提出任意步长的随机微分方程流映射，实现高效采样与可控生成。
Itô maps for any-step SDEs
- 设计Itô映射，单步预测任意时间点状态和路径。
- 在合成数据与图像生成上实现高质量条件采样与强控制性能。
- 为后验采样与随机控制提供可微、低成本的新工具，适合生成模型研究者。
近期单步生成模型通过学习确定性流映射加速采样，但对随机动力系统的精确蒸馏仍无解。本文提出Itô映射，一种任意步长的随机流映射，能以中间状态和布朗路径为输入，单次前向计算预测未来状态。该公式提供廉价且可微的后验样本访问方式，支持推理时控制。实验表明，Itô映射可从固定中间状态生成多样且条件有效的终点样本，在合成数据与图像生成基准上表现优异。结果确立了任意步长SDE积分作为后验采样与随机控制的有效基础构件。
原文摘要 · Abstract (English)
Recent one-step generative models accelerate sampling by learning deterministic flow maps of the underlying dynamics. These methods rely on learning from ordinary differential equations, leaving open how to define an exact distillation procedure for stochastic dynamics. We introduce the Itô map, an any-step stochastic flow map that takes an intermediate state and Brownian path and predicts future states in a single pass. The Itô map formulation yields novel estimators for inference-time control by providing cheap, differentiable access to posterior samples. Empirically, Itô maps produce diverse, conditionally valid endpoint samples from fixed intermediate states and support strong steering performance on synthetic and image-generation benchmarks. These results establish any-step SDE integration as a useful primitive for posterior sampling and stochastic control.
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