AI RESEARCH
Liouville PDE-based sliced-Wasserstein flow
arXiv CS.LG
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ArXi:2505.17204v3 Announce Type: replace-cross The sliced Wasserstein flow (SWF), a nonparametric and implicit generative gradient flow, is transformed into a Liouville partial differential equation (PDE)-based formalism. First, the stochastic diffusive term from the Fokker-Planck equation-based Monte Carlo is reformulated as a Liouville PDE-based transport without the diffusive term, essentially reflecting the probability flow ODE. The involved density estimation is handled by normalizing flows of neural ODE without an explicitly defined score function.