Nonlinear denoising score matching for enhanced learning of structured distributions

• URL: http://arxiv.org/abs/2405.15625v1
• Date: Fri, 24 May 2024 15:14:23 GMT
• Title: Nonlinear denoising score matching for enhanced learning of structured distributions
• Authors: Jeremiah Birrell, Markos A. Katsoulakis, Luc Rey-Bellet, Benjamin Zhang, Wei Zhu,
• Abstract summary: Generalizing to a nonlinear drift allows for additional structure to be incorporated into the dynamics. We demonstrate the effectiveness of this method on several examples.
• Score: 12.428200977408817
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a novel method for training score-based generative models which uses nonlinear noising dynamics to improve learning of structured distributions. Generalizing to a nonlinear drift allows for additional structure to be incorporated into the dynamics, thus making the training better adapted to the data, e.g., in the case of multimodality or (approximate) symmetries. Such structure can be obtained from the data by an inexpensive preprocessing step. The nonlinear dynamics introduces new challenges into training which we address in two ways: 1) we develop a new nonlinear denoising score matching (NDSM) method, 2) we introduce neural control variates in order to reduce the variance of the NDSM training objective. We demonstrate the effectiveness of this method on several examples: a) a collection of low-dimensional examples, motivated by clustering in latent space, b) high-dimensional images, addressing issues with mode collapse, small training sets, and approximate symmetries, the latter being a challenge for methods based on equivariant neural networks, which require exact symmetries.

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