Score-Guided Intermediate Layer Optimization: Fast Langevin Mixing for Inverse Problem

• URL: http://arxiv.org/abs/2206.09104v1
• Date: Sat, 18 Jun 2022 03:47:37 GMT
• Title: Score-Guided Intermediate Layer Optimization: Fast Langevin Mixing for Inverse Problem
• Authors: Giannis Daras and Yuval Dagan, Alexandros G. Dimakis, Constantinos Daskalakis
• Abstract summary: We prove fast mixing and characterize the stationary distribution of the Langevin Algorithm for inverting random weighted DNN generators. We propose to do posterior sampling in the latent space of a pre-trained generative model.
• Score: 97.64313409741614
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We prove fast mixing and characterize the stationary distribution of the Langevin Algorithm for inverting random weighted DNN generators. This result extends the work of Hand and Voroninski from efficient inversion to efficient posterior sampling. In practice, to allow for increased expressivity, we propose to do posterior sampling in the latent space of a pre-trained generative model. To achieve that, we train a score-based model in the latent space of a StyleGAN-2 and we use it to solve inverse problems. Our framework, Score-Guided Intermediate Layer Optimization (SGILO), extends prior work by replacing the sparsity regularization with a generative prior in the intermediate layer. Experimentally, we obtain significant improvements over the previous state-of-the-art, especially in the low measurement regime.

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