arXiv:2509. 02971v2 Announce Type: replace-cross Abstract: Flow-based generative models can face numerical challenges on scientific data with multiscale Fourier spectra, often producing large errors at fine scales.
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%.
Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite-dimensional spaces. Functional Flow Matching (FF...
arXiv:2611.06711v1 Announce Type: new Abstract: Deep generative models, particularly Flow Matching frameworks, have emerged as powerful tools for synthesizing complex physical systems. However, stand...
arXiv:2609.38918v1 Announce Type: cross Abstract: Flow Matching (FM) learns a velocity field whose ODE transports a simple source distribution to a target law. Existing finite-sample theory largely t...
arXiv:2609.38049v1 Announce Type: new Abstract: Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite...
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.
Continuous-time generative frameworks construct probability paths between base and target domains by optimizing time-dependent velocity fields. While theoretical targets favor straight trajectories, empirical networks develop complex path deformations.
The paper presents an amortized neural sampler that merges operator learning with flow-based methods to efficiently sample from invariant measures of stochastic differential equations (SDEs). By mapping SDE coefficient functions to pushforwards from a reference measure, the approach shifts the sampling cost to an initial training phase, after which new SDE instances can be sampled with a single encoder pass and a few ODE solver steps, independent of mixing time. The framework incorporates Lagrangian trajectory sensors and cross attention to handle high-dimensional problems, and the authors provide theoretical guarantees of expressivity and resolution invariance, demonstrating competitive accuracy and significant speedups over MCMC in 1D, 2D, and 64D SDE families.
arXiv:2606. 02177v1 Announce Type: new Abstract: Flow Matching typically relies on white noise sources, a choice often misaligned with the power spectra of natural data, which tend to decay with frequency.
arXiv:2610.01193v1 Announce Type: cross Abstract: Counterfactual generation seeks to sample outcomes under a hypothetical intervention or decision using observational data collected under the factual...
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...