Title: Concept Insertion Success over Time in Diffusion Models through Prompt-Conditioned Interventions
Primary area: interpretability and explainable AI
Keywords: temporal analysis, concept emergence, diffusion models, explainability

Abstract: Diffusion models are usually evaluated by their final outputs, gradually denoising random noise into meaningful images. 
Yet, generation unfolds along a trajectory, and understanding this dynamic process is crucial for explaining how controllable, reliable, and predictable these models are in terms of their success/failure modes. In this work, we ask the question: *when* does noise turn into a specific concept (e.g., age) and lock in the denoising trajectory? We propose PCI Prompt-Conditioned Intervention) to study this question. PCI is a training-free and model-agnostic framework for analyzing concept dynamics through diffusion time. The central idea is the analysis of *Concept Insertion Success* (CIS), defined as the probability that a concept inserted at a given timestep is preserved and reflected in the final image, offering a way to characterize the temporal dynamics of concept formation. Applied to several state-of-the-art text-to-image diffusion models and a broad taxonomy of concepts, PCI reveals diverse temporal behaviors across diffusion models, in which certain phases of the trajectory are more favorable to specific concepts even within the same concept type. These findings also provide actionable insights for text-driven image editing, highlighting *when* interventions are most effective without requiring access to model internals or training. Altogether, we establish temporal concept analysis as a new perspective for understanding and steering diffusion models.

TL;DR: We propose Prompt-Conditioned Intervention (PCI), a framework that reveals how and when concepts can be inserted into diffusion trajectories, showing that timing critically shapes concept success across contexts and models.