Multi-resolution continuous normalizing flows

Recent work has shown that Neural Ordinary Differential Equations (ODEs) can serve as generative models of images using the perspective of Continuous Normalizing Flows (CNFs). Such models offer exact likelihood calculation, and invertible generation/density estimation. In this work we introduce a Mu...

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Bibliographic Details
Published in:Annals of mathematics and artificial intelligence 2024-10, Vol.92 (5), p.1295-1317
Main Authors: Voleti, Vikram, Finlay, Chris, Oberman, Adam, Pal, Christopher
Format: Article
Language:English
Subjects:
Artificial Intelligence
Complex Systems
Computer Science
Differential equations
Mathematics
Neural networks
Ordinary differential equations
Variables
Wavelet transforms
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Summary:Recent work has shown that Neural Ordinary Differential Equations (ODEs) can serve as generative models of images using the perspective of Continuous Normalizing Flows (CNFs). Such models offer exact likelihood calculation, and invertible generation/density estimation. In this work we introduce a Multi-Resolution variant of such models (MRCNF), by characterizing the conditional distribution over the additional information required to generate a fine image that is consistent with the coarse image. We introduce a transformation between resolutions that allows for no change in the log likelihood. We show that this approach yields comparable likelihood values for various image datasets, with improved performance at higher resolutions, with fewer parameters, using only one GPU. Further, we examine the out-of-distribution properties of MRCNFs, and find that they are similar to those of other likelihood-based generative models.
ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-024-09939-5