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We prove fast mixing and characterize the sta- tionary 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 ex- pressivity, 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 sig- nificant improvements over the previous state-of- the-art, especially in the low measurement regime.
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Intermediate Layer Optimization for Inverse Problems using Deep Generative Models
We propose Intermediate Layer Optimization (ILO), a novel optimization algorithm for solving inverse problems with deep generative models. Instead of optimizing only over the initial latent code, we progressively change the input layer obtaining successively more expressive generators. To explore the higher dimensional spaces, our method searches for latent codes that lie within a small l1 ball around the manifold induced by the previous layer. Our theoretical analysis shows that by keeping the radius of the ball relatively small, we can improve the established error bound for compressed sensing with deep generative models. We empirically show that our approach outperforms state-of-the-art methods introduced in StyleGAN-2 and PULSE for a wide range of inverse problems including inpainting, denoising, super-resolution and compressed sensing.
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- Award ID(s):
- 1901281
- PAR ID:
- 10405528
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 139
- ISSN:
- 2640-3498
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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