Data Generation without Function Estimation
This work addresses a fundamental bottleneck in generative modeling for researchers and practitioners by offering a potentially more efficient alternative to existing methods, though it appears incremental as it builds on recent advances in physics.
The paper tackles the challenge of avoiding computationally and statistically expensive function estimation in generative models by proposing an estimation-free method that deterministically updates point locations to transport a uniform distribution to arbitrary data distributions. The result is a novel generative approach that eliminates the need for function estimation, neural network training, and noise injection, supported by theoretical and experimental validation.
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.