Boundary Guided Mixing Trajectory for Semantic Control with Diffusion Models

Applying powerful generative denoising diffusion models (DDMs) for downstream tasks such as image semantic editing usually requires either fine-tuning pre-trained DDMs or learning auxiliary editing networks. In this work, we achieve SOTA semantic control performance on various application settings by optimizing the denoising trajectory solely via frozen DDMs. As one of the first optimization-based diffusion editing work, we start by seeking a more comprehensive understanding of the intermediate high-dimensional latent spaces by theoretically and empirically analyzing their probabilistic and geometric behaviors in the Markov chain. We then propose to further explore the critical step in the denoising trajectory that characterizes the convergence of a pre-trained DDM. Last but not least, we further present our method to search for the semantic subspaces boundaries for controllable manipulation, by guiding the denoising trajectory towards the targeted boundary at the critical convergent step. We conduct extensive experiments on various DPMs architectures (DDPM, iDDPM) and datasets (CelebA, CelebA-HQ, LSUN-church, LSUN-bedroom, AFHQ-dog) with different resolutions (64, 256) as empirical demonstrations.