Interaction of semidiscrete OT couplings with advanced or orthogonal flow-matching methods

Assess how semidiscrete optimal transport couplings—computed via the semidual potential vector g for a finite dataset and used to pair Gaussian noise samples with data points during flow matching—interact with more advanced or orthogonal methods built on flow matching, such as Reflow. Specifically, determine the effects of integrating semidiscrete couplings into these methodologies on training dynamics and generation performance.

Background

The paper introduces Semidiscrete Flow Matching (SD-FM), which leverages semidiscrete optimal transport to more efficiently pair noise and data for training flow-based generative models, avoiding the expensive batch optimal transport computations required by OT-FM. The authors present optimization tools for the semidiscrete dual potential, theoretical convergence analysis, and a generalized Tweedie identity, and demonstrate gains across unconditional, conditional, and mean-flow settings.

Beyond these demonstrated uses, the authors point out that SD couplings may also be applied within more complex approaches that build on flow matching, such as Reflow, which rectifies pretrained flows by repeatedly generating and re-matching samples. They explicitly leave the assessment of how SD couplings interact with such advanced or orthogonal FM extensions as future work.