提出一种基于Sinkhorn散度的生成动力学，提升生成模型稳定性与质量。
Sinkhorn-Drifting Generative Models
- 通过一阶归一化吉布斯核分解漂移场，实现目标分布吸引与自修正。
- 在最低温度下使FFHQ-ALAE的FID从187.7降至37.1，潜空间EMD从453.3降至144.4。
- 解决原有漂移方法的可识别性问题，适合对生成质量要求高的研究者。
我们建立了新提出的“漂移”生成动力学与由Sinkhorn散度诱导的梯度流之间的理论联系。在粒子离散化中，漂移场呈现交叉减自项结构：一个指向目标分布的吸引项，和一个指向当前模型的排斥/自校正项，均由单边归一化吉布斯核表达。我们证明，Sinkhorn散度也具有类似结构，但各项由双边Sinkhorn缩放（即同时强制两个边缘分布）得到的熵最优传输耦合定义。这精确地表明，漂移作用相当于对Sinkhorn散度梯度流的近似，介于单边归一化与完全双边缩放之间。关键的是，该联系解决了先前漂移形式中的可识别性缺口：利用Sinkhorn散度的正定性，我们证明零漂移（动力学平衡）意味着模型与目标测度一致。实验显示，Sinkhorn漂移降低了对核温度的敏感性，并提升了单步生成质量，以额外训练时间为代价换取更稳定优化，不改变漂移方法的推理过程。这些理论优势在实践中转化为低温条件下的显著改进：在评估的最低温度下，对于FFHQ-ALAE，均值FID从187.7降至37.1，均值潜空间EMD从453.3降至144.4；在MNIST上则保持全类别覆盖。
原文摘要 · Abstract (English)
We establish a theoretical link between the recently proposed "drifting" generative dynamics and gradient flows induced by the Sinkhorn divergence. In a particle discretization, the drift field admits a cross-minus-self decomposition: an attractive term toward the target distribution and a repulsive/self-correction term toward the current model, both expressed via one-sided normalized Gibbs kernels. We show that Sinkhorn divergence yields an analogous cross-minus-self structure, but with each term defined by entropic optimal-transport couplings obtained through two-sided Sinkhorn scaling (i.e., enforcing both marginals). This provides a precise sense in which drifting acts as a surrogate for a Sinkhorn-divergence gradient flow, interpolating between one-sided normalization and full two-sided Sinkhorn scaling. Crucially, this connection resolves an identifiability gap in prior drifting formulations: leveraging the definiteness of the Sinkhorn divergence, we show that zero drift (equilibrium of the dynamics) implies that the model and target measures match. Experiments show that Sinkhorn drifting reduces sensitivity to kernel temperature and improves one-step generative quality, trading off additional training time for a more stable optimization, without altering the inference procedure used by drift methods. These theoretical gains translate to strong low-temperature improvements in practice: on FFHQ-ALAE at the lowest temperature setting we evaluate, Sinkhorn drifting reduces mean FID from 187.7 to 37.1 and mean latent EMD from 453.3 to 144.4, while on MNIST it preserves full class coverage across the temperature sweep. Project page: https://mint-vu.github.io/SinkhornDrifting/
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