# HyperbolicDiffusion: Sharp & Scalable Tiled Generation on the Hyperbolic Plane

arXiv: https://arxiv.org/abs/2608.03422 · HTML: https://mlsanity.com/paper/2608.03422/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 10 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generation](https://mlsanity.com/paper/2302.08113/) (2023)
- [SyncDiffusion: Coherent Montage via Synchronized Joint Diffusions](https://mlsanity.com/paper/2306.05178/) (2023)
- [DiffCollage: Parallel Generation of Large Content with Diffusion Models](https://mlsanity.com/paper/2303.17076/) (2023)
- [PanoFree: Tuning-Free Holistic Multi-view Image Generation with Cross-view Self-Guidance](https://mlsanity.com/paper/2408.02157/) (2024)
- [SphereDiff: Tuning-free 360deg Static and Dynamic Panorama Generation via Spherical Latent Representation](https://mlsanity.com/paper/2504.14396/) (2025)

## Abstract (arXiv)

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.