Characteristic Guidance: Non-linear Correction for DDPM at Large Guidance Scale

Popular guidance for denoising diffusion probabilistic model (DDPM) linearly combines distinct conditional models together to provide enhanced control over samples. However, this approach overlooks nonlinear effects that become significant when guidance scale is large. To address this issue, we propose characteristic guidance, a novel method that provides non-linear correction for classifier-free guided DDPMs. Such correction forces the guided DDPMs to respect the Fokker-Planck equation of their underlying diffusion process, in a way that is first-principle, training-free, derivative-free, and compatible with existing sampling methods. Experiments show that characteristic guidance is robust to various applications, offers enhanced control over sample generation, suppresses color and exposure issues even for latent space sampling, and can handle physics problems such as the phase transitions.