# Weakly-Supervised Learning of Dense Functional Correspondences

arXiv: https://arxiv.org/abs/2509.03893 · HTML: https://mlsanity.com/paper/2509.03893/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in VLM benchmarks and visual reasoning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 73 of its 100 references that are in the map.
- First posted on arXiv 4 Sep 2025.

## Placed in

- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 30 of 73)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [Depth Anything: Unleashing the Power of Large-Scale Unlabeled Data](https://mlsanity.com/paper/2401.10891/) (2024)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [Objaverse-XL: A Universe of 10M+ 3D Objects](https://mlsanity.com/paper/2307.05663/) (2023)
- [CogVLM: Visual Expert for Pretrained Language Models](https://mlsanity.com/paper/2311.03079/) (2023)
- [Common Objects in 3D: Large-Scale Learning and Evaluation of Real-life 3D Category Reconstruction](https://mlsanity.com/paper/2109.00512/) (2021)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [Emergent Correspondence from Image Diffusion](https://mlsanity.com/paper/2306.03881/) (2023)
- [Segment Anything in High Quality](https://mlsanity.com/paper/2306.01567/) (2023)
- [Deep ViT Features as Dense Visual Descriptors](https://mlsanity.com/paper/2112.05814/) (2021)
- [OmniObject3D: Large-Vocabulary 3D Object Dataset for Realistic Perception, Reconstruction and Generation](https://mlsanity.com/paper/2301.07525/) (2023)
- [A Tale of Two Features: Stable Diffusion Complements DINO for Zero-Shot Semantic Correspondence](https://mlsanity.com/paper/2305.15347/) (2023)
- [SPHINX: The Joint Mixing of Weights, Tasks, and Visual Embeddings for Multi-modal Large Language Models](https://mlsanity.com/paper/2311.07575/) (2023)

## Built on by (most cited first, 2 of 2)

- [Tac-DINO: Learning Vision-Tactile Features with Patch Alignment](https://mlsanity.com/paper/2606.12069/) (2026)
- [GROW2: Grounding Which and Where for Robot Tool Use](https://mlsanity.com/paper/2606.30632/) (2026)

## Abstract (arXiv)

Establishing dense correspondences across image pairs is essential for tasks such as shape reconstruction and robot manipulation. In the challenging setting of matching across different categories, the function of an object, i.e., the effect that an object can cause on other objects, can guide how correspondences should be established. This is because object parts that enable specific functions often share similarities in shape and appearance. We derive the definition of dense functional correspondence based on this observation and propose a weakly-supervised learning paradigm to tackle the prediction task. The main insight behind our approach is that we can leverage vision-language models to pseudo-label multi-view images to obtain functional parts. We then integrate this with dense contrastive learning from pixel correspondences to distill both functional and spatial knowledge into a new model that can establish dense functional correspondence. Further, we curate synthetic and real evaluation datasets as task benchmarks. Our results demonstrate the advantages of our approach over baseline solutions consisting of off-the-shelf self-supervised image representations and grounded vision language models.