arXiv AI

All in One: Generative Modeling as Mean-Field Game Design

arXiv:2607. 23026v1 Announce Type: cross Abstract: Mean-field games (MFGs) offer a unifying lens on continuous-time generative modeling: a cost tuple recovering twelve prominent models---Continuous Normalizing Flows, OT-Flow, Score-based Models, Schr\"{o}dinger Bridges, and more---as special cases of one variational problem.

arXiv Machine Learning
Aug 20

Bridge Graphical Models: Coupling, Projection, and Current-Preserving Dynamics for Generative Modeling

The paper introduces Bridge Graphical Models (BGMs), a framework that decomposes continuous‑time generative models into independent design choices: endpoint coupling, bridge law, Markovian projection, and current‑preserving dynamics. It defines the Markovization gap as the time‑integrated conditional variance of bridge velocity given the Markov state, quantifying an irreducible loss before training. Experiments on synthetic, latent, and pixel‑space tasks (CIFAR‑10 and Fashion‑MNIST) show that a feature‑space proxy of this gap, estimated quickly before training, predicts downstream training loss and FID in the same direction as full training results.

By Tiantian Zhang
arXiv Machine Learning
Jun 9

Midpoint Generative Models

arXiv:2605. 29920v2 Announce Type: replace Abstract: We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models.

By Daniil Shlenskii, Nikita Gushchin, Lev Novitskiy, Dmitry V. Dylov, Alexander Korotin
arXiv Machine Learning
Aug 20

Self-supervised In-context Operator Learning for Stochastic Mean-Field Control

The paper introduces a mesh‑free, self‑supervised neural operator—called the Normalizing Flow Invertible Solution Transformer (NFIST)—for stochastic mean‑field control (MFC). By reformulating the controlled Fokker–Planck dynamics as a deterministic continuity equation via a probability‑flow ODE and an invertible normalizing‑flow transformer, the authors enable closed‑form score evaluation with linear cost per particle. The resulting operator learns from task prompts (distribution parameters or particle clouds) and can solve unseen MFC tasks in a single forward pass, achieving zero‑shot generalization across applications such as stochastic optimal control, Schrödinger bridges, systemic‑risk control, and obstacle‑avoiding path planning.

By Suyi Gao, Mo Zhou, Rongjie Lai