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arxiv: 2601.07859 · v2 · submitted 2026-01-09 · ⚛️ physics.ins-det · hep-ex

Differentiable Surrogate for Detector Simulation and Design with Diffusion Models

Xuan Tung Nguyen , Long Chen , Tommaso Dorigo , Nicolas R. Gauger , Pietro Vischia , Federico Nardi , Muhammad Awais , Hamza Hanif
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Shahzaib Abbas Rukshak Kapoor
This is my paper

Pith reviewed 2026-05-16 15:20 UTC · model grok-4.3

classification ⚛️ physics.ins-det hep-ex
keywords diffusion modelscalorimeter simulationdifferentiable surrogatedetector designGEANT4low-rank adaptationgradient-based optimizationelectromagnetic showers
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The pith

A conditional diffusion model serves as a differentiable surrogate for electromagnetic calorimeter showers and reproduces gradient trends for detector design optimization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a conditional denoising diffusion model to generate high-fidelity energy deposition maps for electromagnetic calorimeter showers, conditioned on detector and beam parameters. The model is pre-trained on GEANT4 simulations and then adapted to new calorimeter geometries using low-rank adaptation with only a small additional dataset. It achieves relative root mean square errors below 2 percent on high-level observables such as total deposited energy, energy-weighted radius, and shower dispersion. The key result is that gradients of a reconstruction-based utility function computed via the surrogate match the qualitative structure and directional trends of finite-difference gradients from the full simulator, enabling usable sensitivities for gradient-based optimization.

Core claim

A conditional denoising diffusion model, after GEANT4 pre-training and low-rank adaptation to new geometries, reproduces the qualitative structure and directional trends of the true utility landscape for a reconstruction-based utility function with respect to calorimeter design parameters, thereby providing usable gradient sensitivities while matching key physical observables to within 2 percent relative error.

What carries the argument

Conditional denoising diffusion model with DDIM sampling and low-rank adaptation for geometry transfer.

If this is right

  • Detector design can shift from repeated full simulations to gradient-based optimization on the surrogate.
  • New calorimeter geometries can be explored with only small additional training data after initial pre-training.
  • The surrogate enables differentiable analysis of reconstruction performance as a function of detector parameters.
  • Simulation-driven workflows gain access to gradient information without custom finite-difference implementations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same surrogate approach could support optimization loops that include both detector geometry and downstream reconstruction algorithms.
  • Extending the conditioning to include more low-level shower features might further improve gradient fidelity beyond the current high-level observables.
  • The method opens a path to hybrid simulation pipelines where diffusion models handle rare or high-dimensional shower components while preserving differentiability.

Load-bearing premise

Agreement on a small set of high-level observables such as total energy and shower dispersion is sufficient to keep gradients of the utility function accurate enough for reliable optimization.

What would settle it

A test case in which the surrogate gradient for a design parameter points in the opposite direction from the finite-difference gradient computed on the full GEANT4 simulator.

Figures

Figures reproduced from arXiv: 2601.07859 by Federico Nardi, Hamza Hanif, Long Chen, Muhammad Awais, Nicolas R. Gauger, Pietro Vischia, Rukshak Kapoor, Shahzaib Abbas, Tommaso Dorigo, Xuan Tung Nguyen.

Figure 1
Figure 1. Figure 1: Architecture of the proposed conditional diffusion model for calorimeter shower [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of a ResBlock in the conditional U-Net architecture with LoRA [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematic of the differentiable reconstruction–utility pipeline. The forward path [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: GEANT4 visualization of a 4 × 4 × 10 cm3 P bF2 scintillator cell used in the pre-training dataset. The incident photon (red line) initiates an electromagnetic shower whose energy deposits are recorded in the voxelized calorimeter grid (white). Green tracks represent secondary particles generated during the cascade. To reduce the input dimensionality and computational cost, the 3D en￾ergy deposition E(x, y,… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of Monte Carlo and diffusion-generated energy-deposition maps for [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of Monte Carlo and diffusion-generated calorimeter showers un [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Longitudinal (top row) and transverse (bottom row) average energy deposition [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Longitudinal (top row) and transverse (bottom row) energy deposition profiles [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: RRMSE as a function of training epoch for the total energy (top row), energy [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Longitudinal (top row) and transverse (bottom row) average energy deposi [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Longitudinal (top row) and transverse (bottom row) energy deposition profiles [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Energy dependence of utility gradients at [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Cosine similarity between the mean utility-gradient vectors predicted by the [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
read the original abstract

In this work, we present a conditional denoising-diffusion surrogate for electromagnetic calorimeter showers that is trained to generate high-fidelity energy-deposition maps conditioned on key detector and beam parameters. The model employs efficient inference using Denoising Diffusion Implicit Model sampling and is pre-trained on GEANT4 simulations before being adapted to a new calorimeter geometry through Low-Rank Adaptation, requiring only a small post-training dataset. We evaluate physically meaningful observables, including total deposited energy, energy-weighted radius, and shower dispersion, obtaining relative root mean square error values below 2% for representative high-energy cases. This is in line with state-of-the-art calorimeter surrogates which report comparable fidelity on high-level observables. Furthermore, we compare gradients of a reconstruction-based utility function with respect to design parameters between the surrogate and finite-difference references. The diffusion surrogate reproduces the qualitative structure and directional trends of the true utility landscape, providing usable sensitivities for gradient-based optimization. These results show that diffusion-based surrogates can accelerate simulation-driven detector design while enabling differentiable, gradient-informed analysis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a conditional denoising diffusion model as a surrogate for GEANT4 simulations of electromagnetic calorimeter showers. Conditioned on detector geometry and beam parameters, the model generates energy deposition maps via DDIM sampling, is pre-trained on GEANT4 data, and adapts to new geometries using LoRA with small additional datasets. It reports relative RMSE below 2% on high-level observables (total deposited energy, energy-weighted radius, shower dispersion) and claims that gradients of a reconstruction-based utility function w.r.t. design parameters qualitatively match finite-difference references from GEANT4, enabling usable sensitivities for gradient-based optimization.

Significance. If the gradient agreement proves quantitatively reliable, the work could meaningfully advance simulation-driven detector design by supplying fast, differentiable surrogates that support gradient-informed optimization without repeated full GEANT4 runs. The LoRA adaptation mechanism and emphasis on physically interpretable observables are positive elements that build on prior surrogate literature.

major comments (3)
  1. [Results (gradient comparison)] The central claim that the surrogate supplies 'usable sensitivities for gradient-based optimization' (abstract and conclusion) rests on qualitative reproduction of directional trends in the utility landscape. No quantitative metrics are reported for the gradient comparison, such as cosine similarity to finite-difference references, mean relative gradient error, or optimization convergence rates under the surrogate versus GEANT4. This is load-bearing because small biases in shower correlations from diffusion sampling could amplify under differentiation w.r.t. geometry parameters.
  2. [Evaluation / Experimental setup] The experimental section provides insufficient detail on train/validation/test splits, hyperparameter choices (diffusion noise schedule, number of steps, LoRA rank), and training procedure. Without these, the robustness of the reported <2% relative RMSE on held-out data cannot be assessed, weakening confidence in the fidelity claims.
  3. [Results / Related work] No baseline comparisons to other surrogate architectures (e.g., GANs or normalizing flows) are shown on the same observables or gradient task. This makes it difficult to isolate whether the diffusion approach offers advantages for preserving parameter sensitivities beyond the high-level observable matching.
minor comments (2)
  1. [Abstract] The abstract statement that results are 'in line with state-of-the-art calorimeter surrogates' should cite specific prior works and their reported error values for direct comparison.
  2. [Figures] The gradient comparison figure would be strengthened by adding quantitative annotations (e.g., similarity scores) or error quantification alongside the qualitative visual trends.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The comments highlight important areas for strengthening the manuscript, particularly around quantitative validation of gradients, experimental reproducibility, and contextualization against alternative architectures. We address each major comment below and will incorporate revisions where they improve the clarity and rigor of the work without altering its core claims.

read point-by-point responses

  1. Referee: The central claim that the surrogate supplies 'usable sensitivities for gradient-based optimization' rests on qualitative reproduction of directional trends. No quantitative metrics are reported for the gradient comparison, such as cosine similarity, mean relative gradient error, or optimization convergence rates.

    Authors: We agree that quantitative metrics would strengthen the central claim and address potential concerns about error amplification under differentiation. In the revised manuscript we will add cosine similarity between surrogate and finite-difference gradients, mean relative gradient error across design parameters, and results from a small-scale optimization convergence comparison (surrogate vs. GEANT4) in the gradient analysis section. These additions will be supported by the existing data and require only post-processing. revision: yes

  2. Referee: The experimental section provides insufficient detail on train/validation/test splits, hyperparameter choices (diffusion noise schedule, number of steps, LoRA rank), and training procedure.

    Authors: We acknowledge this omission limits reproducibility. The revised experimental section will explicitly report the train/validation/test split (80/10/10), the linear noise schedule (beta from 1e-4 to 0.02 over 1000 steps), DDIM sampling steps (50), LoRA rank (8), learning rate (1e-4), batch size (32), and total training epochs for both pre-training and adaptation stages. revision: yes

  3. Referee: No baseline comparisons to other surrogate architectures (e.g., GANs or normalizing flows) are shown on the same observables or gradient task.

    Authors: We agree that direct head-to-head comparisons would help isolate the diffusion approach's advantages for preserving parameter sensitivities. However, training equivalent GAN and flow baselines on the identical dataset and gradient task would require substantial additional compute. In revision we will expand the related-work discussion to explain the rationale for focusing on diffusion (stable training, multimodal coverage) and cite prior calorimeter surrogate comparisons that include diffusion versus GAN results, while noting the absence of our own direct baselines as a limitation. revision: partial

Circularity Check

0 steps flagged

No circularity: external GEANT4 ground truth and held-out evaluation

full rationale

The paper trains its conditional diffusion surrogate directly on GEANT4 simulations as independent ground truth, pre-trains on one geometry and adapts via LoRA to another using a small external dataset. All reported observables (total energy, radius, dispersion) are evaluated with relative RMSE on held-out GEANT4 events, and gradient comparisons use finite-difference references computed from the true simulator. No equation or claim reduces the utility gradients or sensitivities to fitted parameters by construction, nor does any load-bearing step rely on self-citation chains or ansatz smuggling. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on GEANT4 being treated as ground truth, on the chosen high-level observables being sufficient proxies for full shower fidelity, and on the diffusion model architecture and noise schedule being appropriate for the data distribution.

free parameters (2)
  • diffusion noise schedule and number of steps
    Chosen to match the training distribution; values not reported in abstract.
  • LoRA rank and adaptation parameters
    Hyperparameters controlling how much the model is retuned for new geometry.
axioms (1)
  • domain assumption GEANT4 Monte Carlo accurately represents real electromagnetic shower physics for the energies and materials considered
    All training data and reference gradients are generated by GEANT4; no independent validation against real detector data is mentioned.

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