Learning interaction terms for flow-matching methods

Determine whether techniques from inverse problems can overcome the difficulty that conditional paths must be computed in advance, thereby enabling flow-matching methods to learn interaction terms directly from data.

Background

The paper contrasts TP-DATE with CytoBridge, which incorporates interaction terms directly into the dynamical constraint and can, in principle, learn those interactions using a NeuralODE. Flow-matching methods face an additional difficulty because interaction-dependent conditional paths generally need to be computed before training. The authors identify the use of inverse-problem techniques to overcome this limitation as an unresolved research direction.

References

Whether techniques from inverse problems can be used to overcome this limitation and enable flow matching methods to learn such interactions from the data is therefore a very interesting direction for future research.

— Dynamic Generalized Gromov-Wasserstein Optimal Transport  (2609.20008 - Ying et al., 17 Sep 2026) in Appendix, Section “Relations to other works,” subsection “CytoBridge”