Data Generation without Function Estimation

TL;DR

This paper introduces an estimation-free generative approach that transports a uniform distribution to complex data distributions using deterministic point updates, bypassing traditional function estimation and neural network training.

Contribution

The paper presents a novel data generation method that avoids function estimation by leveraging physics-inspired particle interactions and gradient descent, applicable in the mean field regime.

Findings

Method successfully transports uniform to data distribution without neural networks.

Theoretical analysis supports the effectiveness of the approach.

Experimental results demonstrate practical viability.

Abstract

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.