  In this paper, we present a generic physics-informed generative model called
MPDM that integrates multi-fidelity physics simulations with diffusion models.
MPDM categorizes multi-fidelity physics simulations into inexpensive and
expensive simulations, depending on computational costs. The inexpensive
simulations, which can be obtained with low latency, directly inject contextual
information into DDMs. Furthermore, when results from expensive simulations are
available, MPDM refines the quality of generated samples via a guided diffusion
process. This design separates the training of a denoising diffusion model from
physics-informed conditional probability models, thus lending flexibility to
practitioners. MPDM builds on Bayesian probabilistic models and is equipped
with a theoretical guarantee that provides upper bounds on the Wasserstein
distance between the sample and underlying true distribution. The probabilistic
nature of MPDM also provides a convenient approach for uncertainty
quantification in prediction. Our models excel in cases where physics
simulations are imperfect and sometimes inaccessible. We use a numerical
simulation in fluid dynamics and a case study in heat dynamics within
laser-based metal powder deposition additive manufacturing to demonstrate how
MPDM seamlessly integrates multi-idelity physics simulations and observations
to obtain surrogates with superior predictive performance.
