Simultaneous Learning of Optimal Transports for Training All-to-All Flow-Based Condition Transfer Model

• URL: http://arxiv.org/abs/2504.03188v1
• Date: Fri, 04 Apr 2025 05:32:54 GMT
• Title: Simultaneous Learning of Optimal Transports for Training All-to-All Flow-Based Condition Transfer Model
• Authors: Kotaro Ikeda, Masanori Koyama, Jinzhe Zhang, Kohei Hayashi, Kenji Fukumizu,
• Abstract summary: We introduce a novel cost function that enables simultaneous learning of optimal transports for all pairs of conditional distributions.<n>Our method is supported by a theoretical guarantee that, in the limit, it converges to pairwise optimal transports among infinite pairs of conditional distributions.<n>The learned transport maps are subsequently used to couple data points in conditional flow matching.
• Score: 19.71452214879951
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we propose a flow-based method for learning all-to-all transfer maps among conditional distributions, approximating pairwise optimal transport. The proposed method addresses the challenge of handling 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 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 where continuous physical properties are defined as conditions.

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