揭示流模型与场匹配的内在统一性，推动生成模型理论融合
Unlocking the Duality between Flow and Field Matching
- 通过构建双射关系，证明特定场匹配可等价于条件流模型
- 发现一般场匹配比标准流模型更具表达能力，能建模新类型生成动力学
- 为两类框架提供相互启发的新思路，适用于生成模型研究者
条件流匹配（CFM）统一了扩散模型与流匹配等生成范式。交互场匹配（IFM）是较新框架，推广了源于泊松流生成模型（PFGM）的静电场匹配（EFM）。二者虽均定义生成动态，但起点不同：CFM在数据空间指定条件概率路径，而IFM在扩展数据空间中定义物理启发的交互场。这引发根本问题：两者是否本质不同？我们证明，在一类称为前向仅有的IFM的自然子类中，两者完全一致。具体地，我们构造了CFM与前向仅有IFM之间的双射。进一步，我们发现一般IFM表达能力更强：它包含无法用标准CFM实现的EFM及其他交互场。最后，我们指出这一对偶性可互惠受益：为前向仅有IFM提供概率解释，并催生基于IFM的新技术以改进CFM。
原文摘要 · Abstract (English)
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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