arXiv:2601.06810v2 Announce Type: replace-cross Abstract: The Wasserstein-Fisher-Rao (WFR) metric extends dynamic optimal transport (OT) by coupling displacement with change of mass, providing a principled geometry for modeling unbalanced snapshot dynamics. Existing WFR solvers, however, are often unstable, computationally expensive, and difficult to scale. Here we introduce WFR Flow Matching (WFR-FM), a simulation-free training algorithm that unifies flow matching with dynamic unbalanced OT. Unlike classical flow matching which regresses only a transport vector field, WFR-FM simultaneously regresses a vector field for displacement and a scalar growth rate function for birth-death dynamics, yielding continuous flows under the WFR geometry. Theoretically, we show that minimizing the WFR-FM loss exactly recovers WFR geodesics. Empirically, WFR-FM yields more accurate and robust trajectory inference in single-cell biology, reconstructing consistent dynamics with proliferation and apoptosis, estimating time-varying growth fields, and applying to generative dynamics under imbalanced data. It outperforms state-of-the-art baselines in efficiency, stability, and reconstruction accuracy. Overall, WFR-FM establishes a unified and efficient paradigm for learning dynamical systems from unbalanced snapshots, where not only states but also mass evolve over time. The Python code is available at https://github.com/QiangweiPeng/WFR-FM.

arXiv:2603.29723v1 Announce Type: new Abstract: Retrosynthetic planning is a fundamental task in organic chemistry, yet remains challenging due to its combinatorial complexity. To address this, conventional approaches typically rely on hybrid frameworks that combine single-step predictions with external search heuristics, inevitably fracturing the logical coherence between local molecular transformations and global planning objectives. To bridge this gap and embed sophisticated strategic foresight directly into the model's chemical reasoning, we introduce ReTriP, an end-to-end generative framework that reformulates retrosynthesis as a direct Chain-of-Thought reasoning task. We establish a path-coherent molecular representation and employ a progressive training curriculum that transitions from reasoning distillation to reinforcement learning with verifiable rewards, effectively aligning stepwise generation with practical route utility. Empirical evaluation on RetroBench demonstrates that ReTriP achieves state-of-the-art performance, exhibiting superior robustness in long-horizon planning compared to hybrid baselines.