# JLD: Perceptual Distance Through A Jacobian Lens

arXiv: https://arxiv.org/abs/2610.05967 · HTML: https://mlsanity.com/paper/2610.05967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 46 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 22 of 22)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [VideoMAE: Masked Autoencoders are Data-Efficient Learners for Self-Supervised Video Pre-Training](https://mlsanity.com/paper/2203.12602/) (2022)
- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [DreamSim: Learning New Dimensions of Human Visual Similarity using Synthetic Data](https://mlsanity.com/paper/2306.09344/) (2023)
- [Gradient Magnitude Similarity Deviation: A Highly Efficient Perceptual Image Quality Index](https://mlsanity.com/paper/1308.3052/) (2013)
- [PIPAL: a Large-Scale Image Quality Assessment Dataset for Perceptual Image Restoration](https://mlsanity.com/paper/2007.12142/) (2020)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [PieAPP: Perceptual Image-Error Assessment through Pairwise Preference](https://mlsanity.com/paper/1806.02067/) (2018)
- [Verbalizable Representations Form a Global Workspace in Language Models](https://mlsanity.com/paper/2607.15495/) (2026)
- [Eigen-Distortions of Hierarchical Representations](https://mlsanity.com/paper/1710.02266/) (2017)
- [DeepWSD: Projecting Degradations in Perceptual Space to Wasserstein Distance in Deep Feature Space](https://mlsanity.com/paper/2208.03323/) (2022)
- [DeepDC: Deep Distance Correlation as a Perceptual Image Quality Evaluator](https://mlsanity.com/paper/2211.04927/) (2022)
- [Discriminating image representations with principal distortions](https://mlsanity.com/paper/2410.15433/) (2024)
- [FishBack: Pullback Fisher Geometry for Optimal Activation Steering in Transformers](https://mlsanity.com/paper/2605.17231/) (2026)
- [The Unreasonable Effectiveness of Linear Prediction as a Perceptual Metric](https://mlsanity.com/paper/2310.05986/) (2023)
- [Perceptual Scales Predicted by Fisher Information Metrics](https://mlsanity.com/paper/2310.11759/) (2023)
- [Learning a distance measure from the information-estimation geometry of data](https://mlsanity.com/paper/2510.02514/) (2025)

## Abstract (arXiv)

Image compression, restoration, and generation all require a way to measure how different two images look to a person. Pixel error ignores how people see, while the most accurate perceptual distances are typically fitted to human judgments, tying them to a fixed data and resolution. For example, when image resolution is doubled, the correlation of DISTS with human scores on TID2013 drops from 0.815 to 0.717. We introduce the Jacobian Lens Distance (JLD), which derives its perceptual geometry from a frozen vision encoder rather than from human labels. JLD combines the locality of early patch features with the perceptual sensitivity captured by later encoder representations. Specifically, we use the encoder Jacobian to identify directions in the early feature space that most strongly affect the encoder output, producing a fixed metric tensor, E[J^top J], which we call the Jacobian lens. The lens is fitted only once from 100 unlabeled images, taking about 35 seconds. Locally, this construction defines a pullback metric in pixel space, giving JLD a clear geometric interpretation that can be directly analyzed on real images. Across four standard perceptual databases, JLD achieves state-of-the-art performance and consistently outperforms LPIPS, DISTS, PieAPP, and DreamSim. JLD is also robust to changes in image resolution, on TID2013, its lens-term correlation remains nearly unchanged when the resolution is doubled, decreasing only from 0.850 to 0.845. We further introduce JLD-fast, which is 4× faster than LPIPS-VGG while achieving a mean correlation of 0.911. Finally, JLD naturally extends to video, reaching a correlation of 0.786 on Waterloo IVC 4K compared with 0.611 for VMAF.