  We introduce a score-based generative sampling method for solving the
nonlinear filtering problem with robust accuracy. A major drawback of existing
nonlinear filtering methods, e.g., particle filters, is the low stability. To
overcome this issue, we adopt the diffusion model framework to solve the
nonlinear filtering problem. In stead of storing the information of the
filtering density in finite number of Monte Carlo samples, in the score-based
filter we store the information of the filtering density in the score model.
Then, via the reverse-time diffusion sampler, we can generate unlimited samples
to characterize the filtering density. Moreover, with the powerful expressive
capabilities of deep neural networks, it has been demonstrated that a well
trained score in diffusion model can produce samples from complex target
distributions in very high dimensional spaces. Extensive numerical experiments
show that our score-based filter could potentially address the curse of
dimensionality in very high dimensional problems.
