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. 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 Flow Divergence Sampler (FDS), a training‑free method that refines intermediate states in flow‑matching models by using the divergence of the marginal velocity field to detect and correct misguidance toward low‑density regions. FDS operates during inference, requires no additional training, and can be applied as a plug‑and‑play module with standard solvers and existing flow backbones. Experiments show that FDS consistently improves fidelity in tasks such as text‑to‑image synthesis and inverse problems.
arXiv:2609.18488v1 Announce Type: cross Abstract: Diffusion and flow-matching models are typically trained by corrupting data through independently sampled Gaussian noise. While simple and scalable,...
arXiv:2601. 14430v2 Announce Type: replace-cross Abstract: Controlling generative models is computationally expensive.
arXiv:2605. 00941v4 Announce Type: replace Abstract: Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem.
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. 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:2607. 21427v1 Announce Type: new Abstract: Discrete flow matching provides a flexible framework for generative modeling on discrete structures.
arXiv:2601. 22495v2 Announce Type: replace Abstract: Fine-tuning flow matching models is a central challenge in settings with limited data, evolving distributions, or computational constraints.
arXiv:2604. 27147v3 Announce Type: replace-cross Abstract: In generative modeling, we often wish to produce samples that maximize a user-specified reward such as aesthetic quality or alignment with human preferences, a problem known as \textit{guidance}.
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%.
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.