Unlocking the Duality between Flow and Field Matching

Daniil Shlenskii, Alexander Varlamov, Nazar Buzun, Alexander Korotin

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 yield novel, IFM-driven techniques for CFM.

Primary Area: Deep Learning->Generative Models and Autoencoders

Keywords: Diffusion Models, Conditional Flow Matching, Electrostatic Generative Models, Poisson Flow, Interaction Field Matching

Submission Number: 8404