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arXiv AI

ManifoldCache: Training-Free Diffusion Acceleration via Constraint Manifold Caching

ManifoldCache is a training‑free, data‑free accelerator for Constraint‑Manifold Diffusion Models (CMDMs), which generate samples that must satisfy hard geometric constraints in scientific domains such as medical imaging, molecular design, and 3D scene generation. By decomposing the conditional score into orthogonal normal and tangential components, the method identifies a noise‑schedule midpoint as a safe caching boundary—caching before this point guarantees bounded error, while caching after it leads to mode confusion. The approach also shows that deeper network blocks allow larger certified cache strides, all without requiring calibration data or additional training.

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arXiv Machine Learning
Oct 2

PMosFM: Preconditioned Manifold Matching for One-Step Physics-Constrained Generation

PMosFM introduces a preconditioned manifold matching framework that enables one‑step physics‑constrained generation by encoding constraints in a manifold decoder. The method learns transport in intrinsic coordinates, eliminating the need for residual losses or trajectory unrolling, and employs a geometric preconditioner and covariance transform to improve conditioning. Experiments demonstrate reduced training and sampling time compared to multi‑step baselines while maintaining comparable physical and distributional fidelity.

By Zhangyong Liang, Haibin Ling
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arXiv Machine Learning
Jul 2

Diffeomorphic Optimization

arXiv:2607. 00947v1 Announce Type: new Abstract: Generative models learn data distributions that reside on a low-dimensional manifold within a higher-dimensional ambient space.

By Ludwig Winkler, Andrew Leaver-Fay, Joseph Kleinhenz, Pan Kessel
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arXiv Machine Learning
Jul 2

Geometry-Preserving Neural Architectures on Manifolds with Boundary

arXiv:2602. 03082v2 Announce Type: replace Abstract: A growing number of neural architectures have been proposed to enforce geometric constraints, including projection-based networks, exponential-map updates, constrained output layers, and manifold neural ODEs.

By Karthik Elamvazhuthi, Shiba Biswal, Kian Rosenblum, Arushi Katyal, Tianli Qu, Grady Ma, Rishi Sonthalia
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arXiv AI
Jul 2

SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling

arXiv:2607. 00095v1 Announce Type: cross Abstract: Generative models have emerged as scalable surrogates for physical simulation, yet they offer no guarantee that their outputs respect the conservation laws, boundary conditions, and nonlinear invariants that govern the underlying physics.

By Alaina Kolli, Theodoros Xenakis, Utkarsh Utkarsh, Pengfei Cai, Rafael Gomez-Bombarelli, Alan Edelman, Christopher Vincent Rackauckas
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arXiv AI
Oct 5

Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers

The paper presents a data‑efficient pre‑training framework for neural surrogate models solving PDEs on unstructured 3D geometries. It introduces a geometry‑driven strategy for steady‑state problems that uses intrinsic shape descriptors, and a physics‑driven approach for transient problems that generates synthetic PDE data online. Experiments show faster convergence, higher data efficiency, and improved accuracy during fine‑tuning, especially in low‑data settings.

By Luis Medrano-Navarro, Giacomo Baldan, Qiang Liu, Benjamin Holzschuh, Jan Hagnberger, Mathias Niepert, Nils Thuerey
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