Data Generation without Function Estimation

Estimating the score function (or other population-density-dependent functions) is a fundamental component of most generative models. However, such function estimation is computationally and statistically challenging. Can we avoid function estimation for data generation? We propose an estimation-free generative method: A set of points whose locations are deterministically updated with (inverse) gradient descent can transport a uniform distribution to arbitrary data distribution, in the mean field regime, without function estimation, training neural networks, and even noise injection. The proposed method is built upon recent advances in the physics of interacting particles. We show, both theoretically and experimentally, that these advances can be leveraged to develop novel generative methods.