arXiv:2603. 20467v2 Announce Type: replace-cross Abstract: Stochastic differential equations (SDEs), which serve as the governing equations for dynamical systems in a broad range of applications, can become cost-prohibitive for numerical simulation at scales necessary for quantifying key properties.
arXiv:2608. 05600v1 Announce Type: cross Abstract: Flow-based generative models are typically sampled by solving a deterministic ordinary differential equation (ODE), whereas online reinforcement learning requires stochastic rollouts for policy exploration and optimization.
arXiv:2606. 28808v1 Announce Type: cross Abstract: We study the leading-order fluctuation of stochastic gradient Euler-Maruyama estimators for generalized non-reversible Langevin dynamics.
arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.
arXiv:2607. 19173v1 Announce Type: new Abstract: Neural stochastic differential equations (SDEs) have emerged as powerful tools for learning noisy or stochastic dynamics directly from data; however, existing approaches largely assume uncoupled and continuous noise, limiting their applicability to realistic stochastic drivers, and often scale poorly in time, requiring expensive autoregressive training.
arXiv:2606. 09434v2 Announce Type: replace Abstract: Solving Fokker-Planck equations (FPEs) for multiple initial conditions typically requires repeated computations, leading to substantial computational costs.
arXiv:2604. 08580v2 Announce Type: replace-cross Abstract: Reward fine-tuning of diffusion and flow models and sampling from tilted or Boltzmann distributions can both be formulated as stochastic optimal control (SOC) problems, where learning an optimal generative dynamics corresponds to optimizing a control under SDE constraints.
arXiv:2606. 01086v1 Announce Type: cross Abstract: Flow and diffusion models generate high-quality samples in many modalities; however, many network evaluations are required during inference due to numerical integration of an underlying differential equation.
arXiv:2512.12749v3 Announce Type: replace-cross Abstract: Learning surrogate models for physical systems with latent uncertainty remains challenging in data-scarce regimes: deterministic neural opera...
The paper introduces Hessian-free high-resolution (HFHR) dynamics, an extension of underdamped Langevin dynamics that incorporates reversible position diffusion for sampling in machine learning. It provides an explicit quantitative contraction rate under a position Poincaré inequality, weighted Hessian and Laplacian bounds, and a compact Sobolev embedding, even when the potential is non‑convex. For the HFHR Monte Carlo algorithm, a path‑space Girsanov argument yields a non‑asymptotic convergence bound and an explicit iteration complexity in total variation distance, improving on previous HFHR results and demonstrating benefits of a positive diffusion parameter through numerical experiments.
arXiv:2509.26364v3 Announce Type: replace Abstract: The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certa...
arXiv:2610.01522v1 Announce Type: cross Abstract: Many scientific and machine learning systems, from molecular dynamics to diffusion models and beyond, are governed by stochastic dynamics with low-di...
Flow-based generative models are typically sampled by solving a deterministic ordinary differential equation (ODE), whereas online reinforcement learning requires stochastic rollouts for policy exploration and optimization. Existing GRPO methods for flow models therefore replace the inference-time ODE with a stochastic differential equation (SDE) during training.