Title: Strong Stochastic Flow Maps

Abstract:

While flow and diffusion models are capable of producing high-fidelity samples across various data modalities, they typically demand numerous network evaluations during the inference phase to numerically integrate the underlying differential equations. Flow maps address this computational bottleneck by learning the differential equation’s solution map directly, which facilitates sampling in just a few steps. However, existing approaches are limited to approximating solution maps for Ordinary Differential Equations (ODEs). Although these techniques can be adapted to learn the transition kernel of a Stochastic Differential Equation (SDE), they only yield a solution map that achieves weak convergence—recovering the process's marginal distributions rather than the specific solution paths (strong convergence).

To overcome this limitation, we introduce Strong Stochastic Flow Maps (SSFMs), a new framework designed to learn the strong solution map for SDEs with additive noise, effectively extending deterministic flow maps into the stochastic domain. Additionally, we present a polynomial approximation for Brownian motion and demonstrate its pathwise convergence. These advancements allow for a simulation-free training objective for the solution maps of diffusion models. Our experiments show that SSFMs surpass prior stochastic flow map methods in image generation tasks and successfully enable few-step sampling for molecular systems.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC