提出自适应扩散采样器的稳定传播机制，提升采样精度与可证明性。
Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplers
- 基于径向几何自适应设计传播接口，结合反射耦合与哈代容量分析
- 通过保留尾部斜率和负载约束，实现可证明的收缩率与运输成本
- 适用于高斯平滑去噪场景，适合研究扩散模型理论的学者
许多对扩散采样器的Wasserstein分析依赖于学习漂移的全局稳定性总结，但此类总结可能掩盖径向几何特性：不同宽度的等高扩张区域可能导致不同的传播成本。本文为标量各向同性反向SDE窗口设计了一种适配轮廓的传播接口，提供经认证的学习漂移轮廓。通过编译出一个仿射尾部运输成本，反射耦合将稳定性简化为一维斜率预算，而哈代容量量化了在收缩尾部储备前所承受的负载。编译器输出自适应成本、收缩率及保留的尾部斜率。得分模型与求解器残差作为强迫输入，在自适应Wasserstein距离中叠加传播。仅在终时报告二次Wasserstein误差，使用保留的尾部斜率及尾部、矩或支撑信息。高斯平滑去噪几何为均匀耗散、有界幅值及常见协方差混合窗口提供了逆半径轮廓。固定高度示例显示，不利高度即使存在最终储备，也不决定证书；障碍示例表明负载依赖具有结构性。
原文摘要 · Abstract (English)
Many Wasserstein analyses of diffusion samplers control reverse-time propagation by global stability summaries of the learned drift. These summaries can hide radial geometry: equal-height expansive regions of different width can yield different propagation costs. We give a profile-adapted propagation interface for scalar-isotropic reverse-SDE windows with certified learned-drift profiles. A certified lower radial profile is compiled into an affine-tail transportation cost: reflection coupling reduces stability to a one-dimensional slope budget, and Hardy capacity quantifies the load paid before a contractive tail reserve. The compiler yields an adapted cost, contraction rate, and retained tail slope. Score-modeling and solver residuals are treated as forcing inputs and propagate additively in the adapted Wasserstein distance. Quadratic Wasserstein error is reported only at terminal time, using the retained tail slope with tail, moment, or support information. Gaussian-smoothed denoising geometry supplies inverse-radius profiles for uniformly dissipative, bounded-amplitude, and common-covariance mixture windows. Fixed-height examples show that adverse height, even with eventual reserve, does not determine the certificate; barrier examples show that the load dependence is structural.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。