arXiv:2509. 03910v2 Announce Type: replace-cross Abstract: We formulate inverse problems in a Bayesian framework and aim to train an invertible generative model that is capable of simulation (i.
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.
arXiv:2605.29713v2 Announce Type: replace-cross Abstract: This book provides a compact, derivation-oriented introduction to the mathematical foundations of modern generative artificial intelligence....
The paper introduces a new method for perturbing data distributions in a way that respects equality constraints, allowing generative models to better handle constrained data. By adjusting the distribution while preserving the manifold geometry, the approach ensures support matches the ambient space dimension. Experiments with diffusion models and normalizing flows demonstrate improved data recovery and stable sampling across several tasks.
arXiv:2511. 09002v3 Announce Type: replace-cross Abstract: Self-consuming generative models have received significant attention over the last few years.
arXiv:2601. 21868v2 Announce Type: replace-cross Abstract: Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning.
arXiv:2606. 18071v1 Announce Type: cross Abstract: Score-based diffusion models typically use Brownian perturbations, which provide tractable reverse-time dynamics but impose memoryless noising.
We introduce Glow, a reversible generative model which uses invertible 1x1 convolutions. It extends previous work on reversible generative models and simplifies the architecture.
arXiv:2609.15193v1 Announce Type: new Abstract: Drifting models offer a promising route to faster generative AI: they perform gradual transport during training, while generating new samples in a sing...
arXiv:2607. 21585v1 Announce Type: new Abstract: Flow-based generative models have enabled remarkable progress in fast and controllable generation across continuous and discrete state spaces, yet existing parameterizations are constrained to fixed dimensions or fixed sequence lengths.
arXiv:2608. 08101v1 Announce Type: new Abstract: Generative AI has emerged as one of the most transformative forces in modern artificial intelligence, reshaping how we create, imagine, and interact with digital content.