Improving Flow Matching by Aligning Flow Divergence

• URL: http://arxiv.org/abs/2602.00869v1
• Date: Sat, 31 Jan 2026 19:07:54 GMT
• Title: Improving Flow Matching by Aligning Flow Divergence
• Authors: Yuhao Huang, Taos Transue, Shih-Hsin Wang, William Feldman, Hong Zhang, Bao Wang,
• Abstract summary: Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models.<n>We introduce a new partial differential equation characterization for the error between the learned and exact probability paths, along with its solution.<n>We show that the total variation gap between the two probability paths is bounded above by a combination of the CFM loss and an associated divergence loss.
• Score: 10.1227026659152
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models, achieving remarkable performance for data generation. However, CFM is insufficient to ensure accuracy in learning probability paths. In this paper, we introduce a new partial differential equation characterization for the error between the learned and exact probability paths, along with its solution. We show that the total variation gap between the two probability paths is bounded above by a combination of the CFM loss and an associated divergence loss. This theoretical insight leads to the design of a new objective function that simultaneously matches the flow and its divergence. Our new approach improves the performance of the flow-based generative model by a noticeable margin without sacrificing generation efficiency. We showcase the advantages of this enhanced training approach over CFM on several important benchmark tasks, including generative modeling for dynamical systems, DNA sequences, and videos. Code is available at \href{https://github.com/Utah-Math-Data-Science/Flow_Div_Matching}{Utah-Math-Data-Science}.

Related papers

• Efficiency vs. Fidelity: A Comparative Analysis of Diffusion Probabilistic Models and Flow Matching on Low-Resource Hardware [0.0]
  Denoising Diffusion Probabilistic Models (DDPMs) have established a new state-of-the-art in generative image synthesis.<n>This study presents a comparative analysis of DDPMs against the emerging Flow Matching paradigm.
  arXiv  Detail & Related papers  (2025-11-24T18:19:42Z)
• Simulation-Free Training of Neural ODEs on Paired Data [20.36333430055869]
  We employ the flow matching framework for simulation-free training of NODEs. We show that applying flow matching directly between paired data can often lead to an ill-defined flow. We propose a simple extension that applies flow matching in the embedding space of data pairs.
  arXiv  Detail & Related papers  (2024-10-30T11:18:27Z)
• Local Flow Matching Generative Models [19.859984725284896]
  Flow Matching (FM) is a simulation-free method for learning a continuous and invertible flow to interpolate between two distributions.<n>We introduce a stepwise FM model called Local Flow Matching (LFM), which consecutively learns a sequence of FM sub-models.<n>We empirically demonstrate improved training efficiency and competitive generative performance of LFM compared to FM.
  arXiv  Detail & Related papers  (2024-10-03T14:53:10Z)
• Flow map matching with stochastic interpolants: A mathematical framework for consistency models [15.520853806024943]
  Flow Map Matching is a principled framework for learning the two-time flow map of an underlying generative model.<n>We show that FMM unifies and extends a broad class of existing approaches for fast sampling.
  arXiv  Detail & Related papers  (2024-06-11T17:41:26Z)
• Optimal Flow Matching: Learning Straight Trajectories in Just One Step [89.37027530300617]
  We develop and theoretically justify the novel textbf Optimal Flow Matching (OFM) approach. It allows recovering the straight OT displacement for the quadratic transport in just one FM step. The main idea of our approach is the employment of vector field for FM which are parameterized by convex functions.
  arXiv  Detail & Related papers  (2024-03-19T19:44:54Z)
• Guided Flows for Generative Modeling and Decision Making [55.42634941614435]
  We show that Guided Flows significantly improves the sample quality in conditional image generation and zero-shot text synthesis-to-speech. Notably, we are first to apply flow models for plan generation in the offline reinforcement learning setting ax speedup in compared to diffusion models.
  arXiv  Detail & Related papers  (2023-11-22T15:07:59Z)
• Over-the-Air Federated Learning and Optimization [52.5188988624998]
  We focus on Federated learning (FL) via edge-the-air computation (AirComp) We describe the convergence of AirComp-based FedAvg (AirFedAvg) algorithms under both convex and non- convex settings. For different types of local updates that can be transmitted by edge devices (i.e., model, gradient, model difference), we reveal that transmitting in AirFedAvg may cause an aggregation error. In addition, we consider more practical signal processing schemes to improve the communication efficiency and extend the convergence analysis to different forms of model aggregation error caused by these signal processing schemes.
  arXiv  Detail & Related papers  (2023-10-16T05:49:28Z)
• AdaMerging: Adaptive Model Merging for Multi-Task Learning [68.75885518081357]
  This paper introduces an innovative technique called Adaptive Model Merging (AdaMerging) It aims to autonomously learn the coefficients for model merging, either in a task-wise or layer-wise manner, without relying on the original training data. Compared to the current state-of-the-art task arithmetic merging scheme, AdaMerging showcases a remarkable 11% improvement in performance.
  arXiv  Detail & Related papers  (2023-10-04T04:26:33Z)
• Improving and generalizing flow-based generative models with minibatch optimal transport [90.01613198337833]
  We introduce the generalized conditional flow matching (CFM) technique for continuous normalizing flows (CNFs) CFM features a stable regression objective like that used to train the flow in diffusion models but enjoys the efficient inference of deterministic flow models. A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference.
  arXiv  Detail & Related papers  (2023-02-01T14:47:17Z)
• Flow Matching for Generative Modeling [44.66897082688762]
  Flow Matching is a simulation-free approach for training Continuous Normalizing Flows (CNFs) We find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Training CNFs using Flow Matching on ImageNet leads to state-of-the-art performance in terms of both likelihood and sample quality.
  arXiv  Detail & Related papers  (2022-10-06T08:32:20Z)
• Efficient Learning of Generative Models via Finite-Difference Score Matching [111.55998083406134]
  We present a generic strategy to efficiently approximate any-order directional derivative with finite difference. Our approximation only involves function evaluations, which can be executed in parallel, and no gradient computations.
  arXiv  Detail & Related papers  (2020-07-07T10:05:01Z)

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.