发表机构
Technion - Israel Institute of Technology（以色列理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
基于埃舍尔《版画画廊》的共形映射，提出将去噪步骤与变换及其广义逆编织，生成自指场景，避免仅提示或事后变换的不足。
AI 中文摘要
“我想我这辈子从未做过如此奇特的事情。其中，它展示了一个年轻人饶有兴趣地观看展览墙上的一幅版画，而画中正是他自己。这怎么可能？也许我与爱因斯坦的弯曲宇宙并不遥远。”M.C.埃舍尔如此评价他1956年的石版画《版画画廊》。近半个世纪后，一项数学分析通过共形幂映射 $z \mapsto z^\alpha$（$\alpha \in \mathbb{C}$）将其几何与未扭曲的源图像联系起来。基于这一构造，我们使用冻结的文本到图像扩散模型生成新的自指场景。仅靠提示无法强制实现递归，而事后变换可能导致结构连接不良。在采样过程中应用变换也不够：去噪器可能“修复”预期的扭曲或偏离规定的几何。我们构造了非可逆图像变换 $T$ 的广义逆 $T^\dagger$，使其适应递归约束。在理想化表述中，彭罗斯恒等式 $TT^\dagger T = T$ 使 $TT^\dagger$ 成为几何可接受图像上的幂等投影。然而，即使有投影，仅对变换后的图像进行去噪仍是一项分布外任务。因此，我们将去噪步骤与 $T$ 和 $T^\dagger$ 编织在一起：源空间步骤发展未扭曲的场景，而变换空间步骤在最终几何中细化其外观和连接。我们生成类似《版画画廊》的构图，并探索进一步的变换。我们不是扭曲成品图像，而是让场景及其扭曲共同发展。
英文摘要
I don't think I have ever done anything as peculiar in my life. Among other things, it shows a young man looking with interest at a print on the wall of an exhibition that features himself. How can this be? Perhaps I am not far removed from Einstein's curved universe.'' So wrote M.C. Escher about his 1956 lithograph Print Gallery. Nearly half a century later, a mathematical analysis related its geometry to an untwisted source image through a conformal power map $z \mapsto z^α$, $α\in \mathbb{C}$. Building on this construction, we use a frozen text-to-image diffusion model to generate new self-referential scenes. Prompting alone does not enforce the recursion, while a post-hoc transformation can leave structures poorly connected. Applying the transformation during sampling is also insufficient: the denoiser may "repair" the intended distortion or drift out of the prescribed geometry. We construct a generalized inverse $T^\dagger$ of the non-invertible image transformation $T$, adapted to its recursive constraint. In the idealized formulation, the Penrose identity $TT^\dagger T = T$ makes $TT^\dagger$ an idempotent projection onto geometrically admissible images. Yet denoising only the transformed image remains an out-of-distribution task, even with projection. We therefore braid denoising steps with $T$ and $T^\dagger$: source-space steps develop the untwisted scene, while transformed-space steps refine its appearance and connections in the final geometry. We generate Print Gallery-like compositions and explore further transformations. Rather than distorting a finished image, we let the scene and its distortion develop together.
