aiqbench analysis
This paper introduces Bridge Graphical Models (BGMs) to address the "Markovization gap," a fundamental bottleneck in continuous-time generative models where endpoint-conditioned bridges must be compressed into non-anticipative Markov decoders. By formalizing this irreducible loss as a pre-training diagnostic, the authors provide a framework to compare design choices across diffusion, flow matching, and Schrödinger bridge architectures before neural network training begins. The work offers a rigorous theoretical lens for optimizing generative modeling pipelines by separating coupling, projection, and dynamics into independent variables.
Bridge Graphical Models: Coupling, Projection, and Current-Preserving Dynamics for Generative Modeling
arXiv:2608.19144v1 Announce Type: new Abstract: Continuous-time generative models are often built from endpoint-conditioned bridges, but generation requires a different object: a non-anticipative Markov decoder that only observes the current state and time. We identify this bridge-to-decoder compression as a structural bottleneck shared by diffusion models, flow matching, rectified flow, Schr\"odinger bridges, and field-based generative models. We introduce the \emph{Markovization gap}, the time-integrated conditional variance of the bridge velocity given the Markov state. It is the MMSE of predicting endpoint-conditioned motion from the information available to a sampler, and it measures an irreducible loss incurred before any neural network is trained. To make this bottleneck comparable across model families, we define \emph{Bridge Graphical Models} (BGMs), which separate endpoint coupling, bridge law, Markovian projection, and current-preserving dynamics representation as independent design choices. The same formalism also represents Poisson and electrostatic models as field-line bridge kernels with a corresponding field-line Markovization gap. Across synthetic, latent, and pixel-space pilots on CIFAR-10 and Fashion-MNIST, a feature-space proxy gap estimated in minutes before training ranks design choices in the same direction as downstream training loss and FID under fixed architecture, bridge, sampler, and compute. These results support the Markovization gap as a pre-training diagnostic for bridge and coupling design.
Abstract:Continuous-time generative models are often built from endpoint-conditioned bridges, but generation requires a different object: a non-anticipative Markov decoder that only observes the current state and time. We identify this bridge-to-decoder compression as a structural bottleneck shared by diffusion models, flow matching, rectified flow, Schrödinger bridges, and field-based generative models. We introduce the \emph{Markovization gap}, the time-integrated conditional variance of the bridge velocity given the Markov state. It is the MMSE of predicting endpoint-conditioned motion from the information available to a sampler, and it measures an irreducible loss incurred before any neural network is trained. To make this bottleneck comparable across model families, we define \emph{Bridge Graphical Models} (BGMs), which separate endpoint coupling, bridge law, Markovian projection, and current-preserving dynamics representation as independent design choices. The same formalism also represents Poisson and electrostatic models as field-line bridge kernels with a corresponding field-line Markovization gap. Across synthetic, latent, and pixel-space pilots on CIFAR-10 and Fashion-MNIST, a feature-space proxy gap estimated in minutes before training ranks design choices in the same direction as downstream training loss and FID under fixed architecture, bridge, sampler, and compute. These results support the Markovization gap as a pre-training diagnostic for bridge and coupling design.
Machine Learning (cs.LG)
arXiv:2608.19144 [cs.LG]
(or arXiv:2608.19144v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.19144 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 292 words
