arXiv:2605. 12174v2 Announce Type: replace Abstract: Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning.
arXiv:2608. 07042v1 Announce Type: cross Abstract: Rectified flows, also called flow matching or stochastic interpolants, are generative models that learn a time-dependent vector field steering a probability curve between two probability distributions, usually referred to as latent and target distributions.
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.
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.
The paper introduces COFM, a framework for consistent optimal transport flow matching that uses partially input convex neural networks (PICNN) to parameterize the transport potential. By adding a Hamilton‑Jacobi residual to the training objective, COFM enforces dynamical consistency and supports both one‑step transport and multi‑step ODE sampling without costly inner optimization. Experiments on benchmark datasets show that COFM achieves competitive performance while reducing L^2‑UVP by over 2× and cutting computational time by about 9× compared to state‑of‑the‑art models.
The paper introduces TDAction, a method for one‑step generative modeling that selects transport targets during training based on a cost reflecting shared‑parameter effort and terminal mismatch. By formulating this as a soft‑terminal control problem, the authors derive a closed‑form Batch Tangent Action‑to‑Go value that captures cross‑sample interactions and can be efficiently implemented with randomized tangent probes. Experiments on ImageNet 256×256 demonstrate that TDAction achieves an FID below 1.1 without distillation.
arXiv:2608. 00978v1 Announce Type: new Abstract: Flow Matching trains continuous-time generative models by regressing the velocity field of a probability path between a simple source distribution and a target data distribution.
arXiv:2608. 28262v1 Announce Type: new Abstract: Entropic optimal transport (EOT) has been shown to offer a computationally tractable approximation to exact optimal transport.
arXiv:2605. 12951v2 Announce Type: replace-cross Abstract: We propose Coreset-Induced Conditional Velocity Flow Matching (CCVFM), a generative model that augments hierarchical rectified flow with a data-informed source distribution.
arXiv:2606. 06272v1 Announce Type: new Abstract: Generative Flow Networks (GFlowNets) are a framework for sampling structured objects via stochastic trajectories in a directed graph.
arXiv:2606. 04092v1 Announce Type: cross Abstract: Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution.
The paper investigates how routing—where each noise sample is directed—differs between Flow Matching (FM) and Optimal Transport (OT) even when their transport costs are nearly identical. By separating cost from routing, the authors demonstrate numerically that FM and OT can produce similar costs yet diverge in routing decisions. They further show that incorporating routing information into training improves generation quality compared to a cost-only approach.
The paper investigates training diffusion models to sample from distributions defined by unnormalized densities or energy functions. It benchmarks various diffusion-structured inference techniques, including simulation-based variational methods and off-policy approaches such as continuous generative flow networks, highlighting their relative strengths and challenging some prior claims. Additionally, the authors introduce a new exploration strategy for off-policy methods that employs local search in the target space with a replay buffer, demonstrating improved sample quality across multiple target distributions.