新方法让生成模型路径更灵活，可任意设计中间过渡形态。
Flow Matching with Arbitrary Auxiliary Paths
- 用任意分布的辅助变量构造生成路径，突破传统高斯噪声限制。
- 支持多种分布（高斯、均匀、拉普拉斯等），路径几何特性多样。
- 适合需要结构化引导的任务，如标签控制生成，理论基础扎实。
我们提出一种新的生成建模框架——带任意辅助路径的流匹配（AuxPath-FM），通过引入来自任意分布的辅助变量来推广条件流匹配。与以往方法仅限于高斯噪声不同，该框架允许辅助变量η服从任意分布，生成形式为 $X_t = a(t)X_1 + b(t)X_0 + c(t)η$ 的轨迹。理论上证明此构造保持连续性方程，并维持与边缘形式一致的训练目标。该灵活性使我们能够利用多种先验分布（包括高斯、均匀、拉普拉斯及离散Rademacher分布）设计具有独特几何特性的概率路径。此外，该框架还可用于特定任务，例如通过将结构化语义信息编码至辅助分布实现标签引导生成。总体而言，AuxPath-FM为概率路径设计提供了原理严谨且应用灵活的通用基础，适用于多样化生成建模任务。
原文摘要 · Abstract (English)
We introduce a new generative modeling framework, \textbf{Flow Matching with Arbitrary Auxiliary Paths (AuxPath-FM)}, which generalizes conditional flow matching by incorporating an auxiliary variable drawn from an arbitrary distribution into the probability path. Unlike prior methods that restrict auxiliary components to Gaussian noise, AuxPath-FM allows the variable $η$ to follow any distribution, producing trajectories of the form $X_t = a(t)X_1 + b(t)X_0 + c(t)η$. We theoretically demonstrate that this construction preserves the continuity equation and maintains a training objective consistent with the marginal formulation. This flexibility enables the design of diverse probability paths using various priors, including Gaussian, Uniform, Laplace, and discrete Rademacher distributions, each offering unique geometric properties for generative flows. Furthermore, our framework allows for specialized tasks such as label-guided generation by encoding structured semantic information into the auxiliary distribution. Overall, AuxPath-FM provides a principled and general foundation for probability path design, offering both theoretical generality and practical flexibility for diverse generative modeling tasks.
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