arXiv Machine Learning
PMosFM: Preconditioned Manifold Matching for One-Step Physics-Constrained Generation
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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.
arXiv Machine Learning
Aug 19
Composing Flow-Matching Energies with Known Physics: Generation, OOD Detection, and Inversion on PDE Fields
The paper presents a method that combines flow‑matching models with energy‑based modeling to explicitly construct scalar energy functions for physical fields. These energies are derived from a matching regression objective on a linear Gaussian interpolation, avoiding variational approximations or extra MCMC steps, and can be used for energy‑corrected data generation, out‑of‑distribution detection, and posterior sampling in inverse problems. The approach enables general MCMC samplers that reduce PDE residuals and spectral distance, and it demonstrates that combining data‑driven and physics‑based energies improves OOD detection accuracy.
arXiv Computer Vision
Sep 1
Off-Manifold Refinement: Guiding Video Generators with a Frozen World Model
arXiv:2608.29904v1 Announce Type: new Abstract: Modern video generators routinely fail at physical dynamics: objects float, trajectories violate gravity, contacts vanish. Standard denoising and flow-...
arXiv AI
Jul 1
Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems
arXiv:2508. 09156v3 Announce Type: replace-cross Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.
arXiv AI
Sep 2
Training-Free Refinement of Flow Matching with Divergence-based Sampling
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.
arXiv Machine Learning
Jul 27
Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers
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.