发表机构
Courant Institute of Mathematical Sciences, New York University; University of Toronto; EPFL（纽约大学库朗数学科学研究所; 多伦多大学; 洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出块三角联合漂移方法，通过投影漂移场作用于联合分布，实现一步生成随机轨迹的代理模型，在保持边际分布的同时直接采样条件分布，实验证明其精度与成本权衡优于现有生成式代理模型。
AI 中文摘要
漂移方法为一步生成式模型提供了直接途径，但将其直接应用于随机转移建模时，需要对同一当前状态条件下的下一状态进行多次采样。然而，标准轨迹数据通常仅为每个观测到的当前状态提供一个已实现的下一状态，因此无法对可能的下一状态对应的条件分布进行经验近似。我们引入了块三角联合漂移方法，该方法将投影漂移场应用于连续状态的联合分布（该分布在经验上可获取）。重要的是，块三角架构在保持当前状态边际分布的同时，使其第二个分量成为可能的下一状态条件分布的直接采样器。由此产生的代理模型在每个时间步仅需一次模型评估即可生成随机轨迹，无需在时间步之间进行辅助生成步骤。数值实验表明，与基于确定性、扩散、流和蒸馏的生成式代理模型相比，该方法在边际统计量和轨迹相关统计量上具有准确性，并在精度-成本权衡方面表现出优势。
英文摘要
Drifting provides a direct route to one-step generative models, but applying it directly to stochastic transition modeling requires multiple samples of the next state conditioned on the same current state. Standard trajectory data, however, typically provide only one realized next state for each observed current state and therefore do not provide an empirical approximation of the corresponding conditional distribution over possible next states. We introduce block-triangular joint drifting, which instead applies a projected drift field to the empirically accessible joint distribution of consecutive states. Importantly, the block-triangular architecture preserves the current-state marginal while making its second component a direct sampler of the conditional distribution of possible next states. The resulting surrogate generates stochastic trajectories with one model evaluation per time step, without auxiliary generative steps between time steps. Numerical experiments demonstrate accurate marginal and trajectory-dependent statistics and favorable accuracy-cost tradeoffs compared with deterministic, diffusion-, flow-, and distillation-based generative surrogate models.
