Learning multi-scale local conditional probability models of images

Zahra Kadkhodaie, Florentin Guth, Stéphane Mallat, Eero P Simoncelli

Keywords: Image priors, Markov wavelet conditional models, multi-scale score-based image synthesis, denoising, super-resolution

TL;DR: We develop a spatially Markov wavelet conditional probability model for images, and demonstrate (through, denoising, super-resolution and synthesis) its effectiveness in capturing global dependencies.

Abstract:

Deep neural networks can learn powerful prior probability models for images, as evidenced by the high-quality generations obtained with recent score-based diffusion methods. But the means by which these networks capture complex global statistical structure, apparently without suffering from the curse of dimensionality, remain a mystery. To study this, we incorporate diffusion methods into a multi-scale decomposition, reducing dimensionality by assuming a stationary local Markov model for wavelet coefficients conditioned on coarser-scale coefficients. We instantiate this model using convolutional neural networks (CNNs) with local receptive fields, which enforce both the stationarity and Markov properties. Global structures are captured using a CNN with receptive fields covering the entire (but small) low-pass image. We test this model on a dataset of face images, which are highly non-stationary and contain large-scale geometric structures.
Remarkably, denoising, super-resolution, and image synthesis results all demonstrate that these structures can be captured with significantly smaller conditioning neighborhoods than required by a Markov model implemented in the pixel domain. Our results show that score estimation for large complex images can be reduced to low-dimensional Markov conditional models across scales, alleviating the curse of dimensionality.

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