We study path-flow alignment as a unified training objective for flow matching. Instead of fixing the interpolation path and learning only the velocity field, we jointly train an endpoint-preserving p...
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:2610.01408v1 Announce Type: new Abstract: Trajectory crossing remains a critical bottleneck in Flow Matching (FM), and previous works typically view these crossings from a theoretical optimizat...
arXiv:2609.36348v1 Announce Type: cross Abstract: Generative and representation learning remain asymmetrically connected: semantic representations are used to improve diffusion generation, whereas th...
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%.
The paper examines the common practice in diffusion and flow matching of predicting the clean signal, converting it to a velocity, and training with a velocity-space loss. It shows that this conversion can cause unstable optimization due to singular endpoint amplification, but that prediction–loss alignment removes this source of non‑integrability and ensures a finite second moment for all timesteps, even with uniform sampling. Experiments confirm that aligned objectives remain trainable across different samplers, reconciling theoretical concerns with empirical success.
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.
arXiv:2607. 16294v1 Announce Type: cross Abstract: Paired image-to-image translation underpins a wide range of computer vision tasks, including image editing, sensor translation, and domain adaptation.
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 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 Noise Policy Optimization (NPO), a method for aligning few-step generative models with black-box reward signals. NPO learns an amortized flow policy that transforms initial Gaussian noise into a reward-tilted distribution, allowing the pretrained generator to produce higher-reward outputs without fine-tuning. The approach achieves superior reward-quality trade-offs across image, language, and protein generation tasks while drastically reducing inference cost compared to test-time search methods.
Pixel-space generative models bypass lossy latent compression, yet necessitate joint learning of global structure and fine-grained details in a high-dimensional space. Standard flow matching interpolates noise toward a fixed clean-image endpoint, leaving the spectral evolution to be learned implicitly.