Unlocking the Duality between Flow and Field Matching

• URL: http://arxiv.org/abs/2602.02261v1
• Date: Mon, 02 Feb 2026 16:04:01 GMT
• Title: Unlocking the Duality between Flow and Field Matching
• Authors: Daniil Shlenskii, Alexander Varlamov, Nazar Buzun, Alexander Korotin,
• Abstract summary: Conditional Flow Matching (CFM) unifies conventional generative paradigms such as diffusion models and flow matching.<n> Interaction Field Matching (IFM) is a newer framework that generalizes Electrostatic Field Matching (EFM) rooted in Poisson Flow Generative Models (PFGM)<n>We show that they coincide for a natural subclass of IFM that we call forward-only IFM.
• Score: 86.34409966628323
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conditional Flow Matching (CFM) unifies conventional generative paradigms such as diffusion models and flow matching. Interaction Field Matching (IFM) is a newer framework that generalizes Electrostatic Field Matching (EFM) rooted in Poisson Flow Generative Models (PFGM). While both frameworks define generative dynamics, they start from different objects: CFM specifies a conditional probability path in data space, whereas IFM specifies a physics-inspired interaction field in an augmented data space. This raises a basic question: are CFM and IFM genuinely different, or are they two descriptions of the same underlying dynamics? We show that they coincide for a natural subclass of IFM that we call forward-only IFM. Specifically, we construct a bijection between CFM and forward-only IFM. We further show that general IFM is strictly more expressive: it includes EFM and other interaction fields that cannot be realized within the standard CFM formulation. Finally, we highlight how this duality can benefit both frameworks: it provides a probabilistic interpretation of forward-only IFM and yields novel, IFM-driven techniques for CFM.

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