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

arXiv: https://arxiv.org/abs/2512.10339 · HTML: https://mlsanity.com/paper/2512.10339/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2025.

## Built on by (most cited first, 2 of 2)

- [SurfSpec: Enhancing Off-Target-Agnostic Specificity by Bounding Pocket-Ligand Geometric Mismatch](https://mlsanity.com/paper/2609.02963/) (2026)
- [Risk-Calibrated Proposal Transport for Finite-Particle Diffusion Steering](https://mlsanity.com/paper/2610.04171/) (2026)

## Abstract (arXiv)

Inference-time steering adapts pretrained diffusion and flow models to new tasks without retraining, often utilizing ratio-of-densities constructions that reweight time-indexed marginals with fixed exponents. We identify Marginal Path Collapse, a failure mode in which the intermediate density defined by such compositions becomes non-normalizable despite valid endpoints. This collapse can arise when composing heterogeneous experts trained with mismatched noise schedules (and/or negative exponents / partial supports). To address this, we provide (i) a sharp sufficient Path Existence Criterion that characterizes when the composed intermediate densities are mathematically well-defined, and (ii) Adaptive Path Correction with Exponents (ACE), which generalizes Feynman-Kac steering to support time-varying exponents. Our analysis reveals that ACE controls the quantile radius of the intermediate distributions, providing a theoretical mechanism for path stabilization observed in experiments. On flexible-pose scaffold decoration, a drug design task composed of de-novo, conformer, and protein-conditioned experts, ACE prevents collapse and significantly outperforms constant-exponent baselines. Furthermore, ACE improves attribute success rates in compositional image generation, establishing it as a general framework for compositional sampling. Project Page: https://ziseoklee.github.io/projects/ACE/