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

Recent advances in diffusion transformers (DiTs) have enabled promising single-turn image editing capabilities. However, multi-turn editing often leads to progressive semantic drift and quality degradation.In this work, we study this problem from a latent-space frequency perspective by decomposing the editing process into two functional components: VAE and DiT. Through systematic analysis in the VAE latent space, we uncover that the DiT introduces dominant low-frequency drift that accumulates as semantic misalignment across editing rounds, while the VAE contributes comparatively stable reconstruction bias.Based on this insight, we propose VAE-LFA (Low Frequency Alignment), a training-free, plug-and-play method that performs alignment in VAE latent space. VAE-LFA decomposes latent discrepancies across editing rounds via low-pass filtering, and aligns low-frequency statistics to an exponential moving average of previous rounds, effectively suppressing accumulated semantic drift while preserving high-frequency details.Our method requires no retraining, ground-truth priors, or access to diffusion parameters, making it applicable to both white-box and black-box DiT editors. For white-box models, VAE-LFA is seamlessly integrated into the editing pipeline by eliminating redundant VAE round trips; for black-box models, it operates via an off-the-shelf VAE to perform inter-round latent alignment.Extensive experiments demonstrate that VAE-LFA improves semantic consistency and visual fidelity across diverse multi-turn editing scenarios, including both controlled and in-the-wild images.

Recent advances in Diffusion Transformers (DiTs) demonstrate that aligning noisy latent states with well-trained semantic features-as pioneered by Representation Alignment (REPA)-can substantially accelerate training and improve generation fidelity. Subsequent analysis(e.g., iREPA) suggests that these gains arise primarily from transferring spatial structure contained in pre-trained vision representations. However, mostly existing alignment methods employ point-wise matching objectives or rely on implicit architectural tweaks, which fail to explicitly model the spatial relational geometry inherent in vision foundation models. We argue that such element-wise supervision is insufficient to capture the rich spatial topology of visual representations, and that effective alignment for generation should instead be formulated as an explicit structural constraint. To this end, we propose sREPA, a structural REPresentation Alignment framework to enforce consistency in the relational geometry of feature maps, rather than merely matching individual feature points. By encouraging the model to internalize holistic spatial layouts and structural correlations from pre-trained features, sREPA achieves faster and more stable convergence, along with improved sample quality, compared to state-of-the-art alignment strategies. Our code and models will be released.

Scaling Diffusion Transformers (DiTs) to hundreds of layers introduces a structural vulnerability: networks can enter a silent, mean-dominated collapse state that homogenizes token representations and suppresses centered variation. Through mechanistic auditing, we isolate the trigger event of this collapse as Mean Mode Screaming (MMS). MMS can occur even when training appears stable, with a mean-coherent backward shock on residual writers that opens deep residual branches and drives the network into a mean-dominated state. We show this behavior is driven by an exact decomposition of these gradients into mean-coherent and centered components, compounded by the structural suppression of attention-logit gradients through the null space of the Softmax Jacobian once values homogenize. To address this, we propose Mean-Variance Split (MV-Split) Residuals, which combine a separately gained centered residual update with a leaky trunk-mean replacement. On a 400-layer single-stream DiT, MV-Split prevents the divergent collapse that crashes the un-stabilized baseline; it tracks close to the baseline's pre-crash trajectory while remaining substantially better than token-isotropic gating methods such as LayerScale across the full schedule. Finally, we present a 1000-layer DiT as a scale-validation run at boundary scales, establishing that the architecture remains stably trainable at extreme depth.