Introduction to Stochastic Differential Equations for Generative Machine Learning: A Variational Perspective
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Computer Science > Machine Learning
Title:Introduction to Stochastic Differential Equations for Generative Machine Learning: A Variational Perspective
Abstract:The use of ordinary and stochastic differential equations has led to substantial progress in generative machine learning with applications to, for example, image, video and biomolecule generation. This paper provides a self-contained and informal introduction to the differential equations, the probabilistic framework for using them in generative modeling and the Fokker--Planck equation that governs the temporal evolution of the marginal distribution of the stochastic variables of the differential equations. The variational lower bound on the log-likelihood (the evidence lower bound, ELBO) is derived and used as a general starting point for a discussion of diffusion models, score matching, and flow matching. All of these approaches may be viewed as specific parameterizations of the most general variational approach. A one-dimensional density modeling problem is used as a simple example to compare different parameterizations.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2606.31576 [cs.LG] |
| (or arXiv:2606.31576v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.31576
arXiv-issued DOI via DataCite (pending registration)
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