arXiv Machine Learning
Jun 10
It\^o maps for any-step SDEs
arXiv:2606. 11156v1 Announce Type: cross Abstract: Recent one-step generative models accelerate sampling by learning deterministic flow maps of the underlying dynamics.
Strong Stochastic Flow Maps
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.
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arXiv Machine Learning
Sep 11
Deep operator learning for efficient sampling from invariant measures of stochastic differential equations
The paper presents an amortized neural sampler that merges operator learning with flow-based methods to efficiently sample from invariant measures of stochastic differential equations (SDEs). By mapping SDE coefficient functions to pushforwards from a reference measure, the approach shifts the sampling cost to an initial training phase, after which new SDE instances can be sampled with a single encoder pass and a few ODE solver steps, independent of mixing time. The framework incorporates Lagrangian trajectory sensors and cross attention to handle high-dimensional problems, and the authors provide theoretical guarantees of expressivity and resolution invariance, demonstrating competitive accuracy and significant speedups over MCMC in 1D, 2D, and 64D SDE families.
arXiv AI
Jul 2
Flow-Map GRPO: Reinforcement Learning for Few-Step Flow-Map Generators via Anchored Stochastic Composition
arXiv:2607. 00535v1 Announce Type: cross Abstract: Few-step flow-map generators, such as consistency models and MeanFlow, accelerate sampling by directly learning long-range transport maps between noise and data.
arXiv Machine Learning
Aug 27
Data-driven Effective Modeling of Stochastic Chemical Reaction Networks
The paper introduces a data-driven effective model for stochastic chemical reaction networks that bypasses the high computational cost of the Stochastic Simulation Algorithm (SSA). By approximating the finite-time transition kernel of the SSA-induced continuous-time Markov chain with a generative machine learning model, the method operates on a user-defined coarse time step independent of microscopic reaction events. Using a conditional normalizing flow as the stochastic propagator, the trained model recursively generates statistically consistent trajectories, achieving significant computational savings while maintaining accuracy, as demonstrated through numerous numerical examples.
arXiv Machine Learning
Jun 30
Neural Galerkin Normalizing Flow for Transition Probability Density Functions of Diffusion Models
arXiv:2603. 18907v2 Announce Type: replace Abstract: We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution, parametrically with respect to the location of the initial mass.
arXiv Machine Learning
Aug 10
Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEs
arXiv:2601. 08527v3 Announce Type: replace-cross Abstract: We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants.
arXiv Machine Learning
Jul 30
Flow Map Learning via Nongradient Vector Flow
arXiv:2607. 26398v1 Announce Type: new Abstract: Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration.
arXiv Machine Learning
Sep 1
Data-to-Energy Stochastic Dynamics
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 AI
Aug 28
The Principles of Diffusion Models
The book "The Principles of Diffusion Models" outlines the foundational concepts behind diffusion models, tracing their evolution from a forward process that corrupts data into noise to a reverse process that reconstructs data. It presents three complementary perspectives—variational, score-based, and flow-based—each describing how a time-dependent velocity field transports a simple prior to the data distribution. The text also covers practical guidance for controllable generation, efficient solvers, and diffusion-inspired flow-map models, providing a mathematically grounded framework for readers with basic deep‑learning knowledge.
arXiv Machine Learning
Jul 22
Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise
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 Machine Learning
Jul 2
Goal-oriented learning of stochastic differential equations using error bounds on path-space observables
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 AI
Aug 7
LC-GRPO: Bridging Train-Inference Gap for Flow-Based GRPO with Langevin Correction
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.