Optimal Transport Flow Matching by Design
arXiv:2606. 04092v1 Announce Type: cross Abstract: Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution.
arXiv:2606. 04092v1 Announce Type: cross Abstract: Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution.
arXiv:2607. 19332v1 Announce Type: new Abstract: Generative models have undergone many generations of evolution, from VAEs/GANs to diffusion/flow matching.
arXiv:2602.19600v2 Announce Type: replace Abstract: Many high-dimensional datasets concentrate near a low-dimensional structure embedded in the ambient space. Generative models for such data must con...
Generative models have undergone many generations of evolution, from VAEs/GANs to diffusion/flow matching. Along the way, the underlying techniques have become more complicated and various beliefs about what drives strong empirical performance have taken hold.
arXiv:2607. 12171v1 Announce Type: cross Abstract: In rectified-flow-based generative models, the neural network can be trained to predict two different targets, such as the instantaneous velocity or the data endpoint, to perform denoising.
arXiv:2606. 02453v1 Announce Type: cross Abstract: Despite the remarkable fidelity of generative models, they frequently suffer from mode collapse.
The paper introduces Quantile AlignTree Flow Matching (QAT‑FM), a structured coupling method that builds a hierarchical, quantile‑aligned tree to connect a Gaussian prior with a target distribution. QAT‑FM achieves efficient coupling construction in ≠ Nd log N time and allows per‑pair source sampling in ≠ d time, enabling scalable training for high‑dimensional generative tasks. The authors prove that the coupling preserves marginal consistency, produces non‑crossing interpolation paths, and improves path separation compared to independent coupling, while also extending naturally to conditional generation.
arXiv:2608. 10544v1 Announce Type: cross Abstract: Image restoration is fundamentally constrained by the tradeoff between distortion and perception: minimizing pixel-wise error yields over-smoothed results, whereas optimizing for perceptual realism often introduces structural deviations.
arXiv:2606. 29724v1 Announce Type: new Abstract: Normalizing flows are powerful generative models that learn an invertible mapping between complex data distributions and simple latent distributions, typically a standard normal density.
In rectified-flow-based generative models, the neural network can be trained to predict two different targets, such as the instantaneous velocity or the data endpoint, to perform denoising. Although prior work shows that these parameterizations lead to different empirical behaviors, the mechanisms underlying their respective advantages remain to be underexplored, and how to combine them effectively is still unclear.
The paper introduces CAT-Flow, a pair of lightweight, training‑free algorithms—CAT‑OV and CAT‑OT—that adapt step‑sizes during Flow Matching inference by estimating curvature in time or state space. These methods avoid extra neural evaluations and achieve constant‑order truncation error bounds. Experiments show that CAT‑OV and CAT‑OT improve image quality metrics across four text‑to‑image Flow Matching models, cutting the required generation steps by up to 40%.
arXiv:2505. 04486v4 Announce Type: replace-cross Abstract: Flow matching models have shown great potential in image generation tasks among probabilistic generative models.