一致，为埃舍尔《圆极限》系列提供了提示驱动的生成对应。
原文摘要 · Abstract (English)
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.
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