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

Ziseok Lee, Minyeong Hwang, Sanghyun Jo, Wooyeol Lee, Jihyung Ko, Young Bin Park, Jae-Mun Choi, Eunho Yang, Kyungsu Kim

Keywords: Diffusion Model, Flow Matching, Inference-time Steering, Feynman-Kac, Probability Path, Scaffold Decoration, Compositional Image Generation

TL;DR: Ratio-of-densities steering in diffusion models breaks via Marginal Path Collapse. We introduce ACE, a provably stable correction that prevents collapse, cuts error >5×, and enables reliable molecular design.

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.

Primary Area: generative models

Submission Number: 11251