Reliable quantification of Monte Carlo variability in diffusion-model outputs

Develop a reliable method to determine how much meaningful difference actually exists between outputs produced by different Monte Carlo samples of a trained diffusion model for the inverse design of optical multilayer thin films, enabling principled comparison of stochastic generations for the same spectral target.

Background

The paper employs masked diffusion LLMs for inverse design of optical multilayer stacks and uses Monte Carlo sampling to generate multiple candidate stacks for the same target spectrum. Because diffusion models produce stochastic outputs, assessing variability and selecting among candidates is crucial.

The authors note that despite this need, there is currently no reliable method to quantify how much meaningful difference exists between outputs generated across Monte Carlo samples. They adopt heuristic strategies (e.g., best-so-far selection based on mean absolute spectral error and rule-of-thumb recommendations for the number of runs), underscoring a methodological gap in robust variability assessment.

References

Diffusion models are inherently probabilistic, which means that repeated evaluations of the same trained model on the same input can yield different outputs. However, a reliable method to determine how much meaningful difference actually exists between the results produced by different Monte Carlo samples of the trained model does not exist.

— Inverse Design of Optical Multilayer Thin Films using Robust Masked Diffusion Models  (2604.01106 - Schaible et al., 1 Apr 2026) in Section 4.3, Variability analysis approaches