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

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 necessary-and-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. Our analysis reveals that ACE controls the quantile radius of the intermediate distributions, providing a theoretical mechanism for path stabilization observed in experiments. On flexible-pose scaffold decoration, a drug design task composed of de-novo, conformer, and protein-conditioned experts, ACE prevents collapse and significantly outperforms constant-exponent baselines. Furthermore, ACE improves attribute success rates in compositional image generation, establishing it as a general framework for compositional sampling.