# When Geometry Aligns: Dihedral Hidden-State Transformations in UNet, ViT, and DiT Architectures

arXiv: https://arxiv.org/abs/2607.03580 · HTML: https://mlsanity.com/paper/2607.03580/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 25 of its 29 references that are in the map.
- First posted on arXiv 3 Jul 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 25 of 25)

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- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
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- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
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- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Transformer Interpretability Beyond Attention Visualization](https://mlsanity.com/paper/2012.09838/) (2020)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [PatchUp: A Feature-Space Block-Level Regularization Technique for Convolutional Neural Networks](https://mlsanity.com/paper/2006.07794/) (2020)
- [SDiT: Spiking Diffusion Model with Transformer](https://mlsanity.com/paper/2402.11588/) (2024)
- [On Designing Diffusion Autoencoders for Efficient Generation and Representation Learning](https://mlsanity.com/paper/2506.00136/) (2025)

## Abstract (arXiv)

Diffusion architectures now encompass convolutional UNets as well as transformer-based designs such as Diffusion Transformers (DiTs), inspired by Vision Transformers (ViTs), yet the effects of structured geometric perturbations within these architectures remain poorly understood. We study this question through a unified framework that applies reflection-based elements of the dihedral group to intermediate hidden states as controlled internal interventions, contrasting geometrically consistent and inconsistent variants. Using activation-level diagnostics, including Self-Consistency Shift (SCS), Activation Mass Scatter (AMS), and Drift, we analyze feature stability and geometric drift. We find that consistent transformations improve stability, while inconsistent ones induce predictable, architecture-specific failures. In the main Stable Diffusion 2.1 U-Net study, we evaluate seven intervention modes over three seeds and complement the internal diagnostics with image-level FID, KID, CLIP score, and LPIPS diversity. Taken together with supporting ViT and controlled DiT analyses, these results establish geometric consistency as a key principle for stable hidden-state interventions in spatially structured vision and diffusion models.