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

• URL: http://arxiv.org/abs/2512.10339v1
• Date: Thu, 11 Dec 2025 06:44:08 GMT
• Title: On the Collapse of Generative Paths: A Criterion and Correction for Diffusion Steering
• Authors: Ziseok Lee, Minyeong Hwang, Sanghyun Jo, Wooyeol Lee, Jihyung Ko, Young Bin Park, Jae-Mun Choi, Eunho Yang, Kyungsu Kim,
• Abstract summary: In-time steering enables pretrained diffusion/flow models to be adapted to new tasks without retraining.<n>This construction harbors a critical and previously unformalized failure mode: Marginal Path Collapse.<n>We introduce Adaptive path Correction with Exponents (ACE), which extends Feynman-Kac steering to time-varying exponents.
• Score: 29.633206995806542
• License: http://creativecommons.org/licenses/by/4.0/
• 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 time-indexed 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 time-varying exponents and guarantees a valid probability path. On a synthetic 2D benchmark and on flexible-pose scaffold decoration, ACE eliminates collapse and enables high-guidance compositional generation, improving distributional and docking metrics over constant-exponent baselines and even specialized task-specific scaffold decoration models. Our work turns ratio-of-densities steering with heterogeneous experts from an unstable heuristic into a reliable tool for controllable generation.

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