We show how to estimate a generative model from samples by parameterizing its score function as the electric field of a static charge distribution. The score function is given by the gradient of the model’s log-density, and as such, it must define a conservative vector field. By modeling the score as an electric field, we not only guarantee that it satisfies this curl-free constraint; we can also efficiently compute its divergence, via Maxwell’s equations, from a local charge density. We parameterize the score as a superposition of electric fields from spherically symmetric charge distributions and uniformly charged slabs. We estimate the coefficients in these superpositions by minimizing a Fisher divergence, and notably, the optimal coefficients are given by the closed-form solution of a regularized least-squares problem. On one hand, these models have a natural connection to energy-based models and product-of-expert models, and they include existing kernel estimators as a special case; on the other hand, they can be learned without recourse to iterative gradient-based methods. We present the results of experiments on synthetic data sets as well as problems of higher dimensionality. Our results show that these charge-based models perform competitively with neural and kernel-based baselines, and they do so while using fewer parameters, learning more efficiently, and yielding more geometrically interpretable densities.