Multifidelity Computer Model Emulation Via Diffusion Model Steering and Targeted Maximum Likelihood

Abstract

We develop a multifidelity method for fusing low-resolution simulations with computationally expensive high-resolution simulations, which are run infrequently and are therefore prone to bias. We formulate this fusion as a constrained optimization under missing-not-at-random (MNAR) selection bias. This formulation searches for the exponentially tilted high-resolution distribution that minimizes KL divergence from the biased baseline, subject to moment constraints derived from low-resolution simulations. This optimization requires first estimating the biased baseline conditional density $f$ as a nuisance parameter. We estimate $f$ using a score-based diffusion model. To eliminate the generative model's regularization bias that harms the downstream task, we apply targeted maximum likelihood estimation (TMLE). TMLE debiases $\hat{f}$ via a targeted exponential tilting, rendering the target parameters insensitive to first-order nuisance estimation errors. To execute this computationally, we adapt generative model steering, a technique originally developed for human-preference alignment. Using Feynman-Kac steering with a reward function based on our formulation, we simultaneously execute the exponential tilts for MNAR and TMLE at inference time, avoiding expensive retraining costs. Code available [here](https://github.com/Jong-Min-Moon/multifidel_emul_by_FK).