Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map. In applications like generative modeling, the transport cost itself is irrelevant, and this makes it natural to target maps which are more tractable from either a statistical or computational standpoint.
arXiv:2606. 30574v1 Announce Type: new Abstract: Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map.
By Sivaraman Balakrishnan
The paper develops a statistical framework showing that empirical score matching can achieve minimax optimal performance for diffusion generative models when data lie on a low‑dimensional manifold. It establishes convergence rates for empirical risk minimization over constrained Sobolev classes and demonstrates that the resulting score estimators yield minimax optimal Wasserstein‑1 rates for the generated distribution, up to logarithmic factors. The analysis reveals that the statistical rates depend on the intrinsic dimension of the data manifold rather than its ambient dimension, providing conditions under which score‑based generative modeling generalizes rather than overfits.
By Thomas Bonis, Thanh Mai Pham Ngoc, Viet Chi Tran
The paper introduces a new optimal transport framework that uses the Barron energy—an intrinsic neural network complexity measure—instead of the traditional kinetic energy. By modeling transport as deep residual networks that map a reference distribution to a target distribution, the authors define a new metric on probability measures and analyze its properties for generative modeling. They demonstrate that diffusion generative models are suboptimal in this Barron geometry and explore how adaptivity can improve alternative generative approaches.
By Evan Dogariu, Joan Bruna
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...
By Hoang Phuc Hau Luu, Marcelo Hartmann, Zhongjian Wang
The paper introduces a pullback Riemannian geometry tailored for multimodal data by employing a latent Gaussian mixture model. It defines a smooth, positive‑definite metric based on responsibility‑weighted component precision, extending the standard single‑Gaussian construction. Experiments on synthetic, multi‑view image, and MNIST datasets demonstrate reduced transport distortion, accurate trajectory recovery, and more realistic interpolation.
By Honglei Brinkmann, Lucas Ng, Georgios Batzolis, Mark Girolami, Carola-Bibiane Sch\"onlieb, Willem Diepeveen
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.
By Jannis Chemseddine, Gregor Kornhardt, Richard Duong, Gabriele Steidl
arXiv:2608. 04827v1 Announce Type: cross Abstract: We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds.
By Yizhu Wang, Mu Niu, Xiaochen Yang
The paper introduces Latent Nonlinear Denoising Score Matching (LNDSM), a method that integrates nonlinear, structure-informed latent diffusions with a variational autoencoder framework. LNDSM designs the forward diffusion to admit a chosen reference distribution, such as a Gaussian mixture, and derives a computable approximation to a cross‑entropy upper bound using Euler‑Maruyama discretization. Experiments on benchmark image datasets show that LNDSM improves sample quality, mode balance, and training efficiency compared to conventional latent score‑based generative models.
By Kaichen Shen, Wei Zhu
arXiv:2607. 19332v1 Announce Type: new Abstract: Generative models have undergone many generations of evolution, from VAEs/GANs to diffusion/flow matching.
By Chirag Vashist, Ke Li
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.
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%.
By Lennart Wittke, Vinicius Azevedo