arXiv:2605. 24795v2 Announce Type: replace-cross Abstract: We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics.
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.
The paper introduces a probabilistic generative framework called Schr"odinger Bridges on Lie Group Manifolds, enabling direct modeling of non‑Euclidean data without flattening or coordinate inconsistencies. It develops two computational realizations—Wrapped‑Kernel Bridge Calibration for compact Abelian groups and Reciprocal Conditional‑Control Bridge Matching for compact non‑Abelian groups—while providing a modular error bound that separates various sources of approximation error. Experiments on protein, RNA torsions, SO(3), U(n), and protein conformational pathways demonstrate the method’s feasibility and consistency.
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.
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 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:2609.13758v1 Announce Type: cross Abstract: We establish the equivalence between the stochastic optimal control and path space formulations of the Schr\"odinger bridge problem (SBP) for the kin...
arXiv:2609.27250v1 Announce Type: cross Abstract: The Schr\"odinger bridge owes its computational power to a single structural fact: by Girsanov's theorem the controlled problem is a Kullback--Leible...
arXiv:2602. 22265v2 Announce Type: replace Abstract: Modern vision generators transport a base distribution to data through time-indexed measures, implemented as deterministic flows (ODEs) or stochastic diffusions (SDEs).
arXiv:2608. 02487v1 Announce Type: cross Abstract: Recently, rectified flow has emerged as a fundamental framework for large-scale image generation, powering state-of-the-art systems such as FLUX.
arXiv:2503. 14549v4 Announce Type: replace Abstract: Scientific generative models must turn tractable local decisions into globally correlated samples that respect physical constraints.
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.
arXiv:2410. 01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures.