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

📝 Original Info

• Title: On the Collapse of Generative Paths: A Criterion and Correction for Diffusion Steering
• ArXiv ID: 2512.10339
• Date: 2025-12-11
• Authors: Ziseok Lee, Minyeong Hwang, Sanghyun Jo, Wooyeol Lee, Jihyung Ko, Young Bin Park, Jae-Mun Choi, Eunho Yang, Kyungsu Kim

📝 Abstract

Inference-time steering enables pretrained diffusion/flow models to be adapted to new tasks without retraining. A widely used approach is the ratio-of-densities method, which defines a timeindexed target path by reweighting probability-density trajectories from multiple models with positive, or in some cases, negative exponents. This construction, however, harbors a critical and previously unformalized failure mode: Marginal Path Collapse, where intermediate densities become non-normalizable even though endpoints remain valid. Collapse arises systematically when composing heterogeneous models trained on different noise schedules or datasets, including a common setting in molecular design where de-novo, conformer, and pocket-conditioned models must be combined for tasks such as flexible-pose scaffold decoration. We provide a novel and complete solution for the problem. First, we derive a simple path existence criterion that predicts exactly when collapse occurs from noise schedules and exponents alone. Second, we introduce Adaptive path Correction with Exponents (ACE), which extends Feynman-Kac steering to timevarying exponents and guarantees a vali...

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