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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VS3D performs local 3D asset editing by injecting reconstruction-anchored source signals, partial-mean guidance, and twin-agreement residuals into the velocity sampler to control edit strength and preserve identity.
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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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Velocity-Space 3D Asset Editing
VS3D performs local 3D asset editing by injecting reconstruction-anchored source signals, partial-mean guidance, and twin-agreement residuals into the velocity sampler to control edit strength and preserve identity.