  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.
