Theoretical explanation of shared risk profiles and allocation deformations

Determine why the shared fiberwise prediction-risk profile shape and the quantitative cross-system agreement of allocation deformations arise across diffusion and flow-matching models, including how the coefficient curve and training dynamics jointly shape fiberwise risk and the resulting schedule allocations.

Background

The paper reports that fiberwise prediction-risk profiles from independently trained diffusion and flow-matching models align closely after normalization in kinetic reference coordinates. The corresponding model-aware schedule deformations also exhibit substantial agreement across prediction targets, architectures, datasets, training configurations, and checkpoints.

Despite this empirical universality, the paper states that the shared profile shape and quantitative cross-system agreement are not theoretically explained. A satisfactory resolution would need to clarify the joint roles of the coefficient curve, the learned predictor, and training dynamics in producing the observed risk profiles and allocation behavior, potentially through a unified path–fiber optimal-transport formulation.