Data Generation without Function Estimation

2025-07-10

AI Summary

Can high-fidelity data generation be achieved without estimating density-related quantities (e.g., score functions)? This paper introduces a deterministic particle-based generative paradigm: starting from a uniform point cloud, it iteratively transports particles via gradient descent on an interaction energy functional, progressively transforming the initial distribution into the target data distribution. The method requires no neural network training, function approximation, or stochastic noise injection; instead, it relies solely on mean-field dynamical modeling and pairwise particle interactions governed by a fully deterministic update rule. To our knowledge, this is the first generative framework that completely bypasses density estimation—either explicit or implicit. We establish theoretical convergence guarantees under mild assumptions and empirically demonstrate competitive sample quality across multiple benchmarks. Our approach opens a new, parameter-free pathway for generative modeling, decoupling distribution transformation from parametric function approximation.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

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.

Problem

• Avoid function estimation in data generation
• Propose estimation-free generative method
• Transport uniform to arbitrary distribution deterministically

Innovation

• Deterministic gradient descent updates points
• No function estimation or neural networks
• Leverages physics of interacting particles