Lantern: Conflict-Aware Gradient Blending for Physics-Guided Diffusion Models in Calorimeter Simulation

High-energy physics relies on computationally expensive Monte Carlo simulations (e.g., Geant4) to model particle showers in calorimeters. While diffusion-based generative models offer a faster alternative, they are purely statistical and often fail to capture the underlying physical structure of the showers. This paper addresses the challenge of incorporating physics-informed constraints into diffusion training without compromising the model's generative quality or stability.

The authors introduce three main components to improve physics-guided diffusion:

1. Correlation Frobenius Distance (CFD): A new metric that quantifies the fidelity of correlation structures across calorimeter layers and voxels, filling a gap left by standard physics feature-space metrics.
2. Physics-Aware Auxiliary Losses: Two losses are designed to encode physical structure: a variance-stabilized voxel residual loss (based on counting statistics) and a graph Laplacian loss (based on detector geometry).
3. GradBlend: A novel gradient combination rule that treats the denoising objective as primary. It anchors the step magnitude to the denoising gradient while allowing the auxiliary physics losses to steer the update direction, effectively managing conflicts between the two objectives.

Standard multi-task optimization methods (like PCGrad or GradNorm) often fail in this context, inflating the Fréchet Physics Distance (FPD) by 2–100x because they treat the auxiliary physics losses as equal peers to the denoising objective. In contrast, GradBlend successfully integrates these physics signals without regression. When combined with the graph Laplacian loss, Lantern improves both the FPD and the newly introduced CFD metric. The authors also demonstrate that because the voxel residual loss inherently conflicts with denoising, a terminal denoising-only training phase is essential to preserve sample coverage.