Beyond Gaussian Bottlenecks: Topologically Aligned Encoding of Vision-Transformer Feature Spaces

We present a compact geometry-native latent space as a shared foundation for perception and generation. Visual generators can produce photorealistic frames without preserving a consistent 3D scene. We argue that this is not only a modeling problem but also a representation problem: generators typically evolve appearance-centric latents, while perception models recover geometry in a semantically rich space that encodes cross-view structure. Rather than adding geometry as another output, we reparameterize a geometry foundation model's features into a compact latent space for generation. We realize this shift with the geometry-native autoencoder (GAE), whose latent is jointly decodable to appearance, depth, cameras, and point maps. With this state, a standard conditional flow supports diverse generation tasks. In controlled comparisons that hold the generator and training protocol fixed, replacing the latent with GAE improves both visual quality and independently measured 3D coherence: FVD falls by $12.7\%$ and $23.1\%$ on RealEstate10K and DL3DV, and camera-trajectory error is halved on RealEstate10K. Together, these results show that the latent space is central to geometry-consistent generation and can serve as a shared interface between perception and generation.

Visual Geometry Grounded Transformers (VGGT) have set new benchmarks in high-fidelity 3D scene reconstruction. However, as the sequence length increases, these models suffer from catastrophic geometric forgetting and accumulation drift, primarily due to the quadratic complexity of global attention which necessitates truncated temporal windows. To overcome the resulting geometric drift, we present Mamba-VGGT, an enhanced VGGT framework capable of persistent long-range reasoning. Our key contribution is a Sliding Window Mamba (SWM) memory module that maintains an explicit external memory token across temporal windows. This module leverages selective state-space modeling to distill and propagate global geometric priors, effectively bypassing the memory constraints of traditional transformers. To integrate these long-term temporal cues without disrupting the highly optimized spatial features of the pre-trained VGGT, we propose a Zero-Init Spatial Memory Injector. Utilizing zero-convolutional layers, this injector adaptively fuses persistent memory into the patch token stream, ensuring structural stability and seamless feature alignment. Extensive experiments demonstrate that our approach significantly outperforms existing VGGT-based methods in maintaining spatial consistency and reducing trajectory accumulation errors. Our work provides a scalable, linear-complexity solution for geometry-grounded world modeling in extensive 3D environments.

Visual Geometry Grounded Transformer (VGGT) recovers dense 3D scene structure from multi-view images in one forward pass, but quadratic cross-frame attention limits its scalability. Existing training-free accelerators reduce computation uniformly along one axis, missing layer heterogeneity. Our spectral, probing, and causal analyses reveal three regimes: shallow layers lack cross-view structure, middle layers drive cross-view alignment, and deep layers are redundant for dense geometry yet their cross-frame attention remains essential for pose. RegimeVGGT applies layer-wise U-shaped compression along two axes: Saliency-Guided Banded Merging protects geometry- and edge-salient tokens, while Selectively Protected K/V Downsampling preserves cross-frame spatial coverage and the pose-critical path through a phase-shifted spatial grid, a reference-frame anchor, and uncompressed camera/register tokens. Training-free, RegimeVGGT achieves a 6.7x speedup over VGGT* at matched reconstruction quality.