A Malliavin calculus approach to score functions in diffusion generative models

The recent publication titled 'A Malliavin calculus approach to score functions in diffusion generative models' introduces a novel closed-form expression for the score function, which is essential for modeling complex data distributions. This work utilizes advanced stochastic analysis tools, including Malliavin derivatives and a Bismut-type formula, to derive an expression that eliminates the need for Malliavin derivatives, thereby improving practical applicability. The score function plays a pivotal role in connecting known probability distributions to target data distributions through stochastic differential equations. By providing a principled foundation for advancing score estimation methods, this research not only enhances existing techniques but also paves the way for the development of new sampling algorithms for complex probability distributions. The implications of this work extend to broader classes of stochastic differential equations, marking a significant step forward in t…