提出张量场模型，用可复用条件加速生成过程。
Tensor Field Models
- 构建可分离的张量场结构，通过组件映射生成时变向量场。
- 实验表明性能提升，复用条件实现采样加速。
- 适合需要高效生成与结构化建模的研究者。
本文提出张量场模型（TFMs），一种在生成状态流形上学习算子的数学结构，该算子将可接受的分量截面族的乘积映射为预设的时变切截面族。通过选择可接受的截面族来编码解析与动力学约束，而非由基础定义强加。构造出的可分组件张量丛TFM提供了对该通用对象的结构化改进。在所考虑的条件实现中，结构化条件 $c=(c_1, dots,c_n)$ 被逐成分量映射为可复用的集合 $f H_c=(H_{c_1}^{(1)}, dots,H_{c_n}^{(n)})$。在评估的架构中，各组件表示保持独立，仅通过场算子结合以生成最终向量场。所有模型均使用流匹配（Flow Matching）进行训练。实验显示，TFMs能提升性能，且通过可复用条件表示实现的摊销采样显著加速生成过程。
原文摘要 · Abstract (English)
This paper introduces Tensor Field Models (TFMs), realization-level Mathematical Structures in which a learned Operator maps a product of admissible component-section families to a prescribed family of time-dependent tangent sections on a Generative State Manifold. Analytic and dynamical restrictions are encoded through the choice of admissible families rather than imposed by the root definition. Constructed, component-separable, and Tensor Bundle TFMs provide structured refinements of this common object. In the conditional realizations considered here, a structured condition $c=(c_1,\ldots,c_n)$ is mapped componentwise to a reusable collection $\mathbf H_c=(H_{c_1}^{(1)},\ldots,H_{c_n}^{(n)})$. In the architectures evaluated here, the component representations remain distinct and are combined only by the Field Operator to produce the generated Vector Field. All learned models are trained using Flow Matching. Experiments show that TFMs can improve performance and that amortized sampling enabled by reusable condition representations can accelerate generation.
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