Score-based Generative Modeling Through Backward Stochastic Differential Equations: Inversion and Generation
This work contributes incrementally to score-based generative learning by extending SDE-based methods for real-world problems.
The paper tackles the problem of determining initial conditions for reaching a desired terminal distribution in diffusion models by proposing a BSDE-based approach that adapts an existing score function, with theoretical guarantees and applications in areas like diffusion inversion and conditional diffusion.
The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our model can determine the initial conditions necessary to reach a desired terminal distribution by adapting an existing score function. We demonstrate the theoretical guarantees of the model, the benefits of using Lipschitz networks for score matching, and its potential applications in various areas such as diffusion inversion, conditional diffusion, and uncertainty quantification. Our work represents a contribution to the field of score-based generative learning and offers a promising direction for solving real-world problems.