Pith. sign in

REVIEW 5 major objections 4 minor 1 cited by

CaloTrilogy shows that high-quality calorimeter showers can be generated end-to-end in one or a few network evaluations, matching the fidelity of diffusion models that require hundreds of steps.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-02 12:24 UTC pith:56NPXRGX

load-bearing objection CaloTrilogy's one-step shower quality claim is credible and important; missing error bars, timing, and a clean GMM ablation make it conditional. the 5 major comments →

arxiv 2606.04165 v2 pith:56NPXRGX submitted 2026-06-02 hep-ex cs.LGhep-phphysics.ins-det

CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters

Cheng Jiang , Sitian Qian , Kevin Pedro , Oz Amram , Huilin Qu , Maggie Voetberg This is my paper
classification hep-ex cs.LGhep-phphysics.ins-det
keywords calorimeter simulationgenerative modelsflow matchingMeanFlowphysics-constrained lossGaussian mixture priorfast simulation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to establish that fast calorimeter simulation does not have to choose between speed and fidelity. The authors argue that combining an average-velocity flow integrator (MeanFlow), a learned structured prior in shower space, and physics-informed loss terms applied during training lets a single end-to-end generative model produce showers competitive with state-of-the-art flow and diffusion approaches using only one to six network evaluations. If true, this would remove a major computing bottleneck in collider simulation without giving up the global shower properties that physics analyses rely on. All physics guidance is folded into training-time regularizers, so the speed-up comes with no auxiliary networks or post-processing at inference.

Core claim

On the paper's own terms, the central discovery is that three training-time components—MeanFlow's interval-averaged velocity field, a conditional Gaussian mixture prior that starts sampling near the data manifold, and a layer-energy physics constraint optimized with a Lagrangian scheme—together let a single network produce calorimeter showers in one or six steps at a quality comparable to, and sometimes better than, current state-of-the-art methods that require on the order of hundreds of function evaluations. The physics-constrained loss is computed on a one-step surrogate sample during training, acting purely as a regularizer, so inference remains a direct map from condition to shower with

What carries the argument

Three mechanisms carry the argument. (1) MeanFlow: instead of modeling the instantaneous velocity at each infinitesimal time step, the network learns the average velocity over a time interval, which lets one or a few Euler-like steps traverse the full probability path; the loss enforces self-consistency between a single direct mapping and two-step compositions. (2) A conditional Gaussian mixture model, predicted from the incident energy by a lightweight network, supplies a structured prior that already approximates the target shower distribution, shortening the path the flow needs to travel. (3) A physics-constrained loss, instantiated as layer-wise total energy, is evaluated on a one-step M

Load-bearing premise

The central assumption is that the one-step MeanFlow sample used during training to compute the physics-constrained loss faithfully represents the showers the model will actually generate at inference time; if the surrogate's layer energies are biased, the regularizer optimizes an inconsistent objective and the reported layer-energy improvements could be artifacts of training.

What would settle it

Generate showers with the trained model using both 1 and 6 steps, measure the layer-energy distributions of the actual outputs, and compare them with the one-step surrogate values used during training; a systematic mismatch would show the physics loss optimized the wrong quantity and would undercut the speed-quality claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • End-to-end fast simulation becomes practical: one or six network evaluations replace hundreds of steps, yielding up to two orders of magnitude speed-up with no auxiliary high-level model.
  • Because the physics constraints enter only through training-time regularizers, adding them does not complicate the deployed generator.
  • The reported layer correlations, occupancy, and total-energy distributions suggest the generated showers could be used in production fast-simulation workflows for high-luminosity running.
  • Pretraining on a wide energy and angular range and then fine-tuning improves fidelity, indicating a scalable recipe for other detector geometries.
  • The physics-constrained loss is generic—layer energy is one instance—so the same mechanism can be extended to other calorimeter observables.

Where Pith is reading between the lines

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

  • The paper leaves open whether the one-step surrogate used to compute the physics loss during training faithfully represents the showers produced by six-step sampling; a direct comparison of layer energies between the surrogate and actual outputs would settle this.
  • The paper does not state which MeanFlow prediction target produced the main tables; since the appendix on occupancy shows x-prediction improves occupancy, running the full framework with x-prediction is a natural next step that could strengthen the reported results.
  • The conditional GMM prior is lightweight and trained by maximum likelihood; it could be reused independently as a fast approximate simulator or as an initialization for other generative models, though the paper does not explore these uses.
  • The same 'constrain a one-step surrogate' trick could be applied to other differentiable observables, such as transverse profiles or shower-core moments, where the paper's ablations suggest the largest gains appear in ratio-type observables.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

5 major / 4 minor

Summary. The paper proposes CaloTrilogy, a one- or few-step generative framework for calorimeter shower simulation that combines three components: a MeanFlow-based integrator that learns averaged velocity fields, a conditional Gaussian mixture model (GMM) used as a learned prior, and a physics-constrained loss term (L_PIDM) that enforces layer-energy fidelity during training. The method is evaluated on CaloChallenge datasets 2 and 3 and on the ILD photon dataset against CaloDiffusion and CaloClouds3, with claims that it reaches competitive or superior quality in one or six function evaluations, i.e., one to two orders of magnitude faster than existing diffusion baselines. The paper reports separation powers, Wasserstein distances, Jensen-Shannon divergences, FPD/KPD scores, and AUC classifier metrics, together with histograms of high-level observables.

Significance. If the claims hold, the work provides a practical resolution of the speed-quality tradeoff in fast calorimeter simulation: end-to-end generation with one or six network evaluations at quality comparable to ~200-step diffusion. The study is notable for its use of public CaloChallenge and ILD datasets, broad evaluation across binned and unbinned metrics, and for combining three distinct ideas (MeanFlow, learned GMM prior, physics-constrained loss) in a single end-to-end pipeline. The physics-constrained loss as a training-time regularizer with no inference overhead is an attractive design. However, several load-bearing points require additional evidence before the central claims can be accepted: the main numerical tables lack uncertainty estimates, the GMM component is not ablated, the trained-vs-deployed sampling distribution for the physics loss is not verified, and no timing measurements support the speed advantage.

major comments (5)
  1. [Tables I-III and V] The headline comparisons are reported as single numbers (separation power and Wasserstein distance) without statistical uncertainties or multiple-seed variability. Many of the claimed advantages over CaloDiffusion are small in absolute terms (e.g., Table II Angular Energy 0.000077 vs 0.000138, or Layer Energy 0.000025 vs 0.000080); without error bars it is impossible to judge whether these differences are significant. The paper should provide bootstrap uncertainties or repeat training with different seeds and report the spread. The FPD/AUC values in the text do have errors, but the central tables do not.
  2. [Section II.C, Eq. (L_PIDM)] The physics-constrained loss is computed on a one-step MeanFlow surrogate: E_gen^ell is obtained by applying the learned velocity field to a prior sample. The paper's best few-step results, however, use 6-step Euler sampling (Tables II-III, Figs. 7-10). There is no check that the layer-energy distribution of the 6-step sampler matches the one-step surrogate used to minimize L_PIDM. If multi-step integration drifts from the surrogate distribution, the reported gains in layer energy and energy ratio (Table V) could be artifacts of optimizing on a distribution different from the deployed generator. The authors should compare layer-energy distributions from the one-step surrogate and the 6-step sampler during or after training, or otherwise justify the surrogate's representativeness. In the same vein, reporting layer energy and energy ratio as successes is partly circular because these obser
  3. [Section II.A and Appendix C] The manuscript states in Section II.A that it follows the original MeanFlow formulation, which is v-prediction, but Appendix C demonstrates that x-prediction substantially improves occupancy and Wasserstein distance during training. It is not stated which prediction target produced the main tables and figures. If the main results are v-prediction, the occupancy results may be suboptimal; if they are x-prediction, the statement in Section II.A is misleading. This ambiguity also compounds the L_PIDM surrogate concern, since the surrogate and the final sampler could use different parameterizations. The authors must specify the variant used for each reported result and, ideally, provide the main tables for both variants.
  4. [Section IV.C / Appendix A] CaloTrilogy is defined as three mutually reinforcing components, but only the physics-constrained loss is ablated (Table V). The conditional GMM prior is not ablated; there is no comparison to the same MeanFlow model with a standard isotropic Gaussian prior or with the GMM components fixed. Given that the GMM is a central claimed contributor to few-step accuracy, this omission leaves the contribution of one of the three core modules unquantified and weakens the 'trilogy' claim.
  5. [Section I and Conclusion] The paper claims 'up to two orders of magnitude acceleration' over CaloDiffusion, but no inference timing or wall-clock measurements are reported anywhere. The number-of-function-evaluations argument is plausible, but runtime per generated shower depends on model size, hardware, batching, and data movement. The authors should report generation times (e.g., showers per second on a specified GPU) for CaloTrilogy at 1 and 6 steps and for the competing CaloDiffusion baseline.
minor comments (4)
  1. [Section II.C / IV.C] The loss notation is inconsistent: Section II.C defines L_total = L_MF + beta L_PIDM, while Section IV.C defines L_total = L_MF + lambda(L_PIDM - xi) + sigma/2 (L_PIDM - xi)^2. The relationship between beta and the MDMM parameters should be clarified, including when beta is replaced by the multiplier update.
  2. [Abstract / Introduction] Minor typos: 'This simplify the whole pipeline' (Section I) and 'until the good criteria are satisfied' (Section IV.C). Also, references [10] and [11] appear to duplicate the same Erdmann et al. paper with slightly different title capitalization; one should be removed.
  3. [Figure 4] The figure caption for the PIDM loss panel says 'various scheduling strategies' but the color coding of the vertical lines is explained only partially. The reader must infer which curve corresponds to which schedule from the labels inside the panel; please add a legend or clearer caption.
  4. [Appendix B] The GMM validation on Dataset 1 is useful, but Figure 15 shows only mean layer energy and a few layer distributions. Since the GMM prior is claimed to capture spatial correlations (Figure 2), a quantitative comparison (e.g., Wasserstein distance on the 1-D projections or covariance mismatch) would help substantiate the claim.

Circularity Check

1 steps flagged

Layer-energy and energy-ratio metrics are directly optimized by L_PIDM, so reporting them as successes is partly training-to-metric; the central one/few-step quality claim remains independent.

specific steps
  1. fitted input called prediction [Section II.C (Physics-Constrained Loss); Section V and Tables I, II, V; Fig. 9]
    "LPIDM is instantiated as a layer-wise energy constraint, LPIDM = Σ_ℓ ||E_gen^ℓ − E_true^ℓ||², where E_ℓ denotes the total deposited energy in calorimeter layer ℓ. ... The improved agreement in energy ratio observables can be attributed to the physics-constrained loss, which aligns the global energy sum well during training."

    The reported 'Layer Energy' and related 'Energy Ratio' evaluation metrics are the same quantities that L_PIDM explicitly minimizes during training: the loss is the squared difference between generated and true layer energies summed over layers. Thus the observed improvement on these metrics is, at least in part, a report of the training objective itself rather than an independent validation of the model's physics modeling. The paper is transparent about this attribution, and the headline few-step claim is supported by other, non-optimized metrics (occupancy, radial/angular energy, classifier AUC), so the circularity is partial rather than total.

full rationale

CaloTrilogy's central claim — competitive or superior one/few-step shower quality compared with CaloDiffusion and CaloClouds3 — is tested against external benchmarks and many observables that are not directly included in the training loss (occupancy, radial/angular energy profiles, FPD/KPD, AUC). Those comparisons are self-contained and independent of the authors' prior work. The physics-constrained term L_PIDM does directly optimize layer energies, so reporting layer-energy and energy-ratio agreement as evidence of fidelity is partly fitting-to-metric; this is the one genuine circular element. It is mitigated by the paper's explicit statement that the improvement is 'attributed to the physics-constrained loss,' i.e., the authors do not mislabel it as an unprompted prediction. The self-citations ([49],[51]) appear only in survey reference lists and are not load-bearing. The one-step MeanFlow surrogate used to define E_gen^ℓ during training, and the lack of a check against 6-step sampling, is a possible correctness/transfer risk but not a definitional circularity: it is an approximation that could in principle fail, not an identity. The v-prediction vs x-prediction ambiguity in Appendix C is likewise a reporting gap, not a circular step. Overall score 4 reflects one partial circular step with an otherwise independent central result.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The central claim is an empirical model performance statement. The main unverified inputs are the MeanFlow formulation (from [68]), the Geant4 datasets as ground truth, and the one-step surrogate used for the physics loss. Several hyperparameters (β, MDMM constants, warmup schedule, GMM K) are unspecified or hand-chosen, hindering independent reproduction. No new physical entities are introduced.

free parameters (5)
  • β (PIDM loss weight) = upper bound 0.03 (final value not specified)
    Section II.C sets L_total = L_MF + β L_PIDM with β upper bounded by 0.03; MDMM adaptively tunes the effective weight, so the final β is not a fixed number.
  • MDMM constants λ, ξ, σ = not specified
    Section IV.C defines λ Lagrange multiplier, ξ loss threshold, σ damping coefficient; no numeric values are given, yet they determine how strongly the physics loss is enforced.
  • Warmup schedule = options 0-100, 50-50, 100-120 epochs; final selection not stated
    Figure 4 and Section IV.C describe three schedules; the reported results do not identify which was used.
  • GMM component count K = not stated
    The prior p_0(z|c) is defined with K components in Section II.B and Appendix A, but K is never specified.
  • r ≠ t sampling fraction = 0.75 (1-4 steps), 0.25 (6-10 steps)
    Section IV.B sets the fraction of training samples with r ≠ t; a hand-chosen hyperparameter affecting the MeanFlow consistency objective.
axioms (4)
  • standard math MeanFlow training objective and self-consistency relation are correct as derived in [68].
    The paper imports the MeanFlow loss and JVP derivative without re-deriving; if the base formulation is wrong, the whole model is invalid.
  • domain assumption Geant4 reference showers are ground truth for training and evaluation.
    All metrics compare against Geant4 samples; the accuracy of Geant4 itself is not questioned.
  • domain assumption The logit preprocessing preserves the physical distances used in evaluation metrics.
    Section IV.A normalizes by incident energy, applies logit transform and standard normalization; the Wasserstein distances are computed in this transformed space, so the preprocessing affects the metric.
  • ad hoc to paper One-step surrogate sample is representative of the model's generated shower distribution during training.
    Section II.C uses a one-step MeanFlow sample to compute E_gen for L_PIDM; this approximation is asserted for backprop efficiency but not validated.

pith-pipeline@v1.3.0-alltime-deepseek · 21795 in / 14511 out tokens · 136685 ms · 2026-08-02T12:24:50.641841+00:00 · methodology

0 comments
read the original abstract

High-precision calorimeter simulation at current and future colliders imposes rapidly growing computational demands, motivating the development of machine-learning surrogates for traditional Monte Carlo tools such as Geant4. Flow matching and diffusion-based generative models have become leading approaches for high-dimensional fast simulation because of their sample quality, but typically require ${\cal O}(100)$ function evaluations at inference and often rely on auxiliary networks to constrain global observables, compromising streamlined end-to-end generation. We introduce a unified framework that improves the balance between speed, shower quality, and physics fidelity. The method combines: (i) an average velocity field integrator that enables sampling in one or a few evaluations; (ii) a learned generative prior in shower space, constructed from data rather than random noise; and (iii) physics-guided loss terms that impose inductive biases on key observables during training. These elements are training time regularizers, preserving end-to-end inference with no additional cost. With only one or a few evaluation steps, the model achieves shower quality competitive with state-of-the-art flow and diffusion approaches, tested on several public high granularity calorimeter datasets. The results demonstrate inter-layer shower structure consistent with the underlying physics, providing a strong candidate for future fast simulation workflows.

Figures

Figures reproduced from arXiv: 2606.04165 by Cheng Jiang, Huilin Qu, Kevin Pedro, Maggie Voetberg, Oz Amram, Sitian Qian.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic architecture of the proposed model. Conditional inputs are first mapped to a Gaussian mixture model [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. One-dimensional projections and two-dimensional [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Mean voxel distributions across different layers for [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The main generative loss term (MF, upper) and the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Reciprocal Wasserstein distance and cosine similar [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Comparison of [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Reciprocal Wasserstein distance for various high [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Comparison of [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Distribution of Pearson correlation coefficients and their differences with respect to the reference layer energies for [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. KPD and FPD scores, together with low- and high-level AUC classifier performance, comparing Geant4 and [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Comparison of layer-wise energy distributions and [PITH_FULL_IMAGE:figures/full_fig_p014_15.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Reciprocal Wasserstein distance for various high [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Wasserstein distance and separation power for [PITH_FULL_IMAGE:figures/full_fig_p015_17.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Mean occupancy across layers for MeanFlow [PITH_FULL_IMAGE:figures/full_fig_p015_16.png] view at source ↗

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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

    cs.LG 2026-07 conditional novelty 6.5

    GradBlend anchors diffusion updates to denoising while admitting physics auxiliaries, improving calorimeter shower FPD and CFD where PCGrad, GradNorm, IMTL-G, and ConFIG inflate FPD by 2–100×.

Reference graph

Works this paper leans on

92 extracted references · 66 linked inside Pith · cited by 1 Pith paper

  1. [1]

    CMS Collaboration,The Phase-2 Upgrade of the CMS Endcap Calorimeter, Tech. Rep. CERN-LHCC-2017-023, CMS-TDR-019 (CERN, 2017)

    2017

  2. [2]

    Agostinelliet al.(GEANT4 Collaboration), GEANT4—a simulation toolkit, Nucl

    S. Agostinelliet al.(GEANT4 Collaboration), GEANT4—a simulation toolkit, Nucl. Instrum. Meth. A506, 250 (2003)

    2003

  3. [3]

    Allisonet al., Recent developments in Geant4, Nucl

    J. Allisonet al., Recent developments in Geant4, Nucl. Instrum. Meth. A835, 186 (2016)

    2016

  4. [4]

    Allisonet al., Geant4 developments and applications, IEEE Trans

    J. Allisonet al., Geant4 developments and applications, IEEE Trans. Nucl. Sci.53, 270 (2006)

    2006

  5. [5]

    Pedroet al.(CMS Collaboration), Integration and performance of new technologies in the CMS simulation, EPJ Web Conf.245, 02020 (2020), arXiv:2004.02327 [hep-ex]

    K. Pedroet al.(CMS Collaboration), Integration and performance of new technologies in the CMS simulation, EPJ Web Conf.245, 02020 (2020), arXiv:2004.02327 [hep-ex]

    Pith/arXiv arXiv 2020

  6. [6]

    Paganini, L

    M. Paganini, L. de Oliveira, and B. Nachman, Ac- celerating science with generative adversarial networks: An application to 3D particle showers in multilayer calorimeters, Phys. Rev. Lett.120, 042003 (2018), arXiv:1705.02355 [hep-ex]

    Pith/arXiv arXiv 2018

  7. [7]

    Paganini, L

    M. Paganini, L. de Oliveira, and B. Nachman, Calo- GAN: Simulating 3D high energy particle showers in multilayer electromagnetic calorimeters with generative adversarial networks, Phys. Rev. D97, 014021 (2018), arXiv:1712.10321 [hep-ex]

    Pith/arXiv arXiv 2018

  8. [8]

    de Oliveira, M

    L. de Oliveira, M. Paganini, and B. Nachman, Control- ling physical attributes in GAN-accelerated simulation of electromagnetic calorimeters, J. Phys. Conf. Ser.1085, 042017 (2018), arXiv:1711.08813 [hep-ex]

    Pith/arXiv arXiv 2018

  9. [9]

    Erdmann, L

    M. Erdmann, L. Geiger, J. Glombitza, and D. Schmidt, Generating and refining particle detector simulations us- ing the Wasserstein distance in adversarial networks, Comput. Softw. Big Sci.2, 4 (2018), arXiv:1802.03325 [physics.ins-det]

    Pith/arXiv arXiv 2018

  10. [11]

    Erdmann, J

    M. Erdmann, J. Glombitza, and T. Quast, Precise sim- ulation of electromagnetic calorimeter showers using a wasserstein generative adversarial network, Comput. Softw. Big Sci.3, 4 (2019), arXiv:1807.01954 [physics.ins- det]

    Pith/arXiv arXiv 2019

  11. [12]

    Musella and F

    P. Musella and F. Pandolfi, Fast and accurate simu- lation of particle detectors using generative adversar- ial networks, Comput. Softw. Big Sci.2, 8 (2018), arXiv:1805.00850 [hep-ex]

    Pith/arXiv arXiv 2018

  12. [13]

    Belaynehet al., Calorimetry with deep learning: Par- ticle simulation and reconstruction for collider physics, Eur

    D. Belaynehet al., Calorimetry with deep learning: Par- ticle simulation and reconstruction for collider physics, Eur. Phys. J. C80, 688 (2020), arXiv:1912.06794 [physics.ins-det]

    Pith/arXiv arXiv 2020

  13. [14]

    Butter, S

    A. Butter, S. Diefenbacher, G. Kasieczka, B. Nachman, and T. Plehn, GANplifying event samples, SciPost Phys. 10, 139 (2021), arXiv:2008.06545 [hep-ph]

    Pith/arXiv arXiv 2021

  14. [15]

    ATLAS Collaboration,Fast Simulation of the ATLAS Calorimeter System with Generative Adversarial Net- works, Tech. Rep. ATL-SOFT-PUB-2020-006 (CERN, 2020)

    2020

  15. [16]

    Ghosh, Deep generative models for fast shower simula- tion in ATLAS, J

    A. Ghosh, Deep generative models for fast shower simula- tion in ATLAS, J. Phys. Conf. Ser.1525, 012077 (2020)

    2020

  16. [17]

    Aadet al.(ATLAS), AtlFast3: The next generation of fast simulation in ATLAS, Comput

    G. Aadet al.(ATLAS), AtlFast3: The next generation of fast simulation in ATLAS, Comput. Softw. Big Sci.6, 7 (2022), arXiv:2109.02551 [hep-ex]

    Pith/arXiv arXiv 2022

  17. [18]

    Faucci Giannelli and R

    M. Faucci Giannelli and R. Zhang, CaloShowerGAN, a generative adversarial network model for fast calorimeter shower simulation, Eur. Phys. J. Plus139, 597 (2024), arXiv:2309.06515 [hep-ex]

    Pith/arXiv arXiv 2024

  18. [19]

    Simsek, B

    E. Simsek, B. Isildak, A. Dogru, R. Aydogan, A. B. Bayrak, and S. Ertekin, CALPAGAN: Calorime- try for particles using generative adversarial net- works, Prog. Theor. Exp. Phys.2024, 083C01 (2024), arXiv:2401.02248 [physics.ins-det]

    Pith/arXiv arXiv 2024

  19. [20]

    J. Birk, F. Gaede, A. Hallin, G. Kasieczka, M. Mozzan- ica, and H. Rose, OmniJet-α C : Learning point cloud calorimeter simulations using generative transformers, JINST20(07), P07007, arXiv:2501.05534 [physics.ins- det]

    Pith/arXiv arXiv

  20. [21]

    J. C. Cresswell, B. L. Ross, G. Loaiza-Ganem, H. Reyes- Gonz´ alez, M. Letizia, and A. L. Caterini, CaloMan: Fast generation of calorimeter showers with density estima- tion on learned manifolds, inNeurIPS 2022 Workshop on Machine Learning and the Physical Sciences(2022) arXiv:2211.15380 [cs.LG]

    Pith/arXiv arXiv 2022

  21. [22]

    Hoque, H

    S. Hoque, H. Jia, A. Abhishek, M. Fadaie, J. Q. Toledo- Mar ´ ın, T. Vale, R. G. Melko, M. Swiatlowski, and W. T. Fedorko, CaloQV AE: Simulating high-energy particle- calorimeter interactions using hybrid quantum-classical generative models, Eur. Phys. J. C84, 1244 (2024), arXiv:2312.03179 [hep-ph]

    arXiv 2024

  22. [23]

    Q. Liu, C. Shimmin, X. Liu, E. Shlizerman, S.-C. Li, and S.-C. Hsu, Calo-VQ: Vector-quantized two-stage generative model in calorimeter simulation, (2024), arXiv:2405.06605 [cs.LG]

    Pith/arXiv arXiv 2024

  23. [24]

    Kansal, J

    R. Kansal, J. Duarte, K. Duarte, and M. Pierini, Graph generative models for fast detector simulations in high energy physics 10.48550/arXiv.2106.11535 (2021), arXiv:2106.11535 [hep-ex]

    Pith/arXiv arXiv doi:10.48550/arxiv.2106.11535 2021

  24. [25]

    B. Hashemi, Deep Generative Models for Ultra- High Granularity Particle Physics Detector Simu- lation: A Voyage From Emulation to Extrap- olation 10.5282/edoc.34137 (2023), arXiv:2403.13825 [physics.ins-det]

    Pith/arXiv arXiv 2023

  25. [26]

    Mazurek (LHCb), Machine learning in LHCb Simu- lation: From fast to flash, PoSLHCP2025, 125 (2026), arXiv:2511.02020 [hep-ex]

    M. Mazurek (LHCb), Machine learning in LHCb Simu- lation: From fast to flash, PoSLHCP2025, 125 (2026), arXiv:2511.02020 [hep-ex]

    arXiv 2026

  26. [27]

    Krause and D

    C. Krause and D. Shih, CaloFlow: Fast and accurate generation of calorimeter showers with normalizing flows, Phys. Rev. D107, 113003 (2021)

    2021

  27. [28]

    Krause and D

    C. Krause and D. Shih, CaloFlow II: Even faster and still accurate generation of calorimeter showers with normal- izing flows, Phys. Rev. D107, 113004 (2021)

    2021

  28. [29]

    Krause, I

    C. Krause, I. Pang, and D. Shih, CaloFlow for CaloChallenge dataset 1, SciPost Phys.16, 126 (2024), arXiv:2210.14245 [cs.LG]

    Pith/arXiv arXiv 2024

  29. [30]

    Krause, B

    C. Krause, B. Nachman, I. Pang, D. Shih, and Y. Zhu, Anomaly detection with flow-based fast calorimeter simu- lators, Phys. Rev. D110, 10.1103/PhysRevD.110.0c5036 (2024), arXiv:2312.11618 [hep-ph]

    Pith/arXiv arXiv 2024

  30. [31]

    Ernst, L

    F. Ernst, L. Favaro, C. Krause, T. Plehn, and D. Shih, Normalizing flows for high-dimensional detector simula- tions, SciPost Phys.18, 081 (2025), arXiv:2312.09290 [cs.LG]. 12

    Pith/arXiv arXiv 2025

  31. [32]

    C. Gao, J. Isaacson, and C. Krause, i-flow: High- dimensional integration and sampling with normalizing flows, Mach. Learn. Sci. Technol.4, 045023 (2020)

    2020

  32. [33]

    M. R. Buckley, C. Krause, I. Pang, and D. Shih, Inductive simulation of calorimeter showers with normalizing flows, Phys. Rev. D109, 033006 (2024), arXiv:2305.11934 [cs.LG]

    Pith/arXiv arXiv 2024

  33. [34]

    K¨ ach, D

    B. K¨ ach, D. Kr¨ ucker, I. Melzer-Pellmann, M. Scham, S. Schnake, and A. Verney-Provatas, JetFlow: Generat- ing jets with conditioned and mass constrained normal- ising flows, (2022), arXiv:2211.13630 [hep-ex]

    Pith/arXiv arXiv 2022

  34. [35]

    Diefenbacher, E

    S. Diefenbacher, E. Eren, F. Gaede, G. Kasieczka, C. Krause, I. Shekhzadeh, and D. Shih, L2LFlows: Gen- erating high-fidelity 3D calorimeter images, JINST18 (10), P10017, arXiv:2302.11594 [cs.LG]

    Pith/arXiv arXiv

  35. [36]

    Heimel, R

    T. Heimel, R. Winterhalder, A. Butter, J. Isaacson, C. Krause, F. Maltoni, O. Mattelaer, and T. Plehn, Mad- NIS – neural multi-channel importance sampling, SciPost Phys.15, 141 (2023), arXiv:2212.06172 [hep-ph]

    Pith/arXiv arXiv 2023

  36. [37]

    Heimel, N

    T. Heimel, N. Huetsch, R. Winterhalder, A. Butter, O. Mattelaer, and T. Plehn, The MadNIS reloaded, Sci- Post Phys.17, 023 (2024)

    2024

  37. [38]

    Leigh, J

    M. Leigh, J. A. Raine, K. Zoch, and T. Golling,ν-Flows: Conditional Neutrino Regression, SciPost Phys.14, 159 (2023), arXiv:2207.00664 [cs.LG]

    Pith/arXiv arXiv 2023

  38. [39]

    K¨ ach, D

    B. K¨ ach, D. Kr¨ ucker, and I. Melzer-Pellmann, Point cloud generation using transformer encoders and normal- ising flows, (2022), arXiv:2211.13623 [cs.LG]

    Pith/arXiv arXiv 2022

  39. [40]

    I. Pang, D. Shih, and J. A. Raine, Calorimeter shower super-resolution, Phys. Rev. D109, 092009 (2024)

    2024

  40. [41]

    T. Buss, F. Gaede, G. Kasieczka, C. Krause, and D. Shih, Convolutional L2LFlows: generating accurate showers in highly granular calorimeters using convolutional normal- izing flows, JINST19(09), P09003, arXiv:2405.20407 [physics.ins-det]

    Pith/arXiv arXiv

  41. [42]

    H. Bahl, S. Diefenbacher, N. Elmer, T. Plehn, and J. Spinner, Forecasting generative amplification 10.48550/arXiv.2509.08048 (2025), arXiv:2509.08048 [hep-ph]

    Pith/arXiv arXiv doi:10.48550/arxiv.2509.08048 2025

  42. [43]

    Schnake, D

    S. Schnake, D. Kr¨ ucker, and K. Borras, CaloPointFlow II: Generating calorimeter showers as point clouds 10.48550/arXiv.2403.15782 (2024), arXiv:2403.15782 [physics.ins-det]

    Pith/arXiv arXiv doi:10.48550/arxiv.2403.15782 2024

  43. [44]

    Erdmann, J

    J. Erdmann, J. Kann, F. Mausolf, and P. Wissmann, ParaFlow: Fast calorimeter simulations parameterized in upstream material configurations, Eur. Phys. J. C85, 857 (2025), arXiv:2503.21461 [hep-ph]

    Pith/arXiv arXiv 2025

  44. [45]

    Amram and K

    O. Amram and K. Pedro, Denoising diffusion models with geometry adaptation for high fidelity calorime- ter simulation, Physical Review D108, 072014 (2023), arXiv:2308.03876 [physics.ins-det]

    Pith/arXiv arXiv 2023

  45. [46]

    Mikuni and B

    V. Mikuni and B. Nachman, Score-based generative mod- els for calorimeter shower simulation, Phys. Rev. D106, 092009 (2022), arXiv:2206.11898 [hep-ex]

    Pith/arXiv arXiv 2022

  46. [47]

    F. T. Acosta, V. Mikuni, B. Nachman, M. Arratia, B. Karki, R. Milton, P. Karande, and A. Angerami, Comparison of point cloud and image-based models for calorimeter fast simulation, JINST19(05), P05003, arXiv:2307.04780 [hep-ex]

    Pith/arXiv arXiv

  47. [48]

    Mikuni and B

    V. Mikuni and B. Nachman, CaloScore v2: Single- shot calorimeter shower simulation with diffusion models, JINST19(02), P02001, arXiv:2308.03847 [hep-ex]

    arXiv

  48. [49]

    Jiang, S

    C. Jiang, S. Qian, and H. Qu, Choose your diffusion: Ef- ficient and flexible ways to accelerate the diffusion model in fast high energy physics simulation, SciPost Phys.18, 195 (2025), arXiv:2401.13162 [hep-ex]

    Pith/arXiv arXiv 2025

  49. [50]

    Kobylianskii, N

    D. Kobylianskii, N. Soybelman, E. Dreyer, and E. Gross, Graph-based diffusion model for fast shower generation in calorimeters with irregular geometry, Phys. Rev. D 110, 072003 (2024), arXiv:2402.11575 [hep-ex]

    Pith/arXiv arXiv 2024

  50. [51]

    Jiang, S

    C. Jiang, S. Qian, and H. Qu, BUFF: Boosted decision tree based ultra-fast flow matching 10.48550/arXiv.2404.18219 (2024), arXiv:2404.18219 [hep-ex]

    Pith/arXiv arXiv doi:10.48550/arxiv.2404.18219 2024

  51. [52]

    Brehmer, V

    J. Brehmer, V. Bres´ o, P. de Haan, T. Plehn, H. Qu, J. Spinner, and J. Thaler, A lorentz-equivariant trans- former for all of the LHC, SciPost Phys.19, 108 (2025), arXiv:2411.00446 [hep-ph]

    arXiv 2025

  52. [53]

    Leigh, D

    M. Leigh, D. Sengupta, G. Qu´ etant, J. A. Raine, K. Zoch, and T. Golling, PC-JeDi: Diffusion for particle cloud generation in high energy physics, SciPost Phys.16, 018 (2024), arXiv:2303.05376 [hep-ph]

    Pith/arXiv arXiv 2024

  53. [54]

    Leigh, D

    M. Leigh, D. Sengupta, J. A. Raine, G. Qu´ etant, and T. Golling, Faster diffusion model with improved quality for particle cloud generation, Phys. Rev. D109, 012010 (2024), arXiv:2307.06836 [hep-ex]

    Pith/arXiv arXiv 2024

  54. [55]

    Favaro, A

    L. Favaro, A. Ore, S. P. Schweitzer, and T. Plehn, CaloDREAM – Detector response emulation via at- tentive flow matching, SciPost Phys.18, 088 (2025), arXiv:2405.09629 [hep-ph]

    Pith/arXiv arXiv 2025

  55. [56]

    Vaselli, C

    F. Vaselli, C. Sun, T. Aarrestad, D. Danopoulos, R. Os- kari Niemi, M. M. Glowacki, K. Govorkova, V. Loncar, F. Pantaleo, and M. Pierini, It’s not a F AD: first demon- stration of flows for unsupervised anomaly detection at 40 MHz for use at the Large Hadron Collider, Mach. Learn. Sci. Tech.7, 025052 (2026), arXiv:2508.11594 [hep-ex]

    Pith/arXiv arXiv 2026

  56. [57]

    Favaro, A

    L. Favaro, A. Giammanco, and C. Krause, Fast, accurate, and precise detector simulation with vision transform- ers 10.48550/arXiv.2509.25169 (2025), arXiv:2509.25169 [hep-ph]

    doi:10.48550/arxiv.2509.25169 2025

  57. [58]

    T. Buss, H. Day-Hall, F. Gaede, G. Kasieczka, K. Kr¨ uger, A. Korol, T. Madlener, P. McKeown, M. Mozzanica, and L. Valente, CaloClouds3: Ultra- fast geometry-independent highly-granular calorimeter simulation, JINST21(03), P03018, arXiv:2511.01460 [physics.ins-det]

    arXiv

  58. [59]

    T. Buss, F. Gaede, G. Kasieczka, A. Korol, K. Kr¨ uger, P. McKeown, and M. Mozzanica, CaloHadronic: A diffusion model for the generation of hadronic show- ers 10.48550/arXiv.2506.21720 (2025), arXiv:2506.21720 [physics.ins-det]

    doi:10.48550/arxiv.2506.21720 2025

  59. [60]

    Buhmann, S

    E. Buhmann, S. Diefenbacher, E. Eren, F. Gaede, G. Kasieczka, A. Korol, W. Korcari, K. Kr¨ uger, and P. McKeown, CaloClouds: Fast geometry-independent highly-granular calorimeter simulation, JINST18(11), P11025, arXiv:2305.04847 [physics.ins-det]

    Pith/arXiv arXiv

  60. [61]

    Buhmann, F

    E. Buhmann, F. Gaede, G. Kasieczka, A. Korol, W. Kor- cari, K. Kr¨ uger, and P. McKeown, CaloClouds II: Ultra- fast geometry-independent highly-granular calorimeter simulation, JINST19(04), P04020, arXiv:2309.05704 [physics.ins-det]

    Pith/arXiv arXiv

  61. [62]

    Raikwar, A

    P. Raikwar, A. Zaborowska, P. McKeown, R. Cardoso, M. Piorczynski, and K. Yeo, A generalisable genera- tive model for multi-detector calorimeter simulation 10.48550/arXiv.2509.07700 (2025), arXiv:2509.07700 [physics.ins-det]

    Pith/arXiv arXiv doi:10.48550/arxiv.2509.07700 2025

  62. [63]

    Gaede, G

    F. Gaede, G. Kasieczka, and L. Valente, Cross- 13 geometry transfer learning in fast electromagnetic shower simulation 10.48550/arXiv.2512.00187 (2025), arXiv:2512.00187 [physics.ins-det]

    doi:10.48550/arxiv.2512.00187 2025

  63. [64]

    T. Buss, H. Day-Hall, F. Gaede, G. Kasieczka, and K. Kr¨ uger, AllShowers: One model for all calorimeter showers 10.48550/arXiv.2601.11716 (2026), arXiv:2601.11716 [physics.ins-det]

    doi:10.48550/arxiv.2601.11716 2026

  64. [65]

    Ronneberger, P

    O. Ronneberger, P. Fischer, and T. Brox, U-net: Convo- lutional networks for biomedical image segmentation, in Medical Image Computing and Computer-Assisted Inter- vention – MICCAI 2015, edited by N. Navab, J. Horneg- ger, W. M. Wells, and A. F. Frangi (Springer Interna- tional Publishing, Cham, 2015) p. 234, arXiv:1505.04597 [cs.CV]

    Pith/arXiv arXiv 2015

  65. [66]

    Vaswani, N

    A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin, Attention Is All You Need, in31st International Confer- ence on Neural Information Processing Systems(2017) arXiv:1706.03762 [cs.CL]

    Pith/arXiv arXiv 2017

  66. [67]

    Y. Song, P. Dhariwal, M. Chen, and I. Sutskever, Consistency models 10.48550/arXiv.2303.01469 (2023), arXiv:2303.01469 [cs.LG]

    Pith/arXiv arXiv doi:10.48550/arxiv.2303.01469 2023

  67. [68]

    Z. Geng, M. Deng, X. Bai, J. Z. Kolter, and K. He, Mean flows for one-step generative model- ing 10.48550/arXiv.2505.13447 (2025), arXiv:2505.13447 [cs.LG]

    Pith/arXiv arXiv doi:10.48550/arxiv.2505.13447 2025

  68. [69]

    CaloChallenge Collaboration, CaloChallenge dataset 2: Electromagnetic showers in a high-granularity calorime- ter, (2022)

    2022

  69. [70]

    CaloChallenge Collaboration, CaloChallenge dataset 3: Highly granular calorimeter geometry, (2022)

    2022

  70. [71]

    Amramet al., CaloChallenge 2022: a community chal- lenge for fast calorimeter simulation, Rept

    O. Amramet al., CaloChallenge 2022: a community chal- lenge for fast calorimeter simulation, Rept. Prog. Phys. 88, 116201 (2025), arXiv:2410.21611 [physics.ins-det]

    arXiv 2022

  71. [72]

    Abramowiczet al., International large detector: In- terim design report 10.48550/arXiv.2003.01116 (2020), arXiv:2003.01116 [physics.ins-det]

    H. Abramowiczet al., International large detector: In- terim design report 10.48550/arXiv.2003.01116 (2020), arXiv:2003.01116 [physics.ins-det]

    Pith/arXiv arXiv doi:10.48550/arxiv.2003.01116 2003

  72. [73]

    J. Repondet al., Design and electronics commission- ing of the physics prototype of a Si-W electromagnetic calorimeter for the international linear collider, JINST 3, P08001, arXiv:0805.4833 [physics.ins-det]

    Pith/arXiv arXiv

  73. [74]

    J. Ho, A. Jain, and P. Abbeel, Denoising diffusion probabilistic models 10.48550/arXiv.2006.11239 (2020), arXiv:2006.11239 [cs.LG]

    Pith/arXiv arXiv doi:10.48550/arxiv.2006.11239 2006

  74. [75]

    Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, Score-based generative modeling through stochastic differential equations, ICLR (2021), arXiv:2011.13456 [cs.LG]

    Pith/arXiv arXiv 2021

  75. [76]

    Karras, M

    T. Karras, M. Aittala, T. Aila, and S. Laine, Elu- cidating the design space of diffusion-based genera- tive models, NeurIPS 10.48550/arXiv.2206.00364 (2022), arXiv:2206.00364 [cs.CV]

    Pith/arXiv arXiv doi:10.48550/arxiv.2206.00364 2022

  76. [77]

    Y. Xu, Z. Zhang, Y. Song, and S. Ermon, Restart sampling for improving generative processes 10.48550/arXiv.2306.14878 (2023), arXiv:2306.14878 [cs.LG]

    Pith/arXiv arXiv doi:10.48550/arxiv.2306.14878 2023

  77. [78]

    Lipman, R

    Y. Lipman, R. T. Q. Chen, H. Ben-Hamu, M. Nickel, and M. Le, Flow matching for generative model- ing 10.48550/arXiv.2210.02747 (2023), arXiv:2210.02747 [cs.LG]

    Pith/arXiv arXiv doi:10.48550/arxiv.2210.02747 2023

  78. [79]

    A. Tong, Y. Lipman, R. T. Q. Chen, M. Nickel, and M. Le, Improving and generalizing flow-based generative models with minibatch optimal transport 10.48550/arXiv.2302.00482 (2023), arXiv:2302.00482 [cs.LG]

    Pith/arXiv arXiv doi:10.48550/arxiv.2302.00482 2023

  79. [80]

    Zhang, A

    H. Zhang, A. Siarohin, W. Menapace, M. Vasilkovsky, S. Tulyakov, Q. Qu, and I. Skorokhodov, Al- phaFlow: Understanding and improving meanflow mod- els 10.48550/arXiv.2510.20771 (2025), arXiv:2510.20771 [cs.LG]

    doi:10.48550/arxiv.2510.20771 2025

  80. [81]

    H. You, B. Liu, and H. He, Modular MeanFlow: To- wards stable and scalable one-step generative model- ing 10.48550/arXiv.2508.17426 (2025), arXiv:2508.17426 [cs.LG]

    Pith/arXiv arXiv doi:10.48550/arxiv.2508.17426 2025

Showing first 80 references.