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PC-JeDi: Diffusion for Particle Cloud Generation in High Energy Physics

Matthew Leigh, Debajyoti Sengupta, Guillaume Quétant, John Andrew Raine, Knut Zoch, Tobias Golling

TL;DR

This method uses score-based diffusion models in conjunction with transformers which are well suited to the task of generating jets as particle clouds due to their permutation equivariance to achieve competitive performance with current state-of-the-art methods.

Abstract

In this paper, we present a new method to efficiently generate jets in High Energy Physics called PC-JeDi. This method utilises score-based diffusion models in conjunction with transformers which are well suited to the task of generating jets as particle clouds due to their permutation equivariance. PC-JeDi achieves competitive performance with current state-of-the-art methods across several metrics that evaluate the quality of the generated jets. Although slower than other models, due to the large number of forward passes required by diffusion models, it is still substantially faster than traditional detailed simulation. Furthermore, PC-JeDi uses conditional generation to produce jets with a desired mass and transverse momentum for two different particles, top quarks and gluons.

PC-JeDi: Diffusion for Particle Cloud Generation in High Energy Physics

TL;DR

This method uses score-based diffusion models in conjunction with transformers which are well suited to the task of generating jets as particle clouds due to their permutation equivariance to achieve competitive performance with current state-of-the-art methods.

Abstract

In this paper, we present a new method to efficiently generate jets in High Energy Physics called PC-JeDi. This method utilises score-based diffusion models in conjunction with transformers which are well suited to the task of generating jets as particle clouds due to their permutation equivariance. PC-JeDi achieves competitive performance with current state-of-the-art methods across several metrics that evaluate the quality of the generated jets. Although slower than other models, due to the large number of forward passes required by diffusion models, it is still substantially faster than traditional detailed simulation. Furthermore, PC-JeDi uses conditional generation to produce jets with a desired mass and transverse momentum for two different particles, top quarks and gluons.
Paper Structure (14 sections, 9 equations, 16 figures, 3 tables)

This paper contains 14 sections, 9 equations, 16 figures, 3 tables.

Table of Contents

  1. Related work
  2. Generative diffusion models
  3. Modelling the score function
  4. Generating jets with diffusion
  5. Jet substructure
  6. Datasets
  7. PC-JeDi architecture and training
  8. Evaluation metrics
  9. Results
  10. Inclusive generation of jets
  11. Uncontained top jets
  12. Conditional generation
  13. Timing comparison
  14. Conclusion

Figures (16)

  • Figure 1: Diagram of the PC-JeDi training procedure. Data and noise are mixed together according to the signal and noise schedulers. Then the conditioned model is optimised via a distance loss between the noise it predicts and the original noise.
  • Figure 2: Diagram of the PC-JeDi generation procedure. Random noise is sampled at the beginning of the loop from a standard normal distribution. Then any chosen integration sampler is iteratively applied in order to fully denoise the input towards actual data, using the conditional model as a noise predictor.
  • Figure 3: The relative transverse momentum (left) and invariant mass (right) of gluon jets generated with MPGAN (orange) and PC-JeDi (DDIM solver, green; EM solver, red) compared to the MC simulation (shaded blue). Calculated from the leading 30 $p_{\mathrm{T}}$ constituents using the constituent $p_\mathrm{T}^\mathrm{rel}$ instead of $p_\mathrm{T}$.
  • Figure 4: The relative transverse momentum (left) and invariant mass (right) of top jets generated with MPGAN (orange) and PC-JeDi (DDIM solver, green; EM solver, red) compared to the MC simulation (shaded blue). Calculated from the leading 30 $p_{\mathrm{T}}$ constituents using the constituent $p_\mathrm{T}^\mathrm{rel}$ instead of $p_\mathrm{T}$.
  • Figure 5: Distributions of the leading (left), subleading (middle) and third leading (right) constituent $p_{\mathrm{T}}\xspace^\text{rel}$ for the gluon jets generated with MPGAN (orange) and PC-JeDi (DDIM solver, green; EM solver, red) compared to the MC simulation.
  • ...and 11 more figures