Foundation Models for Variance Reduction in Stochastic Processes

Estimating expectations of functionals of stochastic processes is a fundamental problem in many disciplines, from finance to life sciences and engineering. However, obtaining accurate estimates with Monte Carlo requires prohibitively many samples. We introduce foundation models for variance reduction that use simulator paths and black-box functional evaluations, without access to the explicit dynamics or task parameters. A pretrained model reads a small set of observed paths and outputs a task-specific variance-reduction controller, an importance sampling proposal or control variates integrand. This architecture leads to estimators which are unbiased by construction and adds little computational overhead. Because the models separate identification from estimation, the allocation of paths between the two provides a natural test-time scaling mechanism. We pretrain on a broad family of synthetic stochastic processes, to ensure strong downstream performance even in out-of-distribution applications, especially for importance sampling. We demonstrate the performance of the models on a variety of applications in finance and biology, showing that the proposed model provides significant variance reduction with matched wall-clock speed.