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.

翻译：近期的一步生成模型通过学习底层动力学的确定性流映射来加速采样。这些方法依赖于从常微分方程中学习，但如何为随机动力学定义精确的蒸馏过程仍是一个开放问题。我们提出了伊藤映射（Itô map），这是一种任意步随机流映射，能够以单次前向传播方式，基于中间状态和布朗路径预测未来状态。伊藤映射公式通过提供廉价且可微的后验样本访问路径，为推理时控制引入了新型估计方法。实验表明，从固定中间状态出发，伊藤映射能生成多样且条件成立的有效终点样本，并在合成与图像生成基准测试中展现出强大的控制性能。这些结果验证了任意步SDE积分作为后验采样与随机控制的有用基本工具。