{"ID":6626583,"CreatedAt":"2026-07-15T02:56:36.47817413Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.12922","arxiv_id":"2607.12922","title":"LatentFlow: A General Framework for Conditioning Stochastic Processes","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.","short_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 c...","url_abs":"https://arxiv.org/abs/2607.12922","url_pdf":"https://arxiv.org/pdf/2607.12922v1","authors":"[\"Louis Sharrock\",\"Lachlan Astfalck\",\"Henry Moss\"]","published":"2026-07-14T15:56:44Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"stat.ME\"]","methods":"[]","has_code":false}