Score-Free Energetic Variational Inference via Poisson–Nernst–Planck and Yukawa Dynamics

We develop a score-free framework for particle-based variational inference, built directly from the energy–dissipation law of a classical electrostatic system. Particle-based variational inference ordinarily requires the score of the target, which is unavailable for empirical, simulator-defined, or discrete-support targets, and score-free alternatives prescribe a kernel without physical justi- fication. We instead treat the particles as a cloud of positive charges and the target as a fixed negative-charge background, and evolve the particles along the Wasserstein gradient flow of the re- sulting electrostatic-plus-entropic free energy, which is the classical Poisson–Nernst–Planck (PNP) system. An implicit-Euler discretization of the energy–dissipation law within the energetic varia- tional framework turns each update into a proximal minimization with monotone free-energy de- crease. In high dimension, where the bare Coulomb kernel becomes stiff, we introduce a screened Yukawa variant that is positive definite and characteristic. On two-dimensional benchmarks, a high-dimensional Gaussian sweep, and image generation on MNIST and Fashion-MNIST, the re- sulting schemes match or exceed the strongest score-free particle baselines. Code is available at https://anonymous.4open.science/r/EVI-F322.