arXiv:2606. 15897v1 Announce Type: cross Abstract: Flow matching is a powerful generative modeling framework, valued for its simplicity and strong empirical performance.
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.
arXiv:2608. 01692v1 Announce Type: new Abstract: We propose an instantiation of flow matching that relies on a time-independent velocity field (an \emph{autonomous flow}) to exactly map between two distributions, so long as the target is singular, i.
The paper introduces a flow matching framework that unifies various neural representational dissimilarity metrics under a single theoretical umbrella. By interpreting these metrics as Jeffreys divergences with different velocity constraints, the authors demonstrate that flow matching improves distance estimation for complex distributions and continuous variables. The framework also facilitates the principled design of new dissimilarity measures.
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:2606. 05327v1 Announce Type: new Abstract: Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions.
arXiv:2606. 07481v1 Announce Type: new Abstract: While Computational Fluid Dynamics (CFD) provides high-fidelity flow fields for optimizing indoor environments, its computational cost limits rapid exploration.
arXiv:2606. 09806v1 Announce Type: cross Abstract: We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains.
arXiv:2510. 01894v3 Announce Type: replace Abstract: Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots.
arXiv:2606. 04092v1 Announce Type: cross Abstract: Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution.
arXiv:2601. 22107v2 Announce Type: replace Abstract: We introduce \textit{Prior-Informed Flow Matching (PIFM)}, a conditional flow model for graph reconstruction.
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%.
arXiv:2606. 30053v1 Announce Type: cross Abstract: These notes recapitulate the high level mathematical principles behind different techniques for generative modeling.