Monotone Generative Modeling via a Gromov-Monge Embedding

Wonjun Lee; Yifei Yang; Dongmian Zou; Gilad Lerman

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arXiv · 2311.01375

Monotone Generative Modeling via a Gromov-Monge Embedding

Wonjun Lee·Yifei Yang·Dongmian Zou·Gilad Lerman

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Abstract

Generative adversarial networks (GANs) are popular for generative tasks; however, they often require careful architecture selection, extensive empirical tuning, and are prone to mode collapse. To overcome these challenges, we propose a novel model that identifies the low-dimensional structure of the underlying data distribution, maps it into a low-dimensional latent space while preserving the underlying geometry, and then optimally transports a reference measure to the embedded distribution. We prove three key properties of our method: 1) The encoder preserves the geometry of the underlying data; 2) The generator is $c$-cyclically monotone, where $c$ is an intrinsic embedding cost employed by the encoder; and 3) The discriminator's modulus of continuity improves with the geometric preservation of the data. Numerical experiments demonstrate the effectiveness of our approach in generating high-quality images and exhibiting robustness to both mode collapse and training instability.

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Wonjun Lee, Yifei Yang, Dongmian Zou, Gilad Lerman. 2023-11-02. Monotone Generative Modeling via a Gromov-Monge Embedding. https://arxiv.org/abs/2311.01375

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