Universal Smoothed Score Functions for Generative Modeling

• URL: http://arxiv.org/abs/2303.11669v1
• Date: Tue, 21 Mar 2023 08:23:37 GMT
• Title: Universal Smoothed Score Functions for Generative Modeling
• Authors: Saeed Saremi, Rupesh Kumar Srivastava, Francis Bach
• Abstract summary: We consider the problem of generative modeling based on smoothing an unknown density of interest in $mathbbRd$. We characterize the time complexity of learning the resulting smoothed density in $mathbbRMd$, called M-density. We present results on the sample quality in this class of generative models on the CIFAR-10 dataset.
• Score: 3.626727150596421
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the problem of generative modeling based on smoothing an unknown density of interest in $\mathbb{R}^d$ using factorial kernels with $M$ independent Gaussian channels with equal noise levels introduced by Saremi and Srivastava (2022). First, we fully characterize the time complexity of learning the resulting smoothed density in $\mathbb{R}^{Md}$, called M-density, by deriving a universal form for its parametrization in which the score function is by construction permutation equivariant. Next, we study the time complexity of sampling an M-density by analyzing its condition number for Gaussian distributions. This spectral analysis gives a geometric insight on the "shape" of M-densities as one increases $M$. Finally, we present results on the sample quality in this class of generative models on the CIFAR-10 dataset where we report Fr\'echet inception distances (14.15), notably obtained with a single noise level on long-run fast-mixing MCMC chains.

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