发表机构
University of Utah; Scientific Computing and Imaging (SCI) Institute（犹他大学; 科学计算与成像研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出二阶漂移模型，通过引入人工速度变量将漂移动力学拓展至相空间，结合 Nesterov 加速缓解一阶漂移的频谱刚性，在合成分布匹配等任务上实现了更优的收敛与性能。
AI 中文摘要
漂移模型是一类近期的单步生成模型，训练过程中会利用预定义的基于样本的漂移场更新模型分布。尽管这类模型避免了迭代推理，但它们基于核函数的漂移场会引发依赖频率的训练动态：在线性化 regime 下，密度残差的每个傅里叶模式以由核谱决定的速率衰减，导致精细结构的恢复缓慢。我们提出二阶漂移模型，通过为生成样本增加人工速度变量，将漂移动力学提升至相空间。我们证明，所得的密度扰动在傅里叶空间遵循加速的二阶动力学，将漂移模型与优化理论中著名的 Nesterov 加速联系起来。这提供了一种原则性机制，可缓解一阶漂移的频谱刚性，同时保留单步推理。我们推导了一种实用的半隐式训练算法，并在合成分布匹配、序列数据生成及机器人控制任务上对其进行评估。在所有这些设置中，二阶漂移模型均改善了收敛行为，且相较于一阶漂移基线实现了具竞争力或更优的性能。
英文摘要
Drifting models are a recent class of one-step generative models that evolve the model distribution during training using a predefined sample-based drift field. Although they avoid iterative inference, their kernel-based drift fields induce frequency-dependent training dynamics: In the linearized regime, each Fourier mode of the density residual decays at a rate determined by the kernel spectrum, leading to slow recovery of fine-scale structure. We propose Second-Order Drifting Models, which lift drifting dynamics into phase space by augmenting generated samples with artificial velocity variables. We show that the resulting density perturbations obey accelerated second-order dynamics in Fourier space, connecting drifting models to the celebrated Nesterov acceleration from optimization theory. This provides a principled mechanism for mitigating the spectral stiffness of first-order drifting while preserving one-step inference. We derive a practical semi-implicit training algorithm and evaluate it on synthetic distribution matching, sequential data generation, and robotic control. Across these settings, the second-order drifting model improves convergence behavior and achieves competitive or superior performance over first-order drifting baselines.
Comments20 pages, 4 figures
