# SE-UNet: Singular Equivariant Imaging for Real-World Constrained Generation

arXiv: https://arxiv.org/abs/2607.02628 · HTML: https://mlsanity.com/paper/2607.02628/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 7 of its 9 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 7 of 7)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)

## Abstract (arXiv)

While diffusion models have revolutionized image synthesis, their application to real-world inverse problems is often hampered by the need for massive datasets and the difficulty of imposing strict physical constraints. In this work, we introduce SE-UNet (Singular Equivariant UNet), a framework designed to solve ill-posed imaging tasks without extensive pre-training. By treating generation as an optimization problem constrained by geometric equivariance (D4 group) and singular value gating, SE-UNet effectively standardizes the solution space. We demonstrate that these strong inductive biases allow for state-of-the-art zero-shot inpainting results (80% missing pixels) on CIFAR-10. Our method surpasses Deep Image Prior (DIP) baselines by over 4 dB in PSNR and exhibits a characteristic "singular snap" convergence -- rapidly locking into the signal manifold. SE-UNet thus offers a data-efficient pathway for constrained generation, aligning with the ReALM-GEN goal of bridging theoretical priors with practical deployment.