Diffusion-Based Multi-Fidelity Surrogate Modeling via Noise-Level Supervision Allocation

Learning-based surrogate models for physical fields offer an efficient alternative to repeated numerical simulations, but obtaining sufficient high-fidelity training data remains costly. Multi-fidelity modeling addresses this bottleneck by combining limited high-fidelity data with abundant low-fidelity data, often through correction mappings. Rather than learning a low-to-high correction, we propose a novel diffusion-based method that allocates multi-fidelity supervision across noise levels. At selected higher-noise stages, low-fidelity data substitute for part of the high-fidelity supervision. Our method is motivated by the observation that the discrepancy between noisy high- and low-fidelity distributions decreases as the diffusion noise level increases. For deterministic physical responses, we use the diffusion signal-to-noise ratio to quantify this distributional discrepancy and bound the resulting denoising-target bias. Multi-fidelity data are jointly used to train a single conditional diffusion model that predicts physical fields without low-fidelity inputs at inference. On two thermal-field benchmarks, our method reduces the prediction error by up to 90% relative to the single-fidelity model and achieves accuracy comparable to that of existing multi-fidelity models trained with 50 times as many high-fidelity samples.