# Data Generation without Function Estimation

arXiv: https://arxiv.org/abs/2507.08239 · HTML: https://mlsanity.com/paper/2507.08239/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 48 references that are in the map.
- First posted on arXiv 11 Jul 2025.

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport](https://mlsanity.com/paper/1805.09545/) (2018)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights](https://mlsanity.com/paper/1503.01243/) (2015)
- [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)
- [Proximal Optimal Transport Modeling of Population Dynamics](https://mlsanity.com/paper/2106.06345/) (2021)
- [Large-Scale Wasserstein Gradient Flows](https://mlsanity.com/paper/2106.00736/) (2021)
- [PFGM++: Unlocking the Potential of Physics-Inspired Generative Models](https://mlsanity.com/paper/2302.04265/) (2023)
- [Optimal score estimation via empirical Bayes smoothing](https://mlsanity.com/paper/2402.07747/) (2024)
- [Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networks](https://mlsanity.com/paper/2106.00774/) (2021)
- [Variational Wasserstein gradient flow](https://mlsanity.com/paper/2112.02424/) (2021)
- [Stochastic Particle Gradient Descent for Infinite Ensembles](https://mlsanity.com/paper/1712.05438/) (2017)
- [Efficient Gradient Flows in Sliced-Wasserstein Space](https://mlsanity.com/paper/2110.10972/) (2021)
- [Revisiting the Role of Euler Numerical Integration on Acceleration and Stability in Convex Optimization](https://mlsanity.com/paper/2102.11537/) (2021)
- [Field Matching: an Electrostatic Paradigm to Generate and Transfer Data](https://mlsanity.com/paper/2502.02367/) (2025)
- [Efficient displacement convex optimization with particle gradient descent](https://mlsanity.com/paper/2302.04753/) (2023)
- [Minimizers for an aggregation model with attractive-repulsive interaction](https://mlsanity.com/paper/2307.13769/) (2023)
- [Cryptographic Hardness of Score Estimation](https://mlsanity.com/paper/2404.03272/) (2024)

## Built on by (most cited first, 1 of 1)

- [Transformers as In-Context Samplers: From Closed-Form Diffusion to Estimation-Free Sampling](https://mlsanity.com/paper/2609.08981/) (2026)

## Abstract (arXiv)

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.