HyperbolicDiffusion: Sharp & Scalable Tiled Generation on the Hyperbolic Plane

Hugo Caselles-Dupré

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arXiv · 2608.03422

HyperbolicDiffusion: Sharp & Scalable Tiled Generation on the Hyperbolic Plane

Hugo Caselles-Dupré

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Abstract

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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Hugo Caselles-Dupré. 2026-08-04. HyperbolicDiffusion: Sharp & Scalable Tiled Generation on the Hyperbolic Plane. https://arxiv.org/abs/2608.03422

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