贝克曼运输模型：从自主流到一步映射
Beckmann Transport Models: From Autonomous Flows to One-Step Maps
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中文总结 AI 辅助
该研究提出基于自主流的流匹配实例，构建统一框架实现分布间精确映射，修正现有方法不一致性，在ImageNet 256×256上验证了自主流与一步映射的有效性。
中文摘要 AI 辅助
我们提出一种基于与时间无关的速度场（即自主流，autonomous flow）的流匹配实例，只要目标分布是奇异的（即支撑于低维数据流形上），该方法就能在两个分布间实现精确映射。我们还证明，与该流关联的一步生成映射是一个简单守恒方程的唯一解，可用于直接从样本中学习该映射。这些自主流和映射为贝克曼运输问题的通量约束赋予了动力学意义，其构建提供了一个统一框架，例如可恢复闭式泊松流生成模型及采用二次流匹配回归损失的平衡匹配。我们阐释该理论如何修正现有方法的不一致性，并在ImageNet 256×256上验证了自主流和一步映射的有效性。
英文摘要
We propose an instantiation of flow matching that relies on a time-independent velocity field (an \emph{autonomous flow}) to exactly map between two distributions, so long as the target is singular, i.e.\ supported on a lower-dimensional data manifold. We also show that the one-step generative map associated with this flow is the unique solution of a simple conservation equation, which can be used to learn the map directly from samples. These autonomous flows and maps give a dynamical meaning to the flux constraint of Beckmann's transportation problem. Their construction provides a unifying framework that recovers, for instance, the closed-form Poisson-flow generative model and equilibrium matching with a quadratic flow-matching regression loss. We illustrate how this theory corrects inconsistencies in existing methods and demonstrate the effectiveness of the autonomous flow and the one-step map on ImageNet 256x256.
发表机构
- Harvard University（哈佛大学）
- Capital Fund Management (CFM)（凯鹏华盈资产管理公司）
- University of Oxford（牛津大学）
- New York University（纽约大学）
机构由 AI 辅助整理，请以论文原文为准。
