Diffusion models have achieved remarkable success in generative modeling, and their sampling procedures are often altered to steer generation or improve efficiency. Such modifications introduce perturbations along the sampling trajectory, raising the key question of how these perturbations affect the final output. To answer this, we develop a theoretical framework that combines dynamical analysis of the sampling process with an information‑theoretic characterization of output responses. We quantify perturbation strength by the Kullback‑Leibler (KL) divergence between the perturbed trajectory distribution and the reference trajectory distribution, calling it path cost. Path cost bounds changes in the output distribution but does not uniquely determine them. Moreover, we derive a response identity that links the propagation and accumulation of local perturbations to the information captured by a chosen feature mean, explaining why changes in the output distribution can remain invisible to first‑order responses. Controlled interventions at equal path cost are performed on pretrained diffusion models, revealing distinct patterns of output sensitivity across sampling stages and spatial frequencies. Finally, we apply the framework to cache‑based acceleration approximations, showing that the propagation analysis reliably identifies sampling intervals where caching introduces larger image errors.
Review