Meta-Flow Matching: A Framework for Generating, Adapting, and Optimizing Flow-Matching Models Through Higher-Order Flow Matching
Abstract
Flow matching has emerged as a powerful framework for generative modeling, enabling the learning of continuous-time vector fields that transport probability distributions from simple source distributions toward complex target distributions. However, conventional flow-matching systems primarily learn the transformation that generates data, while their model architectures, vector-field parameterizations, probability paths, conditioning mechanisms, and sampling strategies are generally determined through separate design or optimization procedures. This paper proposes Meta-Flow Matching (Meta-FM) as a framework in which flow matching operates not only at the data-generation level but also at the model-construction level. Instead of treating a flow-matching model as a fixed generative mechanism, Meta-FM treats flow-matching models as objects that can themselves be generated, adapted, combined, and optimized through a higher-order flow-matching process.
We formalize a hierarchy comprising a data-level flow, a model-level flow, and an optional mechanism-level flow. The data-level flow transforms latent samples into generated outputs. The model-level flow transforms an initial representation of a generative model into a task-adapted flow-matching model. The mechanism-level flow can further transform representations of the procedures responsible for constructing and adapting those models. We introduce a task-conditioned meta-vector field, a model-space state representation, an objective combining generative quality and computational costs, and a constrained optimization procedure for higher-order model adaptation. We distinguish this proposal from conventional flow matching, hypernetwork-based generation, neural architecture search, and existing work on Meta Flow Matching, which studies distribution-level dynamics on the Wasserstein manifold. The central distinction proposed here is the use of a learned flow-matching process to construct or adapt flow-matching models themselves.
This paper establishes a conceptual and mathematical framework rather than an empirically validated method. It identifies implementation requirements, theoretical questions, evaluation protocols, and falsifiable hypotheses necessary to determine whether higher-order flow matching can improve adaptation efficiency, model reuse, and generative performance across related tasks.
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BibTeX
@misc{zhang2026metaflow,
title = {{Meta-Flow Matching: A Framework for Generating, Adapting, and Optimizing Flow-Matching Models Through Higher-Order Flow Matching}},
author = {Jincheng Zhang},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23530011},
url = {https://zenodo.org/records/23530011},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Meta-Flow Matching: A Framework for Generating, Adapting, and Optimizing Flow-Matching Models Through Higher-Order Flow Matching
AU - Jincheng Zhang
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23530011
UR - https://zenodo.org/records/23530011
AB - Flow matching has emerged as a powerful framework for generative modeling, enabling the learning of continuous-time vector fields that transport probability distributions from simple source distributions toward complex target distributions. However, conventional flow-matching systems primarily learn the transformation that generates data, while their model architectures, vector-field parameterizations, probability paths, conditioning mechanisms, and sampling strategies are generally determined through separate design or optimization procedures. This paper proposes Meta-Flow Matching (Meta-FM) as a framework in which flow matching operates not only at the data-generation level but also at the model-construction level. Instead of treating a flow-matching model as a fixed generative mechanism, Meta-FM treats flow-matching models as objects that can themselves be generated, adapted, combined, and optimized through a higher-order flow-matching process. We formalize a hierarchy comprising a data-level flow, a model-level flow, and an optional mechanism-level flow. The data-level flow transforms latent samples into generated outputs. The model-level flow transforms an initial representation of a generative model into a task-adapted flow-matching model. The mechanism-level flow can further transform representations of the procedures responsible for constructing and adapting those models. We introduce a task-conditioned meta-vector field, a model-space state representation, an objective combining generative quality and computational costs, and a constrained optimization procedure for higher-order model adaptation. We distinguish this proposal from conventional flow matching, hypernetwork-based generation, neural architecture search, and existing work on Meta Flow Matching, which studies distribution-level dynamics on the Wasserstein manifold. The central distinction proposed here is the use of a learned flow-matching process to construct or adapt flow-matching models themselves. This paper establishes a conceptual and mathematical framework rather than an empirically validated method. It identifies implementation requirements, theoretical questions, evaluation protocols, and falsifiable hypotheses necessary to determine whether higher-order flow matching can improve adaptation efficiency, model reuse, and generative performance across related tasks.
ER -