新方法让生成模型更灵活，可直接设计动态过程。
Generative Modeling with Flux Matching
- 不依赖保守向量场，允许任意设计动态方向
- 在图像数据上表现优秀，支持更快采样
- 适合需要可解释动态或定向依赖的场景
我们提出流形匹配（Flux Matching），一种新的生成建模范式，将现有基于得分的模型扩展到非保守向量场。该方法不要求模型等于数据得分，而是放宽条件，允许无穷多个具有数据平稳分布的向量场存在。这种灵活性使原本无法通过得分匹配学习的模型成为可能，能直接引入归纳偏置、结构先验和动态特性。实验表明，流形匹配在高维图像数据集上表现良好，更重要的是，其自由度拓展了多种应用：包括加速采样、可解释且机制明确的模型，以及编码变量间有向依赖的动力学。总体而言，流形匹配通过将向量场本身作为可设计要素，为生成建模开辟了全新维度。代码已公开于 https://github.com/peterpaohuang/flux_matching。
原文摘要 · Abstract (English)
We introduce Flux Matching, a new paradigm for generative modeling that generalizes existing score-based models to a broader family of vector fields that need not be conservative. Rather than requiring the model to equal the data score, the Flux Matching objective imposes a weaker condition that admits infinitely many vector fields whose stationary distribution is the data. This flexibility enables a class of generative models that cannot be learned under score matching, in which inductive biases, structural priors, and properties of the dynamics can be directly imposed or optimized. We show that Flux Matching performs strongly on high-dimensional image datasets and, more importantly, that our added freedom unlocks a range of applications including faster sampling, interpretable and mechanistic models, and dynamics that encode directed dependencies between variables. More broadly, Flux Matching opens a new dimension in generative modeling by turning the vector field itself into a design choice rather than a fixed target. Code is available at https://github.com/peterpaohuang/flux_matching.
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