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

TL;DR

This paper identifies a failure mode in diffusion model steering called Marginal Path Collapse and provides a criterion and correction method, ACE, to ensure stable, valid probability paths for improved generative control.

Contribution

The authors introduce a path existence criterion and the ACE correction method to prevent collapse in diffusion steering, enabling reliable, high-quality task-specific generative modeling.

Findings

ACE eliminates path collapse in experiments.

ACE improves distributional and docking metrics.

The criterion accurately predicts collapse conditions.

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.