用高阶运动信息提升扩散模型生成稳定性与精度
High-Order Matching for One-Step Shortcut Diffusion Models
- 引入加速度、急动度等高阶监督，改进仅依赖速度的旧方法
- 在高曲率区域实现更平滑轨迹和更好分布对齐，误差显著降低
- 适合追求生成质量与稳定性的视觉生成研究者使用
一步快捷扩散模型在视觉生成中展现出潜力，但其仅依赖一阶轨迹监督，存在根本性局限。该模型仅基于速度的简化方法无法捕捉内在流形几何，导致轨迹不稳定、对齐差，尤其在高曲率区域表现不佳。这源于其无法建模中短期依赖或复杂分布特征。本文提出HOMO（高阶匹配的一步快捷扩散），通过引入加速度、急动度等高阶监督，革新分布传输机制。理论上，高阶监督确保更优近似精度，优于一阶方法；实验上，HOMO在复杂场景中全面领先，尤其在高曲率区域表现突出，实现更平滑轨迹与更优分布对齐，为一步生成模型树立新标准。
原文摘要 · Abstract (English)
One-step shortcut diffusion models [Frans, Hafner, Levine and Abbeel, ICLR 2025] have shown potential in vision generation, but their reliance on first-order trajectory supervision is fundamentally limited. The Shortcut model's simplistic velocity-only approach fails to capture intrinsic manifold geometry, leading to erratic trajectories, poor geometric alignment, and instability-especially in high-curvature regions. These shortcomings stem from its inability to model mid-horizon dependencies or complex distributional features, leaving it ill-equipped for robust generative modeling. In this work, we introduce HOMO (High-Order Matching for One-Step Shortcut Diffusion), a game-changing framework that leverages high-order supervision to revolutionize distribution transportation. By incorporating acceleration, jerk, and beyond, HOMO not only fixes the flaws of the Shortcut model but also achieves unprecedented smoothness, stability, and geometric precision. Theoretically, we prove that HOMO's high-order supervision ensures superior approximation accuracy, outperforming first-order methods. Empirically, HOMO dominates in complex settings, particularly in high-curvature regions where the Shortcut model struggles. Our experiments show that HOMO delivers smoother trajectories and better distributional alignment, setting a new standard for one-step generative models.
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