From Pixels to Initial States: Geometry and Propagation of Source-Induced Sensitivity in Diffusion and Flow Models

Small source-image perturbations can substantially alter image-to-image diffusion and flow outputs. Output differences alone do not reveal the contributions of initial-state displacement magnitude, downstream growth, direction, or their interactions. Contrary to a simple explanation based on displacement magnitude and downstream growth, we argue that source-induced sensitivity requires separating the geometry of the induced initial-state change from its subsequent propagation. We examine this question at the source-conditioned initial state, holding stochastic inputs, conditioning, and generation settings fixed within each clean–perturbed pair. Across SD1.5, SDXL, and FLUX, native sources induce larger initial displacements than tested generic and optimized projection controls; direct interventions show larger mean responses at larger tested radii and different responses across directions at a common prescribed radius. Our primary bounded-source comparison uses 50 FFHQ images and approximately matches native and transferred initial-state radii before output evaluation. Native mean DINOv2 dissimilarity from paired clean outputs is larger in both SDXL and FLUX. Yet native mean normalized trajectory displacement is smaller than transferred in SDXL but larger in FLUX, yielding opposite trajectory-displacement orderings. This cross-target pattern persists under fourfold refinement of the executed integration schedules. The same output ordering thus arises under distinct downstream propagation regimes. A separate 200-image non-face COCO cohort extends the unmatched source-to-state and output comparisons without repeating matched-radius interventions.