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Choose Your Diffusion: Efficient and flexible ways to accelerate the diffusion model in fast high energy physics simulation

by Cheng Jiang, Sitian Qian, Huilin Qu

Submission summary

Authors (as registered SciPost users): Sitian Qian
Submission information
Preprint Link:  (pdf)
Date submitted: 2024-01-26 01:39
Submitted by: Qian, Sitian
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Experiment
  • High-Energy Physics - Phenomenology
Approaches: Experimental, Computational, Phenomenological


The diffusion model has demonstrated promising results in image generation, recently becoming mainstream and representing a notable advancement for many generative modeling tasks. Prior applications of the diffusion model for both fast event and detector simulation in high energy physics have shown exceptional performance, providing a viable solution to generate sufficient statistics within a constrained computational budget in preparation for the High Luminosity LHC. However, many of these applications suffer from slow generation with large sampling steps and face challenges in finding the optimal balance between sample quality and speed. The study focuses on the latest benchmark developments in efficient ODE/SDE-based samplers, schedulers, and fast convergence training techniques. We test on the public CaloChallenge and JetNet datasets with the designs implemented on the existing architecture, the performance of the generated classes surpass previous models, achieving significant speedup via various evaluation metrics.

Current status:
Awaiting resubmission

Reports on this Submission

Anonymous Report 3 on 2024-5-8 (Invited Report)


1- The range of techniques explored in the study is wide
2- The results indicate that a significant reduction in generation time for diffusion models is possible without additional training


1- The descriptions of each technique are brief.
2- Most plots lack error bars, undermining the qualitative comparisons drawn from them.
3- Some claims are not clearly reflected in the results.


This paper presents a study of various noise schedules and samplers for generative diffusion models in the context of high energy particle physics. A focus is placed on training-free sampling techniques, which are under-represented in other studies that use the same datasets. The approaches are evaluated in terms of generation time at fixed sample quality. The results indicate that significant improvement over the baseline approach can be achieved in this regard.

On the other hand, the techniques that aim to improve the convergence during training are not thoroughly studied. Some statements are not clearly supported by the results presented, often because the relevant result is missing from a figure. In general, the clarity of the manuscript should be improved prior to publication.

Requested changes

- In section 2, the loss functions for DDPM and SGM are not given. The authors write “The noise scheduler determines how fast those samplers should learn” but this can only be understood in terms of a loss function. The first loss function in the paper appears in Eq. 9, but it is placed in the JetNet section, which does not seem appropriate.

- The third and fourth schedules in the list on page 5 are written as $t_{i<N} = ...$ , but this is inconsistent with the notation used previously.

- Regarding Figure 2:
- In the first line on page 10, the authors refer to “default EDM training loss weight”, but as far as I can tell, this has not been introduced. Does this refer to the min-SNR weight proposed in [51]? If not, then the Figure is also lacking a comparison between the original minSNR weighting and the one given in Eq. 10.
- Can the authors explain why the minSNR-trained model is so poor at 30 epochs?

- I find Figure 3 to be uninformative, given that there is such a small difference between the plots and no uncertainties are shown. In fact, I question the conclusion that EDM improves with more steps, since it appears as though the 30-step EDM is better.

- In Figures 7,8 (and throughout the paper) it is not made clear whether ‘steps’ refers to the total number of function evaluations or just to the number of integration steps. If the latter is true, then the figures are misleading since a given step would not equate to a fixed sampling time. In this case, I would suggest updating the figures to use number of function evaluations.

- In Figure 5, can the authors explain why the agreement for $E_\mathrm{total}$ is so good while $E_\mathrm{total} / E_\mathrm{inc}$ is poor in Figure 2 ? Given that $E_\mathrm{inc}$ is a constant, I would expect both plots to indicate similar performance. I also note that this figure is not discussed in the text.

- The paragraph starting “However,” on page 12 is difficult to follow. Some claims in the text are not substantiated in the figures because the relevant method is missing. For example, the Uni-PC sampler does not appear in Figs 2-9. I also do not understand what is meant by “The EDM and Restart samplers surpasses the previous 400 steps DDPM samplers at 50, 25 steps correspondingly” since in Figure 7, the DDPM sampler appears to be the worst everywhere.

- Page 14: “The best performances of Restart samplers again are achieved in 30-36 steps.” This does not appear to be true based Table 1, since Restart(79) has better metrics. Uncertainties should be included in the table.

- Why does Table 2 contain such a small subset of the solvers in Table 1?

- Figure 1 contains elements that are not explained in the caption, making the diagram difficult to interpret.

- Page 3: Equation (3) seems redundant.

- Page 5: For completeness, the first sampler in the list should be described.

- Page 6: In the EDM description, the stochasticity is not apparent: from which distribution is $S_{churn}$ sampled?

- Page 8: The relationship between Eqs. 8 and 9 is not made explicit. In particular, $F_\theta$ is not defined.

- Page 9: The separation power should be defined.

- The authors sometimes describe the samplers as ‘learning’ features, but I find this misleading since they are only relevant after the neural network is trained.


Ask for major revision

  • validity: ok
  • significance: ok
  • originality: good
  • clarity: low
  • formatting: reasonable
  • grammar: below threshold

Anonymous Report 2 on 2024-5-7 (Invited Report)


1. The paper provides a comprehensive overview of the impact of different sampling algorithms for diffusion based generative models. The authors assess how these choices impact sample quality and generation time.

2. The authors show significant speedups in generation time with good quality as compared to the baseline sampling methods used in prior works


1.The results from the many samplers tried are not always presented in a clear and organized way, making it overly difficult to draw conclusions.

2. The discussion and results shown on the JetNet dataset are very limited as compared to the results shown on the CaloChallenge dataset

3. The paper is mostly building on and improving prior work and is not very innovative.


The paper overviews various diffusion samplers using previous state of the art models from the literature. It is a useful contribution to the literature of generative models in HEP but some of its clarity should be improved prior to publication.

Requested changes

Major comments:

- The results Sec. 5.1 on pgs 10-13 should be presented in a more organized and clear way. Many different samplers & noise schedules are defined in the introduction, but results are shown for only a subset of them without much organization. Furthermore, different combinations are compared when discussing different shower features.The discussion in the text therefore quite difficult to follow and it is hard to gain insight into what the key takeways of these comparisons are. The text on pg 14 is more clear.

- Comparisons are given in terms of number of sampling steps. However, the metric one will care about in practice is sample generation time, which is directly related to the number of denoising model evaluations required to produce a sample. Some of the samplers used are first order, requiring only one evaluation of the denoising model per step, while others are higher order, requiring multiple model evaluations per step. It would be better to present results (eg Fig. 7, table 1) in terms of number of model evaluations rather than sampling steps. This would give the reader a better understanding of the tradeoff between quality vs generation time of each sampling method

- The discussion of the results on the JetNet dataset is very limited and does not seem to add much to the paper. It seems much fewer combinations of samplers are tried with no justification given as to why. Since all sampling methods are seen to given good performance it would be interesting to try to push towards a lower sampling step regime where there might be more pronounced differences. Plots similar to Fig. 7 and 8 would be informative.

- The authors often provide reasonable ranges for hyper parameters which is useful for building intuition, but the exact hyper parameter choices of the authors are not given. For reproducibility purposes, for any results shown in a plot / table the exact hyperparameters used should be specified somewhere in the text (an appendix is fine)

Minor comments:

- There are many grammatical mistakes or awkward phrasing in the text of the paper. Some of these are innocuous and do not harm the clarity of the ideas, but other times it is difficult to understand the authors meaning. Some examples of sentences I found difficult to understand are:

"This scheduler is even more decreasing than Karras schedulers, so the step size changes more rapidly in low sampling step while more slowly in last steps."

"Because the Restart samplers works with a predefined parameters for configuring the EDM ODE. The generation time is directly proportional with the restart iterations in the configuration, usually longer than default EDM

"All proposed samplers have comparable and better performance with smaller steps. Indeed some of them are struggling to match the low voxel energy, the presence of the tail is probably a consequence of model itself and too low energy threshold"

- When describing the EDM sampler "In our study, such degradation only happens when extreme values are selected." Please clarify what 'extreme' values means in this case

- Description of the Lu (last bullet on pg 5) scheduler is not very clear, particularly the last bullet

- Reference should be given for all samplers on Pg 6, currently not all are properly referenced

- It appears that the JetNet subsection (4.2) covers all the content on pg 8 but it actually only refers to the first three lines. A new subsection (4.3) should be started to better differentiate this

- Fig. 3 caption does seem correct. The caption says it is center of energy but what is being shown is the average energy as a function of the radial bin.

- In general plots should have fully descriptive labels on the plots themselves rather than relying on the figure caption to distinguish otherwise identical labels. Eg in Fig. 2 each plot should have a unique label telling the number of epochs and whether the default or min-SNR reweighting is used.


Ask for major revision

  • validity: good
  • significance: ok
  • originality: low
  • clarity: low
  • formatting: acceptable
  • grammar: below threshold

Anonymous Report 1 on 2024-5-1 (Invited Report)


1: Consideration of multiple solvers for diffusion generative models


1: The text would greatly benefit from a revision. The discussions of the results are hard to follow.
2: The authors aim to have a comprehensive comparison of samplers, but fall short on being through with their studies. How different distributions change with different sampling steps? How their results compare against public results on the same dataset?
3: Even though the JetNet dataset is mentioned, the studies performed using the dataset are considerably limited compared to the previous sections, lacking any conclusive results.


The authors aim to provide a comprehensive comparison between samplers for diffusion generative models. They use 2 public datasets to evaluate the differences between samplers. The calochallenge dataset 2 and the JetNet dataset. While the choice of samplers covers a comprehensive number of modern and traditionally used samplers, the results are hard to follow. In particular, in almost no plot all samplers are shown simultaneously, with only an arbitrary subset chosen for each distribution. This issue is more acute in the JetNet dataset where almost no effort is used to quantify the differences between solvers. Additionally, the authors do not compare their results with public benchmarks, undermining their goal of establishing the choice of better solvers for specific tasks. The goal of comparing multiple solvers is indeed interesting and deserves to be published, but in the current form additional studies and textual improvements are necessary. More detailed feedback is given below.

P2: “As a consequence, the detector simulations for the modern high granularity detectors occupy the most computation resources. ” Citations to support this statement would be great.

P3: “The performance surpasses the previous model by several evaluation metrics.” Where is the evaluation metrics?

P5: “ODE solvers often have smaller discretization errors than SDE solvers in smaller sampling steps.” Is there a reference to support this statement? ODE solvers often require less steps than SDE solvers, which contradicts the argument of bigger time steps given.

P5: VP scheduler: the variance preserving property is determined by the relationship alpha^2 + sigma^2 = 1 and not by the time evolution of sigma. I would point to it when introducing to the VP schedule or changing the name to avoid confusion (for example, cosine is also a VP schedule).

EDM schedule:

- What does churn means in this context? the meaning of S_{churn} is given but would be nicer to define an acronym related the meaning of the acronym.
- “This SDE sampler, unlike other SDEs that only give satisfied result after a very large sampling steps, can converge quickly because of this” satisfying instead of satisfied. What does “this” refer to in the explanation?


- How is the score function of the data x dependent on time? This result is only true for sigma = t, which is only one of the possible schedulers discussed. How is that implemented for the other schedulers?
- What is D?


- How Eq.8 gives you Eq. 9? What if F?
- Define the noise epsilon and the relationship with the noise applied to the data.

P8: “To mitigate the instability of the optimization over the training, …” why is the training unstable to begin with?
How is SNR(t) defined?

Eq. 10: What is the benefit of the function being even? Are negative time values used at any point?

P9: “In addition, a DNN classifier with 2 layers, each comprising 2048 nodes and a 0.2 dropout
rate” how is that determined to be sufficient?

Fig. 2: The authors claim the benefit of the weight function based on the convergence results as a function of the number of training epochs. This argument is unfortunately not sufficient to prove their point as the energy ratio is but a single observable from a high dimensional dataset. Moreover, additional parameters such as the choice of optimizer, learning rate, and batch size will all influence the convergence rate independently from the choice of weighting scheme. Additionally, faster training convergence is a debatable quantity for a generative model, as the main benefit of fast detector simulation is at inference time, with training time corresponding to a small fraction compared to the expected inference time during production.

Fig. 3: The ratio plots should be zoomed in as currently the axis range is too big compared to the plot. The choice of plots is also odd as other schedulers were also discussed in the previous sections. The same plot with all schedulers shown at the same time with zoomed in axis in the ratio plot would be better to compare the differences in generation quality.
Similarly, the number of steps chosen for each scheduler seems arbitrary at this point. How were they chosen?

Figs 3, 4, 5: Again, even though multiple solvers are described, the authors only show results for an arbitrary subset. Either show the results for all samplers, or motivate why the EDM is preferred in these plots.

Fig. 6: Why the ratio is not shown? This is the first distribution showing a bigger set of schedulers and would benefit from the ratio plot. Why EDM is shown with different number of steps? Would the other samplers also improve with more steps? For example, LMS shows a disagreement at low voxel energies, but uses only 36 steps. Similarly to my previous question, the authors should motivate how the choice of steps shown in the comparison plots are motivated, otherwise differences cannot be attributed to the solvers but simply from a poor choice of number of steps.

P10: “Indeed some of them are struggling to match the low voxel energy, the presence of the tail is probably a consequence of model itself and too low energy threshold”. What does that mean? That the model itself is not good enough? If so, then no sampler should be able to get a good agreement in the low energy voxel region, which is not true from Fig. 6.

P11: “LMS sampler involves an additional parameter "order" of the coefficient which makes the generation time longer as it increases”. This sentence is very cryptic as that parameter has not been introduced nor is it explained how it influences anything in the solver.

Fig. 7: Why LMS seems to increase instead of decrease with more steps? This plot and results would be great to show early in the text to motivate the choice of sampling steps picked for individual histograms (if that is true that the number of steps were chosen based on this plot).

Similarly, plots showing, as a function of the number of steps and or each sampler, distributions such as the chi-square or EMD for the 1-dimensional histograms shown before would be a great way to compare the samplers.

P12: “First, much faster convergences have been seen from all new introduced samplers” in the context of this paper, all samplers are new. Please be more specific about the samplers referred to.

Fig. 8: How is separation power defined?

Fig. 9: Again, a ratio plot would be beneficial to aid the discussions on the differences observed between samplers. How many steps is high EMD steps?

P12: “This is crucial for us to perform accurate energy calibration from low-level fast calorimeter simulation later.” I’m missing how the previous discussion reaches this conclusion.

Table 1: What bold entries mean? The best results? In the AUC column, there are lower AUC and FPD values than the ones shown in bold. Uncertainties from multiple runs should also be shown for each metric to identify when differences are actually significant.

P14: “We choose Karras and Lu schedulers to illustrate the impacts of different noise schedulers
on the same samplers.” Why this choice of samplers? Where is this illustrated? The following discussion is very hard to follow without any visual aid.

P16: The jetnet results are incredibly short compared to the calorimeter results. How the sampling quality changes in this case versus the number of steps used? How the values you obtain compare with the many public results on the jetnet dataset?

“It may be because methods are more applicable to UNet and pixelated data than point clouds network.” Why would it be the case? Which studies were performed to reach this conclusion?


Ask for major revision

  • validity: ok
  • significance: ok
  • originality: low
  • clarity: poor
  • formatting: reasonable
  • grammar: mediocre

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