LatentFlow: A General Framework for Conditioning Stochastic Processes
Louis Sharrock, Lachlan Astfalck, Henry Moss
stat.ML, cs.LG, stat.ME
Submitted: 2026-07-14
License: http://creativecommons.org/licenses/by/4.0/
The gist: Stochastic-process models are, as a rule, far easier to simulate than to condition.
Terminology
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(xi 0), with xi 0 sampled from a simple reference distribution. This reduces process-level conditioning to latent-space inference: pull the likelihood back through T, 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.
Sources
- On the Convergence of SGD with Biased Gradients
- Posterior Projection for Inference in Constrained Spaces
- Generalised Bayes Linear Inference
- Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problems
- Schr\"odinger Bridge Samplers
- Uncertainty Quantification with Generative Models
- Neural Processes
- Sampling conditioned diffusions via Pathspace Projected Monte Carlo
- Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approach
- Classifier-Free Diffusion Guidance
- NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport
- Schr{\"o}dinger-F{\"o}llmer Sampler: Sampling without Ergodicity
- Feynman-Kac-Flow: Inference Steering of Conditional Flow Matching to an Energy-Tilted Posterior
- Conditioning Gaussian Processes on Almost Anything
- D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching
- Simulation of infinite-dimensional diffusion bridges
- Neural Conditional Simulation for Complex Spatial Processes
- Latent Diffusion Posterior Sampling with Surrogate Likelihood Guidance for PDE Inverse Problems
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