Learning Stochastic Dyanmics using Diffusion Models
In this blog post, I talk about the project of Learning Stochastic Dynamics using Diffusion models. The repository of this project will be open sourced soon. Problem Definition In this section we discuss the exact mathematical formulation of the learning problem. First, we start with the definition of dataset: in our dataset we assume observing $N$ 3-D trajectories of length $L$, e.g., a data sample is a tuple ${(x_i,y_i,z_i), t_i} \in \mathbb{R}^3 \times [0,T]$ where $T$ is discretized by time stamps ${t_i}_{i=1}^L$....