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.
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:2605. 12174v2 Announce Type: replace Abstract: Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning.
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.
arXiv:2606. 05327v1 Announce Type: new Abstract: Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions.
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:2610.00785v1 Announce Type: new Abstract: Flow matching (FM) learns generative transport by fitting continuous-time motion from a simple source distribution to the data distribution. Most exist...
ParetoTransport is a training‑free guidance method for pre‑trained flow‑matching models that explicitly refines a population‑level distribution in objective space. It iteratively transports the empirical offline distribution toward the Pareto front using Wasserstein matching to intermediate proxy distributions, thereby controlling distributional displacement and mass allocation along the front. The authors prove a convergence result and show state‑of‑the‑art performance on standard offline multi‑objective optimization benchmarks, evaluating beyond hypervolume to generational distance, inverted generational distance, and Wasserstein distance.
The paper introduces Contrastive Noise Alignment (CNA), a training-time method for generative flow models that dynamically aligns Gaussian noise with data samples using a cross-modal InfoNCE objective. By modeling noise as an interacting particle system and regularizing with angular entropy and radial norm penalties, CNA reduces arbitrary data-noise couplings and flow curvature. Empirical results show that CNA improves generation quality, lowering FID by over 50% for few-step pixel-space generation compared to standard rectified flow and outperforming optimal transport baselines by at least 24%.
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: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.
The paper introduces the Variational Incompressible Optimal Transport (VIOT) operator, a generative neural operator that predicts divergence‑free velocity fields for incompressible density transport. VIOT combines a stream‑function representation, a regularized transport objective, and a Fourier Neural Operator backbone to amortize the solve across new source‑target pairs and grid resolutions. Experiments on 2D and 3D benchmarks show that VIOT produces full transport trajectories in seconds, achieving roughly a $10^4 imes$ speedup over per‑instance baselines that require hours of optimization.
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.