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

• URL: http://arxiv.org/abs/2607.03580v1
• Date: Fri, 03 Jul 2026 19:47:07 GMT
• Title: When Geometry Aligns: Dihedral Hidden-State Transformations in UNet, ViT, and DiT Architectures
• Abstract summary: We study the effects of structured geometric perturbations within Diffusion Transformers (DiTs)<n>We find that consistent transformations improve stability, while inconsistent ones induce predictable, architecture-specific failures.<n> Taken together with supporting ViT and controlled DiT analyses, these results establish geometric consistency as a key principle for stable hidden-state interventions.
• Score: 20.803275645784694
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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