发表机构
Mohamed bin Zayed University of Artificial Intelligence; Korea Advanced Institute of Science and Technology (KAIST); Applied AI Institute; AXXX; University of Amsterdam; EPITA（穆罕默德·本·扎耶德人工智能大学; 韩国科学技术院（KAIST）; 应用人工智能研究所; AXXX; 阿姆斯特丹大学; EPITA（法国高等信息技术学院））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在通用训练框架下推导并比较多种几何感知的Wasserstein梯度场，用于约束空间上的一步生成，实验表明最佳场因任务而异，凸显目标选择的重要性。
AI 中文摘要
近年来，漂移模型和Wasserstein梯度流因其将迭代分布细化移至训练阶段并将其摊销到生成器中，从而实现快速推理而受到广泛关注。然而，现有公式主要针对连续欧几里得域（如图像空间）开发，其中粒子允许无约束的加性更新。在约束空间上，这些更新可能离开有效域或忽略其几何结构，使其不适合作为训练目标。近期工作已将这些更新适配到此类空间，但侧重于特定领域或仅提供有限的实证比较。我们在一个用于一步生成器的通用训练框架内推导并比较了几种几何感知场。我们在具有不同结构的数据上测试了该方法，并在每种设置下获得了具有竞争力的一步生成结果。表现最佳的场因任务而异，这说明了在实践中目标选择的重要性。
英文摘要
Recently, Drifting Models and Wasserstein Gradient Flows have attracted substantial attention because they move iterative distributional refinement to training and amortize it into a generator, enabling fast inference. However, existing formulations have been developed largely for continuous Euclidean domains, such as image spaces, where particles admit unconstrained additive updates. On constrained spaces, these updates can leave the valid domain or ignore its geometry, making them unsuitable targets for training. Recent work has adapted updates to these spaces, but has focused on particular fields or offered limited empirical comparison. We derive and compare several geometry-aware fields within a common training framework for one-step generators. We test the method on data with different structures and obtain competitive one-step results in each setting. The best-performing field varies by task, showing why the choice of objective matters in practice.
