SeeSE3: Emergence of 3D Space in Vision Features

In this paper, we ask whether vision foundation models construct representations that reflect the intrinsic properties of 3D Euclidean space. Unlike previous works that probe 3D awareness of vision features by regressing image-centric quantities such as depth or normals, we investigate the relation between the structure of the space of visual features and the group of Euclidean transformations $SE(3)$. We propose a set of probes to evaluate this relation from both topological and geometric perspectives: a mutual neighborhood metric that measures the alignment between feature neighborhoods and spatial topology, and a Poincaré Adapter to test the linear accessibility of the geometry of camera motion from latent displacements in static scenes. We show that self-supervised vision models, which, in principle, have not been trained with direct 3D supervision or active agency, possess latent subspaces that are remarkably strongly correlated with three-dimensional Euclidean space, when probed correctly. Building on this insight we propose a new class of "Latent-Space Navigation" techniques that perform visual odometry and localization purely in the latent space, bypassing the need for explicit 3D reconstruction.

Gen4U: Unifying Video Generation and Understanding via Diffusion

Prior work suggests that diffusion representations capture low-level geometry but struggle with high-level semantics. We demonstrate that state-of-the-art video diffusion models overcome this limitation. By systematically probing their intermediate activations using recent mutual-kNN alignment metrics, we reveal a highly structured latent space where visual representations evolve across both network depth and noise levels. We show that while moderate noise levels yield linearly separable global semantics, fine-grained details persist at lower noise levels but become spatially scattered, requiring attention mechanisms to decode. Building on these insights, we introduce Gen4U (Generation for Understanding), a framework that repurposes these generative representations with a single forward pass. Our experiments establish that frozen, large-scale video diffusion models function as highly competitive video encoders across a wide spectrum of tasks, spanning semantic and non-semantic objectives (video classification, depth estimation, camera pose estimation, image and video captioning). Bypassing fine-tuning, Gen4U unifies the generation and understanding paradigms, achieving strong perception performance while fully preserving the model's ability to generate high-quality video.

The Art of Interrogation: Consistency Amplifies Factuality in Spatial Reasoning

Current Large Reasoning Models (LRMs) exhibit remarkable general capabilities but significantly underperform in spatial reasoning tasks. Existing approaches treat this gap as a knowledge deficit, relying on supervised fine-tuning (SFT) to ingest labeled spatial data from external vision sources or synthetic engines. In contrast, we argue that for many tasks, spatial reasoning capabilities are already present in pre-trained LRMs but require alignment through logical coherence under geometric 2D and 3D constraints. In this work, we propose a self-supervised reinforcement learning (RL) framework that targets the internal reasoning process without requiring ground-truth annotations. By formalizing the notion of consistency verifiers -- reward functions that check for geometric and semantic consistency under transformations -- we demonstrate that models can improve their spatial reasoning abilities. We use both image transformations, like flipping, and textual transformations, like swapping the order of objects in the question, and propose a new optimal transport-based RL strategy, OT-GRPO, which is a minimal-matching variant of group relative policy optimization tailored to pairwise verifiers. We show that this label-free consistency training approaches the accuracy of models trained with ground-truth supervision and achieves similar generalization across diverse tasks and data domains.

FILTR: Extracting Topological Features from Pretrained 3D Models

Recent advances in pretraining 3D point cloud encoders (e.g., Point-BERT, Point-MAE) have produced powerful models, whose abilities are typically evaluated on geometric or semantic tasks. At the same time, topological descriptors have been shown to provide informative summaries of a shape's multiscale structure. In this paper we pose the question whether topological information can be derived from features produced by 3D encoders. To address this question, we first introduce DONUT, a synthetic benchmark with controlled topological complexity, and propose FILTR (Filtration Transformer), a learnable framework to predict persistence diagrams directly from frozen encoders. FILTR adapts a transformer decoder to treat diagram generation as a set prediction task. Our analysis on DONUT reveals that existing encoders retain only limited global topological signals, yet FILTR successfully leverages information produced by these encoders to approximate persistence diagrams. Our approach enables, for the first time, data-driven extraction of persistence diagrams from raw point clouds through an efficient learnable feed-forward mechanism.

Beyond Prompts: Unconditional 3D Inversion for Out-of-Distribution Shapes

Text-driven inversion of generative models is a core paradigm for manipulating 2D or 3D content, unlocking numerous applications such as text-based editing, style transfer, or inverse problems. However, it relies on the assumption that generative models remain sensitive to natural language prompts. We demonstrate that for state-of-the-art native text-to-3D generative models, this assumption often collapses. We identify a critical failure mode where generation trajectories are drawn into latent ``sink traps'': regions where the model becomes insensitive to prompt modifications. In these regimes, changes to the input text fail to alter internal representations in a way that alters the output geometry. Crucially, we observe that this is not a limitation of the model's \textit{geometric} expressivity; the same generative models possess the ability to produce a vast diversity of shapes but, as we demonstrate, become insensitive to out-of-distribution \textit{text} guidance. We investigate this behavior by analyzing the sampling trajectories of the generative model, and find that complex geometries can still be represented and produced by leveraging the model's unconditional generative prior. This leads to a more robust framework for text-based 3D shape editing that bypasses latent sinks by decoupling a model's geometric representation power from its linguistic sensitivity. Our approach addresses the limitations of current 3D pipelines and enables high-fidelity semantic manipulation of out-of-distribution 3D shapes. Project webpage: https://daidedou.sorpi.fr/publication/beyondprompts

From Blobs to Spokes: High-Fidelity Surface Reconstruction via Oriented Gaussians

3D Gaussian Splatting (3DGS) has revolutionized fast novel view synthesis, yet its opacity-based formulation makes surface extraction fundamentally difficult. Unlike implicit methods built on Signed Distance Fields or occupancy, 3DGS lacks a global geometric field, forcing existing approaches to resort to heuristics such as TSDF fusion of blended depth maps. Inspired by the Objects as Volumes framework, we derive a principled occupancy field for Gaussian Splatting and show how it can be used to extract highly accurate watertight meshes of complex scenes. Our key contribution is to introduce a learnable oriented normal at each Gaussian element and to define an adapted attenuation formulation, which leads to closed-form expressions for both the normal and occupancy fields at arbitrary locations in space. We further introduce a novel consistency loss and a dedicated densification strategy to enforce Gaussians to wrap the entire surface by closing geometric holes, ensuring a complete shell of oriented primitives. We modify the differentiable rasterizer to output depth as an isosurface of our continuous model, and introduce Primal Adaptive Meshing for Region-of-Interest meshing at arbitrary resolution. We additionally expose fundamental biases in standard surface evaluation protocols and propose two more rigorous alternatives. Overall, our method Gaussian Wrapping sets a new state-of-the-art on DTU and Tanks and Temples, producing complete, watertight meshes at a fraction of the size of concurrent work-recovering thin structures such as the notoriously elusive bicycle spokes.

SceneTeract: Agentic Functional Affordances and VLM Grounding in 3D Scenes

Embodied AI depends on interactive 3D environments that support meaningful activities for diverse users, yet assessing their functional affordances remains a core challenge. We introduce SceneTeract, a framework that verifies 3D scene functionality under agent-specific constraints. Our core contribution is a grounded verification engine that couples high-level semantic reasoning with low-level geometric checks. SceneTeract decomposes complex activities into sequences of atomic actions and validates each step against accessibility requirements (e.g., reachability, clearance, and navigability) conditioned on an embodied agent profile, using explicit physical and geometric simulations. We deploy SceneTeract to perform an in-depth evaluation of (i) synthetic indoor environments, uncovering frequent functional failures that prevent basic interactions, and (ii) the ability of frontier Vision-Language Models (VLMs) to reason about and predict functional affordances, revealing systematic mismatches between semantic confidence and physical feasibility even for the strongest current models. Finally, we leverage SceneTeract as a reward engine for VLM post-training, enabling scalable distillation of geometric constraints into reasoning models. We release the SceneTeract verification suite and data to bridge perception and physical reality in embodied 3D scene understanding.

Generative Drifting is Secretly Score Matching: a Spectral and Variational Perspective

Generative Modeling via Drifting has recently achieved state-of-the-art one-step image generation through a kernel-based drift operator, yet the success is largely empirical and its theoretical foundations remain poorly understood. In this paper, we make the following observation: \emph{under a Gaussian kernel, the drift operator is exactly a score difference on smoothed distributions}. This insight allows us to answer all three key questions left open in the original work: (1) whether a vanishing drift guarantees equality of distributions ($V_{p,q}=0\Rightarrow p=q$), (2) how to choose between kernels, and (3) why the stop-gradient operator is indispensable for stable training. Our observations position drifting within the well-studied score-matching family and enable a rich theoretical perspective. By linearizing the McKean-Vlasov dynamics and probing them in Fourier space, we reveal frequency-dependent convergence timescales comparable to \emph{Landau damping} in plasma kinetic theory: the Gaussian kernel suffers an exponential high-frequency bottleneck, explaining the empirical preference for the Laplacian kernel. We also propose an exponential bandwidth annealing schedule $σ(t)=σ_0 e^{-rt}$ that reduces convergence time from $\exp(O(K_{\max}^2))$ to $O(\log K_{\max})$. Finally, by formalizing drifting as a Wasserstein gradient flow of the smoothed KL divergence, we prove that the stop-gradient operator is derived directly from the frozen-field discretization mandated by the JKO scheme, and removing it severs training from any gradient-flow guarantee. This variational perspective further provides a general template for constructing novel drift operators, demonstrated with a Sinkhorn divergence drift.

A Mixed Diet Makes DINO An Omnivorous Vision Encoder

Pre-trained vision encoders like DINOv2 have demonstrated exceptional performance on unimodal tasks. However, we observe that their feature representations are poorly aligned across different modalities. For instance, the feature embedding for an RGB image and its corresponding depth map of the same scene exhibit a cosine similarity that is nearly identical to that of two random, unrelated images. To address this, we propose the Omnivorous Vision Encoder, a novel framework that learns a modality-agnostic feature space. We train the encoder with a dual objective: first, to maximize the feature alignment between different modalities of the same scene; and second, a distillation objective that anchors the learned representations to the output of a fully frozen teacher such as DINOv2. The resulting student encoder becomes "omnivorous" by producing a consistent, powerful embedding for a given scene, regardless of the input modality (RGB, Depth, Segmentation, etc.). This approach enables robust cross-modal understanding while retaining the discriminative semantics of the original foundation model.

Beyond ReLU: Bifurcation, Oversmoothing, and Topological Priors

Graph Neural Networks (GNNs) learn node representations through iterative network-based message-passing. While powerful, deep GNNs suffer from oversmoothing, where node features converge to a homogeneous, non-informative state. We re-frame this problem of representational collapse from a \emph{bifurcation theory} perspective, characterizing oversmoothing as convergence to a stable ``homogeneous fixed point.'' Our central contribution is the theoretical discovery that this undesired stability can be broken by replacing standard monotone activations (e.g., ReLU) with a class of functions. Using Lyapunov-Schmidt reduction, we analytically prove that this substitution induces a bifurcation that destabilizes the homogeneous state and creates a new pair of stable, non-homogeneous \emph{patterns} that provably resist oversmoothing. Our theory predicts a precise, nontrivial scaling law for the amplitude of these emergent patterns, which we quantitatively validate in experiments. Finally, we demonstrate the practical utility of our theory by deriving a closed-form, bifurcation-aware initialization and showing its utility in real benchmark experiments.