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arXiv Machine Learning By Tiantian Zhang

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

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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.

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