HyperbolicDiffusion: Sharp & Scalable Tiled Generation on the Hyperbolic Plane

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.