mlsanityData to 7 Oct 2026

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

arXiv 2607.03580 ↗First posted 3 Jul 2026cs.LG cs.CVcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

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.

Key facts. No citing papers in the map yet (data through 7 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.

Builds on

25 of 29 references.

Closest ancestors · 7

Same direction, newest first

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  4. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  6. 2020Denoising Diffusion Implicit Models6 Oct
  7. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 18

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  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,084
  5. 2017mixup: Beyond Empirical Risk Minimizationcited by 5,155
  6. 2020Training data-efficient image transformers & distillation through attentioncited by 4,560
  7. 2019CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Featurescited by 2,875
  8. 2022Locating and Editing Factual Associations in GPTcited by 2,609
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  10. 2020Transformer Feed-Forward Layers Are Key-Value Memoriescited by 1,307
  11. 2016Group Equivariant Convolutional Networkscited by 1,154
  12. 2017Network Dissection: Quantifying Interpretability of Deep Visual Representationscited by 703
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  4. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  5. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  6. 2020PatchUp: A Feature-Space Block-Level Regularization Technique for Convolutional Neural Networkscited by 12

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