The paper introduces Curvature-Adaptive Tubular Correction (CAT), a training‑free plugin that refines diffusion guidance by decomposing the guidance gradient into normal and tangent components and regulating them within a noise‑dependent geometric budget. CAT charges normal displacement at first order and tangent displacement according to directional curvature, solving a one‑dimensional dual equation for optimal magnitudes and using Armijo backtracking to calibrate the step size. Experiments on seven inverse problems with FFHQ and ImageNet demonstrate that CAT consistently improves pixel‑ and latent‑space samplers, enhances perceptual metrics, and achieves the lowest FID across classifier‑free guidance scales while maintaining stable saturation and contrast.
arXiv:2607. 22004v1 Announce Type: new Abstract: Energy natural gradient descent (ENGD) aligns parameter updates with the curvature of an underlying function-space energy, but existing formulations assume an unconstrained Euclidean parameter domain.
Rectified-flow-based diffusion transformers, particularly FLUX, have demonstrated outstanding performance in high-quality image generation. However, achieving fast and accurate inversion--transforming images back to latent noise for faithful reconstruction and editing--remains a challenging bottleneck due to the discretization errors of linear solvers.
The paper introduces Learned End-to-End Guidance Schedules (LEEGS) for diffusion models, which train a time‑dependent guidance schedule to balance data quality and requirement satisfaction while reducing sampling steps. LEEGS minimizes the guidance function over a small set of examples using stochastic gradient descent and employs a gradient approximation to cut training time by a factor of four. Experiments on tasks such as image inpainting, noisy image inverse problems, face‑ID‑guided generation, and PDE problems show that LEEGS outperforms baselines at the same computational budget or matches constant guidance with only 10% of the steps.
Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks. Such problems have a natural geometric interpretation, model predictions form a manifold in data space, while the chosen parameterization can introduce parameter-effects curvature that becomes a dominant source of nonlinearity.
arXiv:2609.40287v1 Announce Type: new Abstract: Physics-constrained generative models aim to generate physical fields that match a target distribution and satisfy prescribed constraints. However, enf...
The paper introduces a geometry‑guided sampling operator that directs feature sampling rather than altering convolution kernels in 3D encoder‑decoder networks. By predicting local orientations and bounded step sizes, the operator samples symmetrically around each voxel, generating compact geometric and boundary cues that improve fine‑structure segmentation. Replacing stride‑1 and stride‑2 operations in a 3D U‑Net yields consistent gains on BraTS, MSD Hepatic Vessel, and TDSC‑ABUS datasets, with better boundary metrics and fewer parameters, and the operator can be integrated into other backbones without architectural changes.
arXiv:2607. 07623v1 Announce Type: new Abstract: Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks.
arXiv:2607. 05866v1 Announce Type: cross Abstract: Under a fixed privacy budget, the utility of differentially private (DP) training is ultimately determined by its optimization efficiency.
arXiv:2502. 08006v3 Announce Type: replace-cross Abstract: Training-free guided generation is a widely used and powerful technique that allows the end user to exert further control over the generative process of flow/diffusion models.
arXiv:2606. 06303v1 Announce Type: new Abstract: Controllable generation with discrete diffusion models is often hindered by high computational overhead or the need for retraining.
arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.
The paper studies classifier‑free guidance (CFG) in Flow Matching, showing that strong guidance can distort the generated distribution by shifting the mean and concentrating trajectories. By interpreting Flow Matching as a time‑varying gradient flow, the authors explain how CFG reshapes the underlying potential and propose a training‑free method, Posterior‑Mean‑Capped CFG (PMC‑CFG), that adaptively limits guidance to the strongest feasible level. Experiments on synthetic and large‑scale image‑generation tasks demonstrate that PMC‑CFG reduces distortion and concentration while improving the alignment–diversity trade‑off, especially when nominal guidance is large.