# Language as Prior, Vision as Calibration: Metric Scale Recovery for Monocular Depth Estimation

arXiv: https://arxiv.org/abs/2601.01457 · HTML: https://mlsanity.com/paper/2601.01457/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 18 references that are in the map.
- First posted on arXiv 4 Jan 2026.

## Builds on (most cited first, 11 of 11)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Depth Anything V2](https://mlsanity.com/paper/2406.09414/) (2024)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [ZoeDepth: Zero-shot Transfer by Combining Relative and Metric Depth](https://mlsanity.com/paper/2302.12288/) (2023)
- [3D Packing for Self-Supervised Monocular Depth Estimation](https://mlsanity.com/paper/1905.02693/) (2019)
- [Prompting Depth Anything for 4K Resolution Accurate Metric Depth Estimation](https://mlsanity.com/paper/2412.14015/) (2024)
- [Can Language Understand Depth?](https://mlsanity.com/paper/2207.01077/) (2022)
- [WorDepth: Variational Language Prior for Monocular Depth Estimation](https://mlsanity.com/paper/2404.03635/) (2024)
- [RSA: Resolving Scale Ambiguities in Monocular Depth Estimators through Language Descriptions](https://mlsanity.com/paper/2410.02924/) (2024)

## Built on by (most cited first, 1 of 1)

- [X-Lens: Real-Time Metric Depth Estimation with Heterogeneous Cameras](https://mlsanity.com/paper/2607.12993/) (2026)

## Abstract (arXiv)

Relative-depth foundation models transfer well, yet monocular metric depth remains ill-posed due to unidentifiable global scale and heightened domain-shift sensitivity. Under a frozen-backbone calibration setting, we recover metric depth via an image-specific affine transform in inverse depth and train only lightweight calibration heads while keeping the relative-depth backbone and the CLIP text encoder fixed. Since captions provide coarse but noisy scale cues that vary with phrasing and missing objects, we use language to predict an uncertainty-aware envelope that bounds feasible calibration parameters in an unconstrained space, rather than committing to a text-only point estimate. We then use pooled multi-scale frozen visual features to select an image-specific calibration within this envelope. During training, a closed-form least-squares oracle in inverse depth provides per-image supervision for learning the envelope and the selected calibration. Experiments on NYUv2 and KITTI improve in-domain accuracy, while zero-shot transfer to SUN-RGBD and DDAD demonstrates improved robustness over strong language-only baselines.