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conditional OT

Conditional optimal transport is an extension of optimal transport theory that determines the most cost-effective way to transform one probability distribution into another in the presence of auxiliary conditioning information or covariates. Rather than computing a single fixed transport map between two static distributions, conditional optimal transport parameterizes the transport problem across context variables, finding a family of optimal transport plans or maps that transform source conditional distributions into target conditional distributions for each given condition. This framework enables the transportation mapping to adapt dynamically to side information, making it valuable in machine learning and computational statistics for tasks such as conditional generative modeling, Bayesian inference, paired sample translation, and controlled data generation.

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