LatentFlow: A General Framework for Conditioning Stochastic Processes

• URL: http://arxiv.org/abs/2607.12922v1
• Date: Tue, 14 Jul 2026 15:56:44 GMT
• Title: LatentFlow: A General Framework for Conditioning Stochastic Processes
• Abstract summary: LatentFlow is a framework for conditioning processes with no learned neural approximations and no training.<n>It enables conditional sampling in seconds on a single desktop CPU across model classes that have never shared a method.
• Score: 7.073210405344711
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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