  Pore-scale simulations accurately describe transport properties of fluids in
the subsurface. These simulations enhance our understanding of applications
such as assessing hydrogen storage efficiency and forecasting CO$_2$
sequestration processes in underground reservoirs. Nevertheless, they are
computationally expensive due to their mesoscopic nature. In addition, their
stationary solutions are not guaranteed to be unique, so multiple runs with
different initial conditions must be performed to ensure sufficient sample
coverage. These factors complicate the task of obtaining representative and
reliable forecasts. To overcome the high computational cost hurdle, we propose
a hybrid method that couples generative diffusion models and physics-based
modeling. Upon training a generative model, we synthesize samples that serve as
the initial conditions for physics-based simulations. We measure the relaxation
time (to stationary solutions) of the simulations, which serves as a validation
metric and early-stopping criterion. Our numerical experiments revealed that
the hybrid method exhibits a speed-up of up to 8.2 times compared to commonly
used initialization methods. This finding offers compelling initial support
that the proposed diffusion model-based hybrid scheme has potentials to
significantly decrease the time required for convergence of numerical
simulations without compromising the physical robustness.
