Discovery and Expansion of New Domains within Diffusion Models

In this work, we study the generalization properties of diffusion models in a few-shot setup, introduce a novel tuning-free paradigm to synthesize the target out-of-domain (OOD) data, and demonstrate its advantages compared to existing methods in data-sparse scenarios with large domain gaps. Specifically, given a pre-trained model and a small set of images that are OOD relative to the model's training distribution, we explore whether the frozen model is able to generalize to this new domain. We begin by revealing that Denoising Diffusion Probabilistic Models (DDPMs) trained on single-domain images are already equipped with sufficient representation abilities to reconstruct arbitrary images from the inverted latent encoding following bi-directional deterministic diffusion and denoising trajectories. We then demonstrate through both theoretical and empirical perspectives that the OOD images establish Gaussian priors in latent spaces of the given model, and the inverted latent modes are separable from their initial training domain. We then introduce our novel tuning-free paradigm to synthesize new images of the target unseen domain by discovering qualified OOD latent encodings in the inverted noisy spaces. This is fundamentally different from the current paradigm that seeks to modify the denoising trajectory to achieve the same goal by tuning the model parameters. Extensive cross-model and domain experiments show that our proposed method can expand the latent space and generate unseen images via frozen DDPMs without impairing the quality of generation of their original domain. We also showcase a practical application of our proposed heuristic approach in dramatically different domains using astrophysical data, revealing the great potential of such a generalization paradigm in data spare fields such as scientific explorations.