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

2026-07-03

AI Summary

This study investigates the impact of structured geometric perturbations on the hidden states of diffusion models such as UNet, ViT, and DiT, emphasizing the critical role of geometric consistency in model stability. By introducing dihedral group reflections as controlled interventions, the authors compare hidden-state dynamics under geometrically consistent versus inconsistent transformations. They evaluate these effects using activation diagnostics—including Self-Consistency Shift and Activation Mass Scatter—alongside image-quality metrics such as FID, CLIP, and LPIPS. The work establishes geometric consistency as a foundational principle for stable interventions, revealing architecture-specific responses to geometric perturbations: consistent transformations markedly enhance feature stability, whereas inconsistent interventions induce predictable, architecture-dependent failures, as validated in models including Stable Diffusion 2.1 U-Net.

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.

Problem

• geometric consistency
• dihedral group
• hidden-state transformations
• diffusion models
• feature stability

Innovation

• dihedral group
• geometric consistency
• hidden-state intervention
• diffusion models
• activation diagnostics