This paper introduces random-bridges—stochastic processes conditioned to hit target distributions at fixed times—as stochastic transports for generative modeling. Random-bridges can be Markovian or non‑Markovian, continuous or discontinuous, depending on the driving process, and the authors develop both theoretical foundations and practical training/simulation algorithms for Gaussian and Lévy (Gamma, Poisson, Stable‑1/2) bridges. Empirical results on the Gaussian case show that the proposed framework produces high‑quality samples with competitive Fréchet Inception Distance scores relative to popular denoising diffusion and flow‑matching methods.
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:2608. 03117v1 Announce Type: new Abstract: The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions.
The paper introduces Bridge Graphical Models (BGMs), a framework that decomposes continuous‑time generative models into independent design choices: endpoint coupling, bridge law, Markovian projection, and current‑preserving dynamics. It defines the Markovization gap as the time‑integrated conditional variance of bridge velocity given the Markov state, quantifying an irreducible loss before training. Experiments on synthetic, latent, and pixel‑space tasks (CIFAR‑10 and Fashion‑MNIST) show that a feature‑space proxy of this gap, estimated quickly before training, predicts downstream training loss and FID in the same direction as full training results.
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:2604. 04342v2 Announce Type: replace Abstract: Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced.
Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map. In applications like generative modeling, the transport cost itself is irrelevant, and this makes it natural to target maps which are more tractable from either a statistical or computational standpoint.
arXiv:2605. 00161v2 Announce Type: replace Abstract: Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps.
arXiv:2606. 08953v1 Announce Type: new Abstract: Modern generative models often define an entire probability path from a simple prior to the data law, rather than only an endpoint map.
arXiv:2509. 21925v2 Announce Type: replace-cross Abstract: This paper investigates the theoretical behavior of generative models under finite training populations.
arXiv:2606. 30574v1 Announce Type: new Abstract: Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map.
arXiv:2605. 29920v2 Announce Type: replace Abstract: We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models.
arXiv:2609.38364v1 Announce Type: cross Abstract: Discrete diffusion models and flow matching have emerged as powerful frameworks for generative modeling over discrete state spaces, yet efficient few...