  Machine learning models are gaining increasing popularity in the domain of
fluid dynamics for their potential to accelerate the production of
high-fidelity computational fluid dynamics data. However, many recently
proposed machine learning models for high-fidelity data reconstruction require
low-fidelity data for model training. Such requirement restrains the
application performance of these models, since their data reconstruction
accuracy would drop significantly if the low-fidelity input data used in model
test has a large deviation from the training data. To overcome this restraint,
we propose a diffusion model which only uses high-fidelity data at training.
With different configurations, our model is able to reconstruct high-fidelity
data from either a regular low-fidelity sample or a sparsely measured sample,
and is also able to gain an accuracy increase by using physics-informed
conditioning information from a known partial differential equation when that
is available. Experimental results demonstrate that our model can produce
accurate reconstruction results for 2d turbulent flows based on different input
sources without retraining.
