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 f̂ 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).
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BibTeX
@misc{mun2026multifidelity,
title = {{Multifidelity Computer Model Emulation Via Diffusion Model Steering and Targeted Maximum Likelihood}},
author = {Jongmin Mun},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30096},
eprint = {2608.30096},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30096},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multifidelity Computer Model Emulation Via Diffusion Model Steering and Targeted Maximum Likelihood
AU - Jongmin Mun
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30096
UR - https://arxiv.org/abs/2608.30096
AB - 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 f̂ 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).
ER -