# Moore, Escher, Penrose: A Conformal Golden Braid

arXiv: https://arxiv.org/abs/2610.02210 · HTML: https://mlsanity.com/paper/2610.02210/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 39 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 22 of 22)

- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data](https://mlsanity.com/paper/2107.10833/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generation](https://mlsanity.com/paper/2302.08113/) (2023)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Diffusion Self-Guidance for Controllable Image Generation](https://mlsanity.com/paper/2306.00986/) (2023)
- [Visual Anagrams: Generating Multi-View Optical Illusions with Diffusion Models](https://mlsanity.com/paper/2311.17919/) (2023)
- [Diffusion Illusions: Hiding Images in Plain Sight](https://mlsanity.com/paper/2312.03817/) (2023)
- [SyncTweedies: A General Generative Framework Based on Synchronized Diffusions](https://mlsanity.com/paper/2403.14370/) (2024)
- [Idempotent Generative Network](https://mlsanity.com/paper/2311.01462/) (2023)
- [ZoomLDM: Latent Diffusion Model for multi-scale image generation](https://mlsanity.com/paper/2411.16969/) (2024)
- [Generative Powers of Ten](https://mlsanity.com/paper/2312.02149/) (2023)
- [Fast constrained sampling in pre-trained diffusion models](https://mlsanity.com/paper/2410.18804/) (2024)
- [Tiled Diffusion](https://mlsanity.com/paper/2412.15185/) (2024)
- [LookingGlass: Generative Anamorphoses via Laplacian Pyramid Warping](https://mlsanity.com/paper/2504.08902/) (2025)
- [Self-Similarity Priors: Neural Collages as Differentiable Fractal Representations](https://mlsanity.com/paper/2204.07673/) (2022)
- [Generative Escher Meshes](https://mlsanity.com/paper/2309.14564/) (2023)
- [Generalized Inversion of Nonlinear Operators](https://mlsanity.com/paper/2111.10755/) (2021)
- [Refracting Reality: Generating Images with Realistic Transparent Objects](https://mlsanity.com/paper/2511.17340/) (2025)
- [Pseudo-Invertible Neural Networks](https://mlsanity.com/paper/2602.06042/) (2026)
- [Comparison of CoModGANs, LaMa and GLIDE for Art Inpainting- Completing M.C Escher's Print Gallery](https://mlsanity.com/paper/2205.01741/) (2022)

## Abstract (arXiv)

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 zα, α ∈ mathbbC. 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.