  Inferring dynamical models from low-resolution temporal data continues to be
a significant challenge in biophysics, especially within transcriptomics, where
separating molecular programs from noise remains an important open problem. We
explore a common scenario in which we have access to an adequate amount of
cross-sectional samples at a few time-points, and assume that our samples are
generated from a latent diffusion process. We propose an approach that relies
on the probability flow associated with an underlying diffusion process to
infer an autonomous, nonlinear force field interpolating between the
distributions. Given a prior on the noise model, we employ score-matching to
differentiate the force field from the intrinsic noise. Using relevant
biophysical examples, we demonstrate that our approach can extract
non-conservative forces from non-stationary data, that it learns equilibrium
dynamics when applied to steady-state data, and that it can do so with both
additive and multiplicative noise models.
