arXiv:2605. 02961v2 Announce Type: replace-cross Abstract: Most modern bridge-diffusion methods achieve finite-time transport by specifying an interpolation, Schrodinger-bridge, or stochastic-control objective and then learning the associated score or drift field with a neural network.
arXiv:2605. 24795v2 Announce Type: replace-cross Abstract: We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics.
arXiv:2607. 16987v1 Announce Type: cross Abstract: Over the past few years, diffusion-based Schr\"odinger bridge models have been proposed to approximate optimal transport dynamics between two prescribed boundary distributions, with successful applications to generative modeling.
The paper introduces a mesh‑free, self‑supervised neural operator—called the Normalizing Flow Invertible Solution Transformer (NFIST)—for stochastic mean‑field control (MFC). By reformulating the controlled Fokker–Planck dynamics as a deterministic continuity equation via a probability‑flow ODE and an invertible normalizing‑flow transformer, the authors enable closed‑form score evaluation with linear cost per particle. The resulting operator learns from task prompts (distribution parameters or particle clouds) and can solve unseen MFC tasks in a single forward pass, achieving zero‑shot generalization across applications such as stochastic optimal control, Schrödinger bridges, systemic‑risk control, and obstacle‑avoiding path planning.
arXiv:2511. 06229v3 Announce Type: replace Abstract: This paper focuses on dynamic origin-destination matrix estimation (DODE), a crucial calibration process necessary for the effective application of microscopic traffic simulations.
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: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...
The paper introduces a new Markov chain Monte Carlo method that samples from multimodal distributions by interpolating along the diffusion path of a noising diffusion process, preserving mode weights and improving mixing. It proposes a Metropolis-adjusted diffusion path (MAD-Path) sampler that corrects for bias from approximate score estimates and discretization errors, ensuring the target distribution remains invariant. Experiments on Bayesian posteriors demonstrate that MAD-Path outperforms tempering-based MCMC and unadjusted diffusion samplers in global exploration and accurate mode-weight estimation.
arXiv:2608. 10777v1 Announce Type: new Abstract: Linear Quadratic Stochastic Optimal Control (LQ-SOC) establishes a fundamental framework for steering noisy dynamical systems and has recently gained renewed interest in the machine learning community.
arXiv:2605.29371v2 Announce Type: replace-cross Abstract: We study the subclass of potential mean-field games in which the running interaction cost and the terminal target cost are both expressed thr...
The paper introduces the Distributionally Robust Schr"odinger Bridge (DRSB), a method that learns a single controller capable of handling uncertainty in the initial distribution for stochastic transport tasks. DRSB’s objective combines control energy with a KL penalty on the terminal distribution, and it seeks to minimize the worst‑case value of this objective over an ambiguity set around the nominal initial distribution. The authors derive a variational formulation, connect it to stochastic optimal control and distributionally robust optimization, and propose an alternating algorithm with Wasserstein and Sinkhorn variants. Experiments on two‑dimensional transport and image‑to‑image translation demonstrate improved robustness to input perturbations compared to standard SB, while also achieving lower mean sliced Wasserstein distance on Gaussian mixture transport.
arXiv:2606. 15359v1 Announce Type: new Abstract: Diffusion models have emerged as powerful tools for planning and control by learning multimodal distributions over actions and trajectories.
arXiv:2606. 03820v1 Announce Type: cross Abstract: We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps.