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

2026-07-27

AI Summary

This work addresses critical limitations in traditional diffusion models for calorimeter simulation, which neglect underlying physical structures, and highlights that existing physics-guided approaches struggle to apply to stochastic shower processes lacking explicit PDE constraints. Furthermore, conventional evaluation metrics fail to capture inter-layer and inter-voxel correlations. To overcome these issues, the authors propose Lantern, which introduces the Correlation Frobenius Distance (CFD) to holistically quantify multi-scale correlation fidelity. Lantern incorporates a voxel-wise residual loss based on count statistics and a detector geometry-aware graph Laplacian regularizer, along with a conflict-aware GradBlend gradient fusion strategy that effectively reconciles gradient conflicts between denoising objectives and physical constraints. Evaluated on CaloChallenge Dataset 2, Lantern significantly outperforms baseline methods in both FPD and CFD metrics, avoiding the performance degradation commonly observed in conventional multi-task learning formulations.

Abstract

Monte Carlo simulation of calorimeter showers is a principal bottleneck for the High-Luminosity LHC, and diffusion models have emerged as fast, high-fidelity surrogates. Their denoising objective is purely statistical, however: a model can minimize it while placing the physics wrong. Existing physics-informed generative methods cannot close this gap, because they assume a closed-form law, a governing PDE residual or a hard per-sample constraint, that a shower does not supply: no per-sample PDE governs a stochastic cascade, and energy conservation fixes only one scalar per shower. Standard metrics ignore the correlation structure across calorimeter layers and voxels, comparing showers only in a physics feature space. We address both gaps. We introduce the Correlation Frobenius Distance (CFD), a single normalized score for correlation fidelity at layer-wise and voxel-wise scales. We then encode the soft per-sample structure available in a shower as two physics-aware auxiliary losses: a variance-stabilized voxel residual loss grounded in counting statistics, and a graph Laplacian loss over the detector geometry. We combine both with denoising through GradBlend, which anchors the step magnitude to the denoising gradient while letting the auxiliary steer its direction, yielding Lantern, a physics-guided diffusion surrogate. On CaloChallenge Dataset 2, injecting the physics losses through task-symmetric rules such as PCGrad, GradNorm, IMTL-G, and ConFIG inflates FPD by 2-100x relative to denoising alone, whereas GradBlend admits the same signal without regression and, with the Laplacian loss, Lantern improves both FPD and CFD. Our ablation on the auxiliary loss scheduler shows that the voxel residual loss, whose gradient conflicts with denoising, requires a terminal denoising-only phase to preserve shower fidelity, whereas the non-conflicting Laplacian loss is insensitive to the schedule.

Problem

• calorimeter simulation
• diffusion models
• physics-guided learning
• correlation structure
• gradient conflict

Innovation

• physics-guided diffusion
• gradient blending
• correlation fidelity
• auxiliary losses
• calorimeter simulation