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Through this perspective, we investigate the well-posedness and MFGs, therefore, enables the study of generative models through the theory of Their associated MFG's optimality condition, which is a set of coupledįorward-backward nonlinear partial differential equations (PDEs). Mathematical structure and properties of each generative model by studying We derive these three classes of generative models through differentĬhoices of particle dynamics and cost functions. MFGs and major classes of flow and diffusion-based generative models includingĬontinuous-time normalizing flows, score-based models, and Wasserstein gradientįlows. The various flow and diffusion-based generative models have some commonįoundational structure and interrelationships. There is a pervasive sense in the generative modeling community that Mathematical framework for explaining, enhancing, and designing generative Katsoulakis Download PDF Abstract: In this paper, we demonstrate the versatility of mean-field games (MFGs) as a Download a PDF of the paper titled A mean-field games laboratory for generative modeling, by Benjamin J.
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