AI 中文总结
研究提出LatentFlow框架，通过将随机过程写作潜在创新的确定性图像，把过程级条件设定转化为潜在空间推理，无需训练，能在几秒内对多种模型类别进行条件采样，解决了不同模型难以共享可扩展条件设定方法的问题。
AI 中文摘要
随机过程模型通常模拟比条件设定更容易。非线性观测、非高斯似然、黑箱信息和全局约束都会导致难以处理的条件律，需要特定于模型的定制构造。我们引入LatentFlow，一个用于条件随机过程的单一框架，无需学习神经近似和训练。我们将随机过程写为可处理的潜在创新的确定性图像$f_0 = T_{\vartheta}(\xi_0)$，其中$\xi_0$从简单参考分布中采样。这将过程级条件设定简化为潜在空间推理。这种构造在目标律层面上被证明是精确的，在实践中，近似仅通过有限终端噪声、蒙特卡罗引导和连续时间动力学的时间离散化进入，每种都很明确且可系统地减少。由于LatentFlow无需训练，条件设定简化为求解单个反向时间的随机微分方程。这使得能够在单个桌面CPU上几秒内对从未共享可扩展方法的模型类别进行条件采样，包括经典空间先验、非线性随机动力学、物理和生命科学的机械模型、随机偏微分方程、重尾和极值、点和离散状态过程以及神经或模拟器定义的过程。
英文摘要
Stochastic-process models are, as a rule, far easier to simulate than to condition. Non-linear observations, non-Gaussian likelihoods, black-box information, and global constraints all induce intractable conditional laws, requiring bespoke, model-specific constructions. We introduce LatentFlow, a single framework for conditioning stochastic processes, with no learned neural approximations and no training. Our starting point is to write the stochastic process as the deterministic image of a tractable latent innovation, $f_0 = T_{\vartheta}(ξ_0)$, with $ξ_0$ sampled from a simple reference distribution. This reduces process-level conditioning to latent-space inference: pull the likelihood back through $T_{\vartheta}$, sample the resulting latent law with a tractable guided probability flow, and push the samples forward. This construction is provably exact at the level of the target law; in practice, approximation enters only through finite terminal noising, Monte Carlo guidance, and time discretisation of the continuous-time dynamics, each of which is explicit and systematically reducible. As LatentFlow is training-free, conditioning reduces to solving a single reverse-time SDE. This enables conditional sampling in seconds on a single desktop CPU across model classes that have never shared a scalable method: classical spatial priors, nonlinear stochastic dynamics, mechanistic models from the physical and life sciences, stochastic PDEs, heavy-tails and extremes, point and discrete-state processes, and neural or simulator-defined processes.
