Many natural and artificial high-dimensional data sets are controlled by few lower-dimensional factors or drivers. As a result, the data is often highly structured and does not fill uniformly the high-dimensional space. In this talk, we present a differential stochastic sensing framework for inferring the independent controlling factors (or drivers) of high-dimensional time series. This approach provides intrinsic global modeling for noisy observations based on anisotropic diffusion and local dynamical models. The idea is to implicitly solve local differential equations based on local density estimates in a global graph-based mechanism that inverts the observation function and reveals the underlying structure. Moreover, it implicitly recovers the dynamical model of the data. Hence, it provides a foundation for sequential processing that is applied to nonlinear tracking problems. We revisit classical Bayesian filtering methods and discuss their relationship to the proposed approach. In addition, we show that the proposed intrinsic modeling is invariant under different observation schemes and is noise resilient. Hence, it may be applied to a wide variety of applications. In this talk, we demonstrate applications to the processing of financial and neuroscience time series, and biological and medical imaging.