# UOT-Gap: A Variational Principle for the Modality Gap in Vision-Language Models via Unbalanced Optimal Transport

arXiv: https://arxiv.org/abs/2609.10224 · HTML: https://mlsanity.com/paper/2609.10224/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in MLLM training and visual instruction tuning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Placed in

- Multimodal LLMs / vision-language models / [MLLM training and visual instruction tuning](https://mlsanity.com/mllm/mllm-training-and-visual-instruction-tuning/)

## Builds on (most cited first, 15 of 15)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [ViLBERT: Pretraining Task-Agnostic Visiolinguistic Representations for Vision-and-Language Tasks](https://mlsanity.com/paper/1908.02265/) (2019)
- [Deep Visual-Semantic Alignments for Generating Image Descriptions](https://mlsanity.com/paper/1412.2306/) (2014)
- [Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning](https://mlsanity.com/paper/2203.02053/) (2022)
- [On Unbalanced Optimal Transport: An Analysis of Sinkhorn Algorithm](https://mlsanity.com/paper/2002.03293/) (2020)
- [Identifiability Results for Multimodal Contrastive Learning](https://mlsanity.com/paper/2303.09166/) (2023)
- [Two Effects, One Trigger: On the Modality Gap, Object Bias, and Information Imbalance in Contrastive Vision-Language Models](https://mlsanity.com/paper/2404.07983/) (2024)
- [Explaining and Mitigating the Modality Gap in Contrastive Multimodal Learning](https://mlsanity.com/paper/2412.07909/) (2024)

## Abstract (arXiv)

Vision-language models such as CLIP embed images and text in a shared space, where modality-specific distributions often remain separated. Existing accounts connect this modality gap to initialization, contrastive dynamics, and information imbalance, while its distributional and pairwise contributions to retrieval remain unresolved. We introduce UOT-Gap, a training-free variational diagnostic that models frozen image and text embeddings with unbalanced entropic optimal transport (UOT). The UOT optimum separates transport, coupling complexity, and marginal mass variation; a complementary pair-aware residual compares observed image-caption pairs with the UOT soft matching. On Flickr8K and COCO-1K with frozen CLIP, OpenCLIP, and SigLIP encoders, caption degradation reduces Flickr8K Recall@1 from 0.559 to 0.003. Across six dataset-model conditions, the pair-aware residual tracks retrieval degradation with mean absolute Spearman 0.973, compared with 0.392 for the mean gap. The association remains stable across five random COCO-1K subsets at 0.954±0.026, with a minimum of 0.943. UOT barycentric updates reduce the transport objective while degrading retrieval, distinguishing geometric objective descent from task improvement. These results establish UOT-Gap as a diagnostic for caption quality, modality alignment, and retrieval robustness.