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.
By Zhangyong Liang, Huanhuan Gao
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.
By Aneesh Barthakur, Mathias Niepert, Luiz F. O. Chamon
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...
By Zhangyong Liang, Haibin Ling
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.
By Sizhe Wang, Himashi Peiris, Zhaolin Chen