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. Leveraging recent advances in mathematical physics, we prove that the proposed method samples from the true underlying data distribution in the asymptotic regime, without making any structural assumptions on the distribution.