Tackling the Singularities at the Endpoints of Time Intervals in Diffusion Models
This solves brightness limitations in diffusion models for image generation applications, though it appears incremental.
The paper addresses singularities at time interval endpoints in diffusion models, showing that the t=1 singularity is conditionally removable while t=0 is inherent, and proposes SingDiffusion to resolve brightness issues and improve generation quality, achieving notable lower FID scores.
Most diffusion models assume that the reverse process adheres to a Gaussian distribution. However, this approximation has not been rigorously validated, especially at singularities, where t=0 and t=1. Improperly dealing with such singularities leads to an average brightness issue in applications, and limits the generation of images with extreme brightness or darkness. We primarily focus on tackling singularities from both theoretical and practical perspectives. Initially, we establish the error bounds for the reverse process approximation, and showcase its Gaussian characteristics at singularity time steps. Based on this theoretical insight, we confirm the singularity at t=1 is conditionally removable while it at t=0 is an inherent property. Upon these significant conclusions, we propose a novel plug-and-play method SingDiffusion to address the initial singular time step sampling, which not only effectively resolves the average brightness issue for a wide range of diffusion models without extra training efforts, but also enhances their generation capability in achieving notable lower FID scores.