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.
The paper introduces ReCouple, a framework that constructs coarse-grained optimal transport (OT) couplings to improve flow matching without requiring rollouts. Extensions ReCouple+ and ReCouple++ address continuous-source settings and add spatial regularization, respectively. Experiments show that these methods balance coupling optimality, neural network realizability, and generation quality, especially in low NFE regimes.
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%.
The paper introduces Cumulative Marginal Matching (CMM), a new objective for training few‑step diffusion and flow‑matching models. CMM treats flow‑matching as a sequence of intermediate marginal distributions and directly optimizes the cumulative Wasserstein‑2 discrepancy between the base and few‑step models across the entire trajectory. It derives a tractable surrogate for this objective, shows that Shortcut‑CSL is a first‑order approximation of CMM, and reports improved generation quality on standard benchmarks under the same training budget.
arXiv:2610.02260v1 Announce Type: new Abstract: Flow matching models excel at generative modeling, and many downstream applications require their samples to satisfy prescribed constraints, such as ob...
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:2610.29075v1 Announce Type: new Abstract: We aim to address the problem of Out-of-Distribution (OOD) Mode Averaging, a critical problem that emerges when distilling Flow Matching (FM) based beh...
The paper introduces data‑space iteration, a few‑step generation framework that eliminates the need for a fixed probability‑flow discretization. By refining predictions directly in data space with a shared generator, each iteration is trained to produce the best possible sample within its capacity. Experiments on class‑conditional ImageNet 256×256 show that data‑space iteration outperforms standard discretization baselines and matches or improves upon schedule‑searched variants without schedule‑specific training.
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 introduces Function Projection for Flow Matching (FP‑FM), an algorithm that conditions generative models directly on samples from a target distribution. FP‑FM learns basis functions spanning velocity fields for training distributions and adapts to new distributions via a simple least‑squares projection, enabling efficient sample generation without additional training at inference time. Variants of the method trade expressivity for computational cost by enriching coefficient calculations, and the approach shows markedly better precision and recall than baselines, especially on unseen distributions.