Data-driven generative simulation of SDEs using diffusion models

This paper introduces a new approach to generating sample paths of stochastic differential equations (SDEs) using diffusion models, a class of generative AI models commonly employed in image and video applications. Unlike traditional Monte Carlo methods, which require explicit specification of the drift and diffusion coefficients of the SDE, our method takes a model-free approach. Given a finite set of sample paths from an unknown SDE, we propose a data-driven framework that utilizes conditional diffusion models to generate new, synthetic paths of the same SDE. To demonstrate the effectiveness of our approach, we conduct comprehensive experiments on various SDEs and compare its performance with alternative benchmark methods including neural SDEs. Furthermore, we explore the potential of leveraging these synthetically generated sample paths to enhance the performance of reinforcement learning algorithms in continuous-time mean-variance portfolio selection, hinting at promising applications of diffusion models in financial analysis and decision-making.