Modeling Depth Ambiguity: A Mixture-Density Representation for Flying-Point-Free Depth Estimation

Monocular depth foundation models generalize well across scenes, yet they are typically optimized with uniform pixel-wise objectives that do not distinguish user-specified or task-relevant target regions from the surrounding context. We therefore introduce Focusable Monocular Depth Estimation (FDE), a region-aware depth estimation task in which, given a specified target region, the model is required to prioritize foreground depth accuracy, preserve sharp boundary transitions, and maintain coherent global scene geometry. To prioritize task-critical region modeling, we propose FocusDepth, a prompt-conditioned monocular relative depth estimation framework that guides depth modeling to focus on target regions via box/text prompts. The core Multi-Scale Spatial-Aligned Fusion (MSSA) in FocusDepth spatially aligns multi-scale features from Segment Anything Model 3 to the Depth Anything family and injects them through scale-specific, gated conditional fusion. This enables dense prompt cue injection without disrupting geometric representations, thereby endowing the depth estimation model with focused perception capability. To study FDE, we establish FDE-Bench, a target-centric monocular relative depth benchmark built from image-target-depth triplets across five datasets, containing 252.9K/72.5K train/val triplets and 972 categories spanning real-world and embodied simulation environments. On FDE-Bench, FocusDepth consistently improves over globally fine-tuned DA2/DA3 baselines under both box and text prompts, with the largest gains appearing in target boundary and foreground regions while preserving global scene geometry. Ablations show that MSSA's spatial alignment is the key design factor, as disrupting prompt-geometry correspondence increases AbsRel by up to 13.8%.

This work presents $\textbf{Lapis}$, a $\textbf{l}$inear-$\textbf{a}$ttention-based $\textbf{pi}$xel-$\textbf{s}$pace generative framework that achieves efficient and high-fidelity depth estimation with one-step diffusion. While generative frameworks have significantly advanced monocular depth estimation with superior detail fidelity, the $\mathcal{O}(N^2)$ complexity of standard attention and the multi-step denoising process introduce prohibitive computational costs when scaling them to high-resolution image applications. Although linear attention and one-step prediction are intuitively viable, directly applying them leads to poor structural consistency, detail loss, and noise. Lapis rectifies these limitations through a coarse-to-fine hierarchy. Specifically, a Patch-level Consistency Module restores structural coherence by integrating semantic and spatial priors. Subsequently, a Pixel-level Refinement Module recovers sharp geometric boundaries via skip-connection-based pixel correspondence. Furthermore, to mitigate sampling noise inherent in one-step diffusion, we leverage the manifold assumption and adopt a direct $\mathbf{x}$-prediction strategy to target the clean data manifold. Extensive evaluations on multiple benchmarks demonstrate that Lapis consistently achieves state-of-the-art (SOTA) accuracy and boundary sharpness across various resolutions, reducing inference latency by up to 7.6$\times$ at 1080P and 10.9$\times$ at 1440P resolution compared to previous SOTA generative models.

Transparent objects are common in daily life, and it is important to understand their multilayer depth, including the transparent surface and the objects behind it. Existing methods for multilayer depth typically extend single-layer prediction. They define layers by the front-to-back ordering of 3D points and predict the layers sequentially. However, as layered geometry can admit multiple valid groupings of 3D points into layers, a predefined grouping strategy is inherently restrictive. In this work, we propose SeeGroup, a multi-layer depth estimation method that avoids imposing a predefined grouping and allows the model itself to adaptively assign surfaces to depth maps. We formulate per-pixel multi-layer depth as a point process, treating depth layers as unordered events along each camera ray. This induces a permutation-invariant likelihood over the observed depth layers, yielding a loss that naturally supports arbitrary layer groupings. Experiments demonstrate that our method significantly advances the state of the art of multi-layer depth estimation, improving quadruplet relative depth accuracy on LayeredDepth benchmark from 61.34% to 70.09%. Code is available at https://github.com/princeton-vl/SeeGroup.