On the Collapse of Generative Paths: A Criterion and Correction for Diffusion Steering 文章

arXiv:2512.10339v2 Announce Type: replace Abstract: Inference-time steering adapts pretrained diffusion and flow models to new tasks without retraining, often utilizing ratio-of-densities constructions that reweight time-indexed marginals with fixed exponents. We identify Marginal Path Collapse, a failure mode in which the intermediate density defined by such compositions becomes non-normalizable despite valid endpoints. This collapse can arise when composing heterogeneous experts trained with mismatched noise schedules (and/or negative exponents / partial supports). To address this, we provide (i) a sharp sufficient Path Existence Criterion that characterizes when the composed intermediate densities are mathematically well-defined, and (ii) Adaptive Path Correction with Exponents (ACE), which generalizes Feynman-Kac steering to support time-varying exponents.