  This study introduces a hybrid fluid simulation approach that integrates
generative diffusion models with physics-based simulations, aiming at reducing
the computational costs of flow simulations while still honoring all the
physical properties of interest. These simulations enhance our understanding of
applications such as assessing hydrogen and CO$_2$ storage efficiency in
underground reservoirs. Nevertheless, they are computationally expensive and
the presence of nonunique solutions can require multiple simulations within a
single geometry. To overcome the computational cost hurdle, we propose a hybrid
method that couples generative diffusion models and physics-based modeling. We
introduce a system to condition the diffusion model with a geometry of
interest, allowing to produce variable fluid saturations in the same geometry.
While training the model, we simultaneously generate initial conditions and
perform physics-based simulations using these conditions. This integrated
approach enables us to receive real-time feedback on a single compute node
equipped with both CPUs and GPUs. By efficiently managing these processes
within one compute node, we can continuously evaluate performance and stop
training when the desired criteria are met. To test our model, we generate
realizations in a real Berea sandstone fracture which shows that our technique
is up to 4.4 times faster than commonly used flow simulation initializations.
