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AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learning

by Vikas Kanaujia, Mathias S. Scheurer, Vipul Arora

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Vipul Arora
Submission information
Preprint Link:  (pdf)
Date accepted: 2024-05-07
Date submitted: 2024-04-12 10:18
Submitted by: Arora, Vipul
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Experiment
  • Condensed Matter Physics - Computational
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


Deep generative models complement Markov-chain-Monte-Carlo methods for efficiently sampling from high-dimensional distributions. Among these methods, explicit generators, such as Normalising Flows (NFs), in combination with the Metropolis Hastings algorithm have been extensively applied to get unbiased samples from target distributions. We systematically study central problems in conditional NFs, such as high variance, mode collapse and data efficiency. We propose adversarial training for NFs to ameliorate these problems. Experiments are conducted with low-dimensional synthetic datasets and XY spin models in two spatial dimensions.

Author comments upon resubmission

We have incorporated and made changes in the script as per the referee comments . We have also mentioned the places where we have made changes in the reply to the referee's comment. Please refer the link below.

List of changes

1. In Section Introduction, page no. 4, paragraph 2, line no. 20, we have added the advantages of our method as well as reply to the first point raised in Report 2 by the referee.

2. In Appendix C, under Hyperparameter Details, we have addressed the third point raised in Report 2 .

3. Figs. 5 & 6 have been updated along with captions as referred to in points 5, 6, and 7 raised in Report 2.

4.Typo above Eq. 7 has been amended as raised in point 10 in Report 2.

5. We have added the results for 32x32 lattice size trained on 10 temperature settings in the revised manuscript in Table 8 and Fig.7 .

6. In Conclusion, Paragraph 4, Page no. 18, line no 12, we have discussed the second point raised in Report 1.

7. In Conclusion, last paragraph, Page-19, we have included the future work addressing scaling up to large lattices with factorizable model.

Published as SciPost Phys. 16, 132 (2024)

Reports on this Submission

Anonymous Report 2 on 2024-4-29 (Invited Report)


The revision has answered all the questions raised by the reviewer and met the standard of the publication for Scipost.


Publish (surpasses expectations and criteria for this Journal; among top 10%)

  • validity: top
  • significance: top
  • originality: top
  • clarity: top
  • formatting: perfect
  • grammar: perfect

Anonymous Report 1 on 2024-4-19 (Invited Report)


The authors have addressed all comments adequately. I deem the manuscript suitable for publication.


Publish (meets expectations and criteria for this Journal)

  • validity: good
  • significance: good
  • originality: good
  • clarity: high
  • formatting: excellent
  • grammar: good

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