Characteristic Guidance: Non-linear Correction for Diffusion Model 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 sampling method that provides first-principle 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 training-free, derivative-free, and compatible with existing sampling methods. Experiments show that characteristic guidance enhances control and reduces color and exposure issues in image generation, proving effective in diverse applications ranging from latent space sampling to solving physics problems like magnet phase transitions.