arXiv:2510. 12636v5 Announce Type: replace-cross Abstract: The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones.
arXiv:2602.19600v2 Announce Type: replace Abstract: Many high-dimensional datasets concentrate near a low-dimensional structure embedded in the ambient space. Generative models for such data must con...
arXiv:2604. 04342v2 Announce Type: replace Abstract: Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced.
arXiv:2606. 30310v1 Announce Type: cross Abstract: The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along random projections.
arXiv:2502. 07580v4 Announce Type: replace Abstract: We present a novel view of diffusion-like generative modeling from the perspective of iterative Gaussian posterior inference.
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:2607. 19332v1 Announce Type: new Abstract: Generative models have undergone many generations of evolution, from VAEs/GANs to diffusion/flow matching.
arXiv:2505. 06835v5 Announce Type: replace Abstract: Sliced optimal transport (SOT), or sliced Wasserstein (SW) distance, is widely recognized for its statistical and computational scalability.
arXiv:2605. 13175v2 Announce Type: replace Abstract: Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity.
The paper presents a new one‑step generative modeling framework for finite state spaces, leveraging discrete Wasserstein geometry to define a target‑relative KL gradient flow over a reversible Markov kernel. The authors implement this flow at the particle level using Markov jumps and encode the resulting transport updates into a latent‑conditioned generator, enabling one‑step inference after training. Experiments on a controlled setting confirm KL dissipation, consistency between particle dynamics and probability flow, and accurate numerical scaling, while a finite‑capacity neural generator successfully tracks the exact transport targets.
Generative models have undergone many generations of evolution, from VAEs/GANs to diffusion/flow matching. Along the way, the underlying techniques have become more complicated and various beliefs about what drives strong empirical performance have taken hold.
arXiv:2610.01034v1 Announce Type: cross Abstract: Bayesian inference increasingly uses informative but implicit priors represented only by samples, such as historical ensembles, simulator outputs, an...
arXiv:2606. 04092v1 Announce Type: cross Abstract: Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution.