Reproduce “A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems” on OpenResearch

About this paper

Yanfang Liu, Yuan Chen, Dongbin Xiu, Guannan Zhang

Researchers introduce a training-free conditional diffusion model to learn unknown Stochastic Differential Equations (SDEs) directly from observational data. This approach analytically estimates the conditional score function, enabling the generation of labeled data for supervised training of a generative model, which then accurately predicts SDE flow maps with enhanced computational efficiency, outperforming GAN-based baselines across various SDE types.

Key insights

• It is feasible to analytically derive and efficiently estimate the score function for a conditional diffusion model directly from observational data, eliminating the need for computationally intensive neural network training.
• Converting the stochastic reverse process of a diffusion model into a deterministic reverse ODE allows for the generation of synthetic, labeled data, effectively transforming an unsupervised learning problem into a more stable and efficient supervised one.
• A model trained with this approach can accurately predict long-term behaviors and global dynamics of complex SDEs, including spontaneous transitions in multi-stable systems like the double-well potential, even when trained on short-term observational data where such transitions are not directly observed.

Summary by alphaXiv.