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...
arXiv:2510. 01894v3 Announce Type: replace Abstract: Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots.
arXiv:2608. 08594v1 Announce Type: new Abstract: Diffusion bridge models leverage Doob's \(h\)-transform to construct stochastic transports between arbitrary endpoint distributions, and have shown strong potential in image-to-image translation and restoration.
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.
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.
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:2606. 16610v1 Announce Type: cross Abstract: Diffusion Flow Matching (DFM) has recently emerged as a versatile framework for generative modeling, yet its theoretical convergence properties remain only partially understood.
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.
arXiv:2609.25444v1 Announce Type: new Abstract: This work studies prediction parameterization for stochastic generative dynamics in diffusion models. Existing velocity-based generative models provide...
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:2602.15396v2 Announce Type: replace Abstract: Diffusion models often yield highly curved trajectories and noisy score targets due to an uninformative, memoryless forward process that induces in...