# Diffusion Transport Alignment

arXiv: https://arxiv.org/abs/2206.07305 · HTML: https://mlsanity.com/paper/2206.07305/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 15 Jun 2022.

## Builds on (most cited first, 8 of 8)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [MAGAN: Aligning Biological Manifolds](https://mlsanity.com/paper/1803.00385/) (2018)
- [Kernel Manifold Alignment](https://mlsanity.com/paper/1504.02338/) (2015)
- [MIMA: MAPPER-Induced Manifold Alignment for Semi-Supervised Fusion of Optical Image and Polarimetric SAR Data](https://mlsanity.com/paper/1906.05512/) (2019)
- [Harmonic Alignment](https://mlsanity.com/paper/1810.00386/) (2018)
- [Multimodal Data Visualization and Denoising with Integrated Diffusion](https://mlsanity.com/paper/2102.06757/) (2021)
- [Optimal Transport for Deep Joint Transfer Learning](https://mlsanity.com/paper/1709.02995/) (2017)

## Built on by (most cited first, 7 of 7)

- [Multimodal Alignment and Fusion: A Survey](https://mlsanity.com/paper/2411.17040/) (2024)
- [Manifold Alignment with Label Information](https://mlsanity.com/paper/2210.12774/) (2022)
- [Graph Integration for Diffusion-Based Manifold Alignment](https://mlsanity.com/paper/2410.22978/) (2024)
- [Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets](https://mlsanity.com/paper/2407.01718/) (2024)
- [Guided Manifold Alignment with Geometry-Regularized Twin Autoencoders](https://mlsanity.com/paper/2509.22913/) (2025)
- [Changes from Classical Statistics to Modern Statistics and Data Science](https://mlsanity.com/paper/2211.03756/) (2022)
- [Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment](https://mlsanity.com/paper/2602.00974/) (2026)

## Abstract (arXiv)

The integration of multimodal data presents a challenge in cases when the study of a given phenomena by different instruments or conditions generates distinct but related domains. Many existing data integration methods assume a known one-to-one correspondence between domains of the entire dataset, which may be unrealistic. Furthermore, existing manifold alignment methods are not suited for cases where the data contains domain-specific regions, i.e., there is not a counterpart for a certain portion of the data in the other domain. We propose Diffusion Transport Alignment (DTA), a semi-supervised manifold alignment method that exploits prior correspondence knowledge between only a few points to align the domains. By building a diffusion process, DTA finds a transportation plan between data measured from two heterogeneous domains with different feature spaces, which by assumption, share a similar geometrical structure coming from the same underlying data generating process. DTA can also compute a partial alignment in a data-driven fashion, resulting in accurate alignments when some data are measured in only one domain. We empirically demonstrate that DTA outperforms other methods in aligning multimodal data in this semisupervised setting. We also empirically show that the alignment obtained by DTA can improve the performance of machine learning tasks, such as domain adaptation, inter-domain feature mapping, and exploratory data analysis, while outperforming competing methods.