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

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.

HybridLinker: Topology-Guided Posterior Sampling for Enhanced Diversity and Validity in 3D Molecular Linker Generation

Linker generation is critical in drug discovery applications such as lead optimization and PROTAC design, where molecular fragments are assembled into diverse drug candidates. Existing methods fall into PC-Free and PC-Aware categories based on their use of 3D point clouds (PC). PC-Free models prioritize diversity but suffer from lower validity due to overlooking PC constraints, while PC-Aware models ensure higher validity but restrict diversity by enforcing strict PC constraints. To overcome these trade-offs without additional training, we propose HybridLinker, a framework that enhances PC-Aware inference by providing diverse bonding topologies from a pretrained PC-Free model as guidance. At its core, we propose LinkerDPS, the first diffusion posterior sampling (DPS) method operating across PC-Free and PC-Aware spaces, bridging molecular topology with 3D point clouds via an energy-inspired function. By transferring the diverse sampling distribution of PC-Free models into the PC-Aware distribution, HybridLinker significantly and consistently surpasses baselines, improving both validity and diversity in foundational molecular design and applied property optimization tasks, establishing a new DPS framework in the molecular and graph domains beyond imaging.