Repulsive Latent Score Distillation for Solving Inverse Problems
Nicolas Zilberstein Morteza Mardani Santiago Segarra
Score Distillation Sampling (SDS) has been pivotal for leveraging pre-trained diffusion models in downstream tasks such as inverse problems, but it faces two major challenges: $(i)$ mode collapse and $(ii)$ latent space inversion, which become more pronounced in high-dimensional data. 
To address mode collapse, we introduce a novel variational framework for posterior sampling. 
Utilizing the Wasserstein gradient flow interpretation of SDS, we propose a multimodal variational approximation with a \emph{repulsion} mechanism that promotes diversity among particles by penalizing pairwise kernel-based similarity. 
This repulsion acts as a simple regularizer, encouraging a more diverse set of solutions. 
To mitigate latent space ambiguity, we extend this framework with an \emph{augmented} variational distribution that disentangles the latent and data. 
This repulsive augmented formulation balances computational efficiency, quality, and diversity. 
Extensive experiments on linear and nonlinear inverse tasks with high-resolution images ($512 \times 512$) using pre-trained Stable Diffusion models demonstrate the effectiveness of our approach.
Inverse problems, Score distillation, Diffusion models, Mode collapse, Variational inference
We propose Repulsive Latent Score Distillation, a particle-based variational method to solve inverse problem  at 512 x 512 resolution using latent diffusion models as prior.