# Pairwise Optimal Transports for Training All-to-All Flow-Based Condition Transfer Model

arXiv: https://arxiv.org/abs/2504.03188 · HTML: https://mlsanity.com/paper/2504.03188/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 50 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Builds on (most cited first, 30 of 33)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [A Neural Algorithm of Artistic Style](https://mlsanity.com/paper/1508.06576/) (2015)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [Inversion-Based Style Transfer with Diffusion Models](https://mlsanity.com/paper/2211.13203/) (2022)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equations](https://mlsanity.com/paper/2207.06635/) (2022)
- [Talk-to-Edit: Fine-Grained Facial Editing via Dialog](https://mlsanity.com/paper/2109.04425/) (2021)
- [Stochastic interpolants with data-dependent couplings](https://mlsanity.com/paper/2310.03725/) (2023)
- [Learning Multimodal Graph-to-Graph Translation for Molecular Optimization](https://mlsanity.com/paper/1812.01070/) (2018)
- [Metric Flow Matching for Smooth Interpolations on the Data Manifold](https://mlsanity.com/paper/2405.14780/) (2024)
- [Functional Flow Matching](https://mlsanity.com/paper/2305.17209/) (2023)
- [Optimizing Molecules using Efficient Queries from Property Evaluations](https://mlsanity.com/paper/2011.01921/) (2020)
- [Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold](https://mlsanity.com/paper/2408.14608/) (2024)
- [Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching](https://mlsanity.com/paper/2403.18705/) (2024)
- [Conditional Optimal Transport on Function Spaces](https://mlsanity.com/paper/2311.05672/) (2023)
- [Dynamic Conditional Optimal Transport through Simulation-Free Flows](https://mlsanity.com/paper/2404.04240/) (2024)
- [Wasserstein Style Transfer](https://mlsanity.com/paper/1905.12828/) (2019)
- [Multimarginal generative modeling with stochastic interpolants](https://mlsanity.com/paper/2310.03695/) (2023)
- [Extended Flow Matching: a Method of Conditional Generation with Generalized Continuity Equation](https://mlsanity.com/paper/2402.18839/) (2024)

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

- [Flow Matching from Viewpoint of Proximal Operators](https://mlsanity.com/paper/2602.12683/) (2026)

## Abstract (arXiv)

In this paper, we propose a flow-based method for learning all-to-all transfer maps among conditional distributions that approximates pairwise optimal transport. The proposed method addresses the challenge of handling the case of continuous conditions, which often involve a large set of conditions with sparse empirical observations per condition. We introduce a novel cost function that enables simultaneous learning of optimal transports for all pairs of conditional distributions. Our method is supported by a theoretical guarantee that, in the limit, it converges to the pairwise optimal transports among infinite pairs of conditional distributions. The learned transport maps are subsequently used to couple data points in conditional flow matching. We demonstrate the effectiveness of this method on synthetic and benchmark datasets, as well as on chemical datasets in which continuous physical properties are defined as conditions. The code for this project can be found at https://github.com/kotatumuri-room/A2A-FM