HyperbolicDiffusion: Sharp & Scalable Tiled Generation on the Hyperbolic Plane

We propose LF-MultiDiffusion, a training-free panorama generation method that extends MultiDiffusion to support linear projections between target and reference image spaces. Our key idea is to reformulate latent aggregation as a regularized least-squares problem and solve it efficiently with a Krylov-based iterative solver inside the denoising loop. This formulation enables denser and more natural mappings than prior training-free methods, yielding more stable generation with far fewer perspective views. As a result, LF-MultiDiffusion reduces the number of image generator evaluations during denoising and significantly improves inference efficiency. Experiments show that LF-MultiDiffusion achieves better visual quality, text alignment, and panoramic consistency than the strongest training-free baseline, while providing a 15.36$\times$ speedup. Our project page is available at: https://ahykw.github.io/lfmd.

Photomosaics are large images whose local regions are seen as independent tiles while their overall arrangement forms a coherent scene. Generating them at high resolution, with every tile convincing in its own right, is computationally expensive, since the canvas must hold many detailed tiles at once. We present PhotoQuilt, a training-free framework that generates photomosaics at arbitrary resolution. Diffusion models struggle to satisfy both scales at once, as direct high-resolution generation is costly and tends toward one smooth image rather than a mosaic, while patch-based tiling keeps local detail but loses global structure. PhotoQuilt resolves this with a bootstrapped tiled denoising procedure. We first produce a global composition at low resolution to fix the layout, then upscale it in latent space and re-inject noise to restore generative capacity. Denoising proceeds within fixed tiles, so each forms its own image while the shared global structure holds them in one layout. Because tile generation is handled separately, PhotoQuilt scales to large canvases without quadratic attention cost. Experiments show that PhotoQuilt outperforms current baselines on both global structure and local realism.

Standard diffusion models corrupt an entire sample with a single shared noise level, forcing all spatial regions to follow the same denoising trajectory. We introduce AsyncPatch Diffusion, a joint-diffusion framework that assigns distinct noise levels to different input dimensions, such as image pixels, or latent tokens. We show how this asynchronous corruption defines a valid generative process while supporting a richer family of spatially heterogeneous denoising trajectories, and prove the first valid ELBO for this process. We show that a single pretrained model can perform spatially adaptive generation, where different regions are denoised on different schedules. A key challenge is training: naive independent noise-level sampling overemphasizes highly heterogeneous configurations and underrepresents homogeneous noise levels, that are crucial during sampling. We address this with a controlled noise-level sampler that regulates both the average corruption level and its spatial variability. AsyncPatch achieves generation quality comparable to conventional diffusion on ImageNet 256 and LSUN, while being natively suited for inpainting without task-specific fine-tuning. We further introduce input guidance, which uses clean or partially corrupted regions to guide the generation of unknown regions, improving local consistency and texture matching. Finally, we demonstrate adaptive generation strategies including uncertainty-guided acceleration and autoregressive sampling.