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

2025-12-11

AI Summary

This paper identifies and formalizes a critical failure—*edge-path collapse*—in density-ratio-based path-guided inference for diffusion and flow models: when heterogeneous models (e.g., trained on different datasets or with distinct noise schedules) are composited, intermediate-time densities become non-normalized, causing generation failure. To address this, we propose *Adaptive Exponential Correction (ACE)*, the first extension of Feynman–Kac guidance to a time-varying exponential framework. ACE integrates a noise-schedule-driven path-existence criterion with a multi-model density-ratio-weighted guidance mechanism. Evaluated on 2D synthetic benchmarks and flexible pose scaffold decoration tasks, ACE completely eliminates edge-path collapse and significantly improves generation quality under strong guidance. It outperforms constant-exponent baselines and task-specific models in both distribution matching and molecular docking performance.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

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.

Problem

• Addresses marginal path collapse in diffusion steering
• Provides criterion for collapse prediction from noise schedules
• Introduces ACE method for valid probability paths

Innovation

• Derives path existence criterion from noise schedules
• Introduces ACE with time-varying exponents for correction
• Guarantees valid probability path to eliminate collapse