# Minimizing f-Divergences by Interpolating Velocity Fields

arXiv: https://arxiv.org/abs/2305.15577 · HTML: https://mlsanity.com/paper/2305.15577/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 50 references that are in the map.
- First posted on arXiv 24 May 2023.

## Builds on (most cited first, 20 of 20)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem](https://mlsanity.com/paper/1802.08089/) (2018)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation](https://mlsanity.com/paper/2006.00702/) (2020)
- [HyperImpute: Generalized Iterative Imputation with Automatic Model Selection](https://mlsanity.com/paper/2206.07769/) (2022)
- [SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence](https://mlsanity.com/paper/2006.02509/) (2020)
- [Refining Deep Generative Models via Discriminator Gradient Flow](https://mlsanity.com/paper/2012.00780/) (2020)
- [Deep Generative Learning via Variational Gradient Flow](https://mlsanity.com/paper/1901.08469/) (2019)
- [Projected Wasserstein gradient descent for high-dimensional Bayesian inference](https://mlsanity.com/paper/2102.06350/) (2021)
- [Divergence Optimization for Noisy Universal Domain Adaptation](https://mlsanity.com/paper/2104.00246/) (2021)
- [MonoFlow: Rethinking Divergence GANs via the Perspective of Wasserstein Gradient Flows](https://mlsanity.com/paper/2302.01075/) (2023)
- [Density Ratio Estimation and Neyman Pearson Classification with Missing Data](https://mlsanity.com/paper/2302.10655/) (2023)

## Built on by (most cited first, 8 of 8)

- [Density Ratio Estimation with Conditional Probability Paths](https://mlsanity.com/paper/2502.02300/) (2025)
- [Missing Data Imputation by Reducing Mutual Information with Rectified Flows](https://mlsanity.com/paper/2505.11749/) (2025)
- [Statistical and Geometrical properties of regularized Kernel Kullback-Leibler divergence](https://mlsanity.com/paper/2408.16543/) (2024)
- [Guiding Time-Varying Generative Models with Natural Gradients on Exponential Family Manifold](https://mlsanity.com/paper/2502.07650/) (2025)
- [Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspective](https://mlsanity.com/paper/2602.01182/) (2026)
- [Generative Modeling under Non-Monotone MAR Missingness via Approximate Wasserstein Gradient Flows](https://mlsanity.com/paper/2604.04567/) (2026)
- [Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimization](https://mlsanity.com/paper/2606.27767/) (2026)
- [Sobolev Regularized Score Difference Estimation in Diffusion Models](https://mlsanity.com/paper/2608.18237/) (2026)

## Abstract (arXiv)

Many machine learning problems can be seen as approximating a textittarget distribution using a textitparticle distribution by minimizing their statistical discrepancy. Wasserstein Gradient Flow can move particles along a path that minimizes the f-divergence between the target and particle distributions. To move particles, we need to calculate the corresponding velocity fields derived from a density ratio function between these two distributions. Previous works estimated such density ratio functions and then differentiated the estimated ratios. These approaches may suffer from overfitting, leading to a less accurate estimate of the velocity fields. Inspired by non-parametric curve fitting, we directly estimate these velocity fields using interpolation techniques. We prove that our estimators are consistent under mild conditions. We validate their effectiveness using novel applications on domain adaptation and missing data imputation.