Simulation-free formulation of CytoBridge

Determine whether CytoBridge can be converted into a fully simulation-free flow-matching formulation despite the loss of linearity or locality in its nonlocal dynamical constraint.

Background

CytoBridge models unbalanced mean-field Schrödinger bridge dynamics with interaction terms embedded directly in the dynamical equation. The paper explains that standard marginalization arguments underlying simulation-free flow matching no longer apply because this interaction makes the dynamical constraint nonlocal in the measure flow. The authors therefore leave open whether a simulation-free version of CytoBridge can be constructed, suggesting that travelling-pair flow matching may provide a possible starting point.

References

Another interesting question is whether CytoBridge can be made simulation-free.

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