Analytic Distribution of Classifier-Free Guidance for Schedule Design

תקציר מקורי באנגליתarXiv:2607.19725v1 Announce Type: new Abstract: Classifier-free guidance (CFG) is the default mechanism for conditional generation in diffusion models, but the distribution sampled by its deterministic guided dynamics is not captured by the usual product-distribution heuristic $p_0^\omega q_0^{1-\omega}$. We analyze CFG through the probability flow ODE and derive exact analytic path-integral representations of the induced distributions for both constant and time-dependent guidance. The resulting formulas show that CFG modifies $p_{t_0}$ by an exponential path-integral correction, and that a time-dependent schedule enters this correction through the weight $\omega(t)-1$. This characterization explains how score discrepancies accumulate along sampling trajectories and motivates Distribution-