# Approximate inference with Wasserstein gradient flows

arXiv: https://arxiv.org/abs/1806.04542 · HTML: https://mlsanity.com/paper/1806.04542/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2018.

## Built on by (most cited first, 12 of 12)

- [Large-Scale Wasserstein Gradient Flows](https://mlsanity.com/paper/2106.00736/) (2021)
- [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)
- [Sqrt(d) Dimension Dependence of Langevin Monte Carlo](https://mlsanity.com/paper/2109.03839/) (2021)
- [Scalable Wasserstein Gradient Flow for Generative Modeling through Unbalanced Optimal Transport](https://mlsanity.com/paper/2402.05443/) (2024)
- [Efficient Gradient Flows in Sliced-Wasserstein Space](https://mlsanity.com/paper/2110.10972/) (2021)
- [Mean-field Variational Inference via Wasserstein Gradient Flow](https://mlsanity.com/paper/2207.08074/) (2022)
- [Wasserstein Proximal of GANs](https://mlsanity.com/paper/2102.06862/) (2021)
- [Dynamic Flows on Curved Space Generated by Labeled Data](https://mlsanity.com/paper/2302.00061/) (2023)
- [Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimization](https://mlsanity.com/paper/2205.13098/) (2022)
- [Adaptive Annealed Importance Sampling with Constant Rate Progress](https://mlsanity.com/paper/2306.15283/) (2023)
- [Proximal Mean Field Learning in Shallow Neural Networks](https://mlsanity.com/paper/2210.13879/) (2022)

## Abstract (arXiv)

We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of implicit Euler steps that follow the gradients of a particular free energy functional. Existing methods for computing Wasserstein gradient flows rely on discretization of the domain of the diffusion, prohibiting their application to domains in more than several dimensions. We propose instead a discretization-free inference method that computes the Wasserstein gradient flow directly in a space of continuous functions. We characterize approximation properties of the proposed method and evaluate it on a nonlinear filtering task, finding performance comparable to the state-of-the-art for filtering diffusions.