Neural solver for Wasserstein Geodesics and optimal transport dynamics

• URL: http://arxiv.org/abs/2602.22003v1
• Date: Wed, 25 Feb 2026 15:21:24 GMT
• Title: Neural solver for Wasserstein Geodesics and optimal transport dynamics
• Authors: Hailiang Liu, Yan-Han Chen,
• Abstract summary: We introduce a sample-based neural solver for computing the Wasserstein geodesic between a source and target distribution.<n>We recast the constrained optimization as a minimax problem, using deep neural networks to approximate the relevant functions.<n>We demonstrate the effectiveness of our method through experiments on both synthetic and real datasets.
• Score: 2.4493299476776778
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce a sample-based neural solver for computing the Wasserstein geodesic between a source and target distribution, along with the associated velocity field. Building on the dynamical formulation of the optimal transport (OT) problem, we recast the constrained optimization as a minimax problem, using deep neural networks to approximate the relevant functions. This approach not only provides the Wasserstein geodesic but also recovers the OT map, enabling direct sampling from the target distribution. By estimating the OT map, we obtain velocity estimates along particle trajectories, which in turn allow us to learn the full velocity field. The framework is flexible and readily extends to general cost functions, including the commonly used quadratic cost. We demonstrate the effectiveness of our method through experiments on both synthetic and real datasets.

Related papers

• Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching [60.37045080890305]
  We provide the first analysis of the sample complexity for flow-matching based generative models.<n>We decompose the velocity field estimation error into neural-network approximation error, statistical error due to the finite sample size, and optimization error due to the finite number of optimization steps for estimating the velocity field.
  arXiv  Detail & Related papers  (2025-12-01T05:14:25Z)
• Improving Neural Optimal Transport via Displacement Interpolation [16.474572112062535]
  Optimal Transport (OT) theory investigates the cost-minimizing transport map that moves a source distribution to a target distribution.<n>We propose a novel method to improve stability and achieve a better approximation of the OT Map by exploiting displacement.<n>We demonstrate that DIOTM outperforms existing OT-based models on image-to-image translation tasks.
  arXiv  Detail & Related papers  (2024-10-03T16:42:23Z)
• Dynamical Measure Transport and Neural PDE Solvers for Sampling [77.38204731939273]
  We tackle the task of sampling from a probability density as transporting a tractable density function to the target. We employ physics-informed neural networks (PINNs) to approximate the respective partial differential equations (PDEs) solutions. PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently.
  arXiv  Detail & Related papers  (2024-07-10T17:39:50Z)
• Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference [1.740133468405535]
  We present two solutions of solutions of $D1450F454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454 5454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454545454 54545454545454545454545454545454545
  arXiv  Detail & Related papers  (2023-10-25T20:20:09Z)
• Manifold Interpolating Optimal-Transport Flows for Trajectory Inference [64.94020639760026]
  We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) MIOFlow learns, continuous population dynamics from static snapshot samples taken at sporadic timepoints. We evaluate our method on simulated data with bifurcations and merges, as well as scRNA-seq data from embryoid body differentiation, and acute myeloid leukemia treatment.
  arXiv  Detail & Related papers  (2022-06-29T22:19:03Z)
• Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark [133.46066694893318]
  We evaluate the performance of neural network-based solvers for optimal transport. We find that existing solvers do not recover optimal transport maps even though they perform well in downstream tasks.
  arXiv  Detail & Related papers  (2021-06-03T15:59:28Z)
• Learning High Dimensional Wasserstein Geodesics [55.086626708837635]
  We propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagrange multipliers to the dynamic formulation of the optimal transport (OT) problem, we derive a minimax problem whose saddle point is the Wasserstein geodesic. We then parametrize the functions by deep neural networks and design a sample based bidirectional learning algorithm for training.
  arXiv  Detail & Related papers  (2021-02-05T04:25:28Z)
• A Near-Optimal Gradient Flow for Learning Neural Energy-Based Models [93.24030378630175]
  We propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs) We derive a second-order Wasserstein gradient flow of the global relative entropy from Fokker-Planck equation. Compared with existing schemes, Wasserstein gradient flow is a smoother and near-optimal numerical scheme to approximate real data densities.
  arXiv  Detail & Related papers  (2019-10-31T02:26:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.