{"ID":2830128,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.10339","arxiv_id":"2512.10339","title":"On the Collapse of Generative Paths: A Criterion and Correction for Diffusion Steering","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.","short_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...","url_abs":"https://arxiv.org/abs/2512.10339","url_pdf":"https://arxiv.org/pdf/2512.10339v1","authors":"[\"Ziseok Lee\",\"Minyeong Hwang\",\"Sanghyun Jo\",\"Wooyeol Lee\",\"Jihyung Ko\",\"Young Bin Park\",\"Jae-Mun Choi\",\"Eunho Yang\",\"Kyungsu Kim\"]","published":"2025-12-11T06:44:08Z","proceeding":"cs.AI","tasks":"[\"cs.AI\"]","methods":"[\"Diffusion Model\"]","has_code":false}