Lagrangian flow matching reformulates flow matching paths via the least-action principle, recovering optimal-transport and trigonometric diffusion paths as special cases of kinetic and harmonic Lagrangians while enabling new paths.
arXiv preprint arXiv:2504.10612 , year=
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Wasserstein Lagrangian Mechanics formalizes second-order dynamics in Wasserstein space and provides an algorithm to learn them from observed marginals without specifying the Lagrangian, outperforming gradient flows on various dynamics.
Training and sampling in static scalar energy generative models are two instances of the same Lyapunov-driven density transport dynamics on Wasserstein space, differing only by initial condition, which yields a finite stopping criterion for Langevin sampling and additive composition rules that keep
EnFlow integrates flow-based conformer generation with energy landscape modeling to enable joint ensemble generation and ground-state identification using only 1-2 ODE steps.
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Lagrangian Flow Matching: A Least-Action Framework for Principled Path Design
Lagrangian flow matching reformulates flow matching paths via the least-action principle, recovering optimal-transport and trigonometric diffusion paths as special cases of kinetic and harmonic Lagrangians while enabling new paths.
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Wasserstein Lagrangian Mechanics formalizes second-order dynamics in Wasserstein space and provides an algorithm to learn them from observed marginals without specifying the Lagrangian, outperforming gradient flows on various dynamics.
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Training and sampling in static scalar energy generative models are two instances of the same Lyapunov-driven density transport dynamics on Wasserstein space, differing only by initial condition, which yields a finite stopping criterion for Langevin sampling and additive composition rules that keep
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