Learning Active Matter Behavior of Poxvirus Spreading through Time-lapse Image Generation by Denoising Diffusion Probabilistic Model

Complex dynamic processes occurring in nature may be captured by time-lapse imaging.
However, understanding and reproducing these processes remains a challenge. These
processes range from mass transfer in fluids to the complex behaviour of live active matter
dynamics in cell motility driven by poxvirus infection spread in a monolayer of cells.
Understanding these processes can be attempted through time-lapse sequence synthesis by
means of generative modelling. Here, we present a novel method to predict behaviour from
video sequences, where the underlying mechanics are governed by differential equations with
known and unknown characteristics. Our method is an extension of residual video diffusion in
which we learn an approximation of the underlying differential equation separating the drift
term and the stochastic term. We evaluate it with the reaction-diffusion equation in which we
hide the inhibitor variable from the model and the incompressible Navier-Stokes equation with
a stochastic forcing parameter. Our model accurately predicts the inhibitor variable in the
reaction-diffusion equations and the stochastic forcing parameter in the Navier-Stokes
equation. Additionally, we evaluate the model's capability to learn distinct biological behaviours
of the active matter when trained on time-lapse microscopy of poxvirus spread phenotypes.
The results confirm the model's potential in capturing meaningful equation embeddings, thus
contributing to a deeper understanding of biological dynamics. To assess the accuracy of
poxvirus prediction, we measured the mean absolute error when close to the initial condition.
To evaluate the generation of longer sequences, we employed a qualitative analysis in which
our model achieved excellent results.