Rigorous stochastic treatment of SUDO and RUOT-like dynamics

Establish a rigorous theoretical formulation and analysis of stochastic dynamics for the SUDO framework and its regularized unbalanced optimal transport (RUOT)-like setting.

Background

The paper develops its theoretical formulation for deterministic UDOT, whose constraint is a continuity equation with a source term. It also presents an empirical stochastic extension for RUOT-like settings by replacing conditional unbalanced flow matching with conditional unbalanced score matching. However, the authors explicitly identify the absence of a rigorous treatment of these stochastic dynamics as an unresolved limitation.

References

First, while SUDO provides an empirical approach for RUOT-like settings, its theoretical formulation is currently developed for deterministic dynamics, leaving a rigorous treatment of stochastic dynamics for future work.

— Simulation-free Unbalanced Dynamic Optimal Transport with General Growth Penalty  (2609.04710 - Ying et al., 4 Sep 2026) in Section 6, “Conclusion”