# A Wasserstein Minimum Velocity Approach to Learning Unnormalized Models

arXiv: https://arxiv.org/abs/2002.07501 · HTML: https://mlsanity.com/paper/2002.07501/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2020.

## Built on by (most cited first, 9 of 9)

- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Estimating High Order Gradients of the Data Distribution by Denoising](https://mlsanity.com/paper/2111.04726/) (2021)
- [Target Score Matching](https://mlsanity.com/paper/2402.08667/) (2024)
- [Stable Target Field for Reduced Variance Score Estimation in Diffusion Models](https://mlsanity.com/paper/2302.00670/) (2023)
- [Stable Velocity: A Variance Perspective on Flow Matching](https://mlsanity.com/paper/2602.05435/) (2026)
- [Moment Matching Denoising Gibbs Sampling](https://mlsanity.com/paper/2305.11650/) (2023)
- [Variance reduction of diffusion model's gradients with Taylor approximation-based control variate](https://mlsanity.com/paper/2408.12270/) (2024)
- [Geometric constraints improve inference of sparsely observed stochastic dynamics](https://mlsanity.com/paper/2304.00423/) (2023)
- [Gaussian Process Tilted Nonparametric Density Estimation using Fisher Divergence Score Matching](https://mlsanity.com/paper/2504.03485/) (2025)

## Abstract (arXiv)

Score matching provides an effective approach to learning flexible unnormalized models, but its scalability is limited by the need to evaluate a second-order derivative. In this paper, we present a scalable approximation to a general family of learning objectives including score matching, by observing a new connection between these objectives and Wasserstein gradient flows. We present applications with promise in learning neural density estimators on manifolds, and training implicit variational and Wasserstein auto-encoders with a manifold-valued prior.