Depth ambiguity is a fundamental challenge in spatial scene understanding, especially in transparent scenes where single-depth estimates fail to capture full 3D structure. Existing models, limited to deterministic predictions, overlook real-world multi-layer depth. To address this, we introduce a paradigm shift from single-prediction to multi-hypothesis spatial foundation models. We first present \texttt{MD-3k}, a benchmark exposing depth biases in expert and foundational models through multi-layer spatial relationship labels and new metrics. To resolve depth ambiguity, we propose Laplacian Visual Prompting (LVP), a training-free spectral prompting technique that extracts hidden depth from pre-trained models via Laplacian-transformed RGB inputs. By integrating LVP-inferred depth with standard RGB-based estimates, our approach elicits multi-layer depth without model retraining. Extensive experiments validate the effectiveness of LVP in zero-shot multi-layer depth estimation, unlocking more robust and comprehensive geometry-conditioned visual generation, 3D-grounded spatial reasoning, and temporally consistent video-level depth inference. Our benchmark and code will be available at https://github.com/Xiaohao-Xu/Ambiguity-in-Space.

Visual geolocalization is a cost-effective and scalable task that involves matching one or more query images, taken at some unknown location, to a set of geo-tagged reference images. Existing methods, devoted to semantic features representation, evolving towards robustness to a wide variety between query and reference, including illumination and viewpoint changes, as well as scale and seasonal variations. However, practical visual geolocalization approaches need to be robust in appearance changing and extreme viewpoint variation conditions, while providing accurate global location estimates. Therefore, inspired by curriculum design, human learn general knowledge first and then delve into professional expertise. We first recognize semantic scene and then measure geometric structure. Our approach, termed CurriculumLoc, involves a delicate design of multi-stage refinement pipeline and a novel keypoint detection and description with global semantic awareness and local geometric verification. We rerank candidates and solve a particular cross-domain perspective-n-point (PnP) problem based on these keypoints and corresponding descriptors, position refinement occurs incrementally. The extensive experimental results on our collected dataset, TerraTrack and a benchmark dataset, ALTO, demonstrate that our approach results in the aforementioned desirable characteristics of a practical visual geolocalization solution. Additionally, we achieve new high recall@1 scores of 62.6% and 94.5% on ALTO, with two different distances metrics, respectively. Dataset, code and trained models are publicly available on https://github.com/npupilab/CurriculumLoc.