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REVIEW 3 major objections 5 minor 2 cited by

Wavelet Flow For Extragalactic Foreground Simulations

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A Wavelet Flow jointly trained on lensing convergence and cosmic infrared background maps generates new samples whose power spectra match the simulation within a few percent, with Minkowski functionals matching to 2.5%.

desk verdict A useful proof of concept for joint κ–CIB generation with flows, but the validation split likely leaks spatial information and the finest-scale prior makes small-scale power agreement partly by construction. read the letter →

arxiv 2505.21220 v2 pith:I2MVP2E4 submitted 2025-05-27 astro-ph.CO cs.LG

M. Mebratu , W. L. K. Wu This is my paper
classification astro-ph.COcs.LG
keywords cosmicmicrowavebackgroundCMBlensingconvergenceinfrarednormalizingflowswaveletflowfield-levelsimulationMinkowskifunctionalsforeground
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks whether one generative model can reproduce the joint, field-level statistics of two correlated extragalactic CMB signals: the lensing convergence field $\kappa$ and the cosmic infrared background (CIB). It claims yes: a Wavelet Flow trained on cutouts from the Agora simulation generates new $\kappa$ and CIB maps whose average auto- and cross-power spectra match held-out validation maps to within about 2\u20132.5% at every scale, and whose Minkowski functionals match to within 2.5%. This matters because current and upcoming CMB experiments need many realistic realizations of non-Gaussian foregrounds for simulation-based inference, covariance estimation, and pipeline testing, and no analytic form for these joint distributions exists.

What carries the argument

The carrying mechanism is the Wavelet Flow: a Haar discrete wavelet transform decomposes each $256\times256$ map into seven resolution levels, and a separate Glow-style normalizing flow models the conditional distribution of the detail coefficients at each level using affine coupling layers. Sampling starts from the coarsest $2\times2$ block and rebuilds the image through inverse wavelet transforms, so large-scale correlations and small-scale features are handled at separate resolutions. The hybrid component-correlated prior assigns a white-noise prior at coarse scales and, at the finest scale only, a prior whose covariance is the measured auto- and cross-power spectra of the wavelet coefficients; this is what lets the model capture small-scale non-Gaussianity while avoiding the near-100% large-scale failures seen when correlated priors are used everywhere.

What would settle it

Evaluate the trained flow on an independent $\kappa$-CIB dataset\u2014for example, maps from a different simulation pipeline or reconstructed lensing convergence and Planck CIB data\u2014and compute the same auto-spectra, cross-spectrum, and Minkowski functionals; if the bias against this external dataset exceeds a few percent, the claimed field-level accuracy does not generalize beyond the training simulation.

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Extended reading notes

Core claim

The central claim is that a Wavelet Flow, jointly trained on $\kappa$ and CIB maps, statistically recovers the input fields themselves: generated samples reproduce the mean power spectra of the Agora validation maps to within a few percent across all scales, including the $\kappa$-CIB cross-spectrum, and their Minkowski functionals are accurate at the 2.5% level, demonstrating that the model has learned non-Gaussian structure beyond two-point statistics. The paper presents this as the first flow-based model for correlated multi-component CMB secondaries at field level. A hybrid prior\u2014white noise at coarse wavelet scales and a component-correlated prior, built from the measured per-scale auto- and cross-spectra, at the finest scale\u2014improves small-scale power recovery by up to 3 percentage points and reduces the maximum Minkowski-functional bias from roughly 10% to 2.5%.

Load-bearing premise

The few-percent accuracy is measured on held-out cutouts from the same Agora simulation used for training, so the central claim assumes that this simulation's $\kappa$-CIB statistics are close enough to the real sky that in-distribution fidelity transfers to actual CMB analyses.

Editorial extensions

If this is right

  • Generated $\kappa$-CIB pairs can serve as the foreground-simulation step in simulation-based inference, producing foreground-added lensed CMB maps for realistic mock skies.
  • The learned joint distribution can act as a prior in posterior-based delensing and foreground-cleaning pipelines, where no current method includes a non-Gaussian foreground model.
  • At few-percent power-spectrum accuracy, the model contributes a small fraction of the roughly 10%-per-bin lensing measurement uncertainty and can differentiate foreground biases to lensing spectra of order 5\u201310%.
  • The scale-dependent prior recipe\u2014independent optimization of each wavelet level\u2014extends to additional foreground components such as tSZ, kSZ, and radio sources, which the paper identifies as the next step.
  • Because the flow gives tractable log-likelihoods, the same trained model is usable for density estimation and inference, not only for generating samples.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the few-percent accuracy transfers to real sky data\u2014an untested step, since the model is trained at fixed cosmological and astrophysical parameters\u2014field-level simulation-based inference for CMB analyses becomes practical without expensive hydrodynamical simulations.
  • The finding that correlated priors hurt at coarse scales but help at the finest scale suggests a general recipe for other non-Gaussian cosmological fields: use physically motivated priors only where the flow struggles, which could be tested directly on tSZ or 21-cm maps.
  • A practical bottleneck is map size: the current $2^\circ\times2^\circ$ cutouts fall far short of the thousands of square degrees covered by current experiments, so tiling or outpainting would be needed for full-sky applications.
  • Because the paper validates only sample statistics, the flow's exact log-likelihood remains untested on real $\kappa$-CIB patches; scoring held-out sky patches by log-likelihood would be a sharper test than summary-statistic agreement.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper trains a Wavelet Flow (Glow-based normalizing flows applied to Haar wavelet coefficients) to jointly model 256×256, 0.5-arcmin cutouts of CMB lensing convergence κ and cosmic infrared background (CIB) maps drawn from the Agora simulations. A key methodological contribution is a 'Hybrid Component Correlated' (HCC) prior: white-noise priors at coarse wavelet scales and a component-correlated Gaussian prior, built from training-set auto- and cross-power spectra, at the finest wavelet scale. The authors report that generated samples reproduce validation power spectra to within a few percent across scales and Minkowski functionals to within 1--2.5%, and they argue this is the first flow-based model for correlated multi-component CMB secondaries at field level. The paper also releases code and trained models.

Significance. If the reported accuracy is robust, the paper demonstrates a useful and practical capability: fast, field-level generation of correlated κ and CIB maps for simulation-based inference, covariance estimation, and mock-sky pipelines. The scale-dependent prior design is an interesting extension of Wavelet Flow and is presented with concrete comparisons (Figures 5--7). The release of code and trained models is a strength that will facilitate reproducibility and follow-up work. The central limitation is that validation is performed on cutouts from the same simulation used for training, so the in-distribution fidelity claims need to be scrutinized before they can support the paper's conclusions.

major comments (3)
  1. [§5, Figure 4] The validation protocol does not establish that validation cutouts are spatially disjoint from training cutouts. The paper states (Section 4.1) that 52,000 training and 13,000 validation 256×256 cutouts are projected from the full-sky Agora maps, but it never states that the validation patch centers are chosen to avoid the training patch centers. A 256-pixel cutout at 0.5 arcmin corresponds to about 2.13° on a side, so 65,000 cutouts cover roughly seven times the full sky. If centers were drawn randomly, almost every validation patch overlaps one or more training patches, and the reported few-percent power-spectrum and Minkowski-functionals agreement in Figures 3 and 4 could be substantially inflated by this leakage. This is load-bearing because the abstract and Section 5 claim statistical recovery of held-out inputs. The authors should specify the sampling scheme for training and validation patches, demonstrate that validation patches are spatially separated from all training patches, or re-run the validation on an independent Agora realization (or otherwise non-overlapping sky regions).
  2. [§3.4 and §5] The Minkowski functional comparisons are presented without any error bars or uncertainty intervals. The text states that model outputs remain 'within 1% for all κ functionals' and 'within 2.5% for all CIB functionals,' but with no statistical uncertainty on either the validation estimates or the model-sample estimates, these numbers cannot be assessed for significance. The paper should add error bars (e.g., standard errors over the 13,000 validation and generated samples) or a quantitative compatibility measure such as a χ² statistic, and should state the number of thresholds/bins used and how the percentile range was chosen.
  3. [§3.4, §5] The finest-scale CC prior is constructed directly from the training-set power and cross-spectra (Eqs. 3.10--3.14), and the text notes that this makes the wavelet coefficients 'exhibit the same power spectrum as the prior or latent distribution.' Consequently, the agreement of the generated small-scale power spectra with the validation data is partly enforced by construction rather than learned by the flow. This does not invalidate the method, but it means the power-spectrum comparisons at the finest scale are not an independent test of the learned model. The paper should state this explicitly and quantify what the flow adds at that scale, for example by comparing against samples drawn directly from the CC prior and by quoting the all-WN-prior results from Figure 6 in the main text.
minor comments (5)
  1. [§3.3 heading] The heading 'W avelet Flow' contains an unintended space; it should read 'Wavelet Flow.'
  2. [§4.1 heading] The heading 'T raining Data and preprocessing' contains a stray capital 'T'; it should read 'Training Data and Preprocessing.'
  3. [Appendix A] There are typos in the prior-selection appendix: 'combintations' should be 'combinations' and 'leve1' should be 'level 1' in the Figure 5 caption and surrounding text.
  4. [§5] The statement that 'the κ power spectrum bias remains within 1% for most multipoles' should specify the multipole range and the binning used in Figure 3, and the text should clarify whether the quoted percentages refer to the mean fractional difference or the maximum across bins.
  5. [§4.1] The description of the κ map preprocessing says Gaussian noise is added 'after the Nyquist frequency'; since a map has no power beyond Nyquist, this should be clarified as adding noise to the highest-frequency wavelet coefficients or to the map before the DWT, and the exact amplitude of the added noise should be stated.

Circularity Check

1 steps flagged · score 6.0 of 10

Fine-scale two-point statistics are preloaded by the CC prior, making part of the claimed power-spectrum recovery circular; coarse scales and non-Gaussian statistics remain genuinely learned.

  1. fitted input called prediction [Section 3.4 (Eqs. 3.10-3.14) with Section 5 and Appendix A]
    "The entries in the covariance matrices in Eqs. 3.12 and 3.14 are computed by applying a DWT decomposition to the training data up to the appropriate wavelet level (corresponding to the level being trained) and calculating the average power spectrum or cross-spectrum of the wavelet coefficients across the entire dataset. This approach ensures that when using the CC prior, the wavelet coefficients (green boxes in Figure 1) exhibit the same power spectrum as the prior or latent distribution (blue boxes in Figure 1)."

    The fiducial HCC prior applies the CC prior to the highest-frequency wavelet level, and the CC covariance is built directly from the average auto- and cross-power spectra of the training-set wavelet coefficients. The validation cutouts come from the same Agora simulation, so the fine-scale kappa and CIB power spectra and the kappa-CIB cross-spectrum that Section 5 reports as 'recovered within a few percent' are the same quantities inserted into the prior. The small-scale two-point agreement is therefore an expected consequence of the prior construction, not an independent prediction of the learned flow; the claim 'across all scales' inherits this by-construction component at the finest scale.

full rationale

The paper's derivation is otherwise self-contained: the Wavelet Flow architecture is imported from external references [36, 37], no uniqueness theorem is invoked, and the only self-citation (Ref. [56]) supports an external uncertainty statement rather than the central result. The coarse wavelet scales use WN priors and are genuinely learned, and the Minkowski-functional agreement is a non-Gaussian statistic that a Gaussian CC prior does not encode, so that part of the validation is not circular. The circular element is confined to the highest-frequency level: its CC prior is defined from the very power/cross-spectra that are then reported as predicted. The paper is transparent about this construction, but it still means the 'few percent across all scales' power-spectrum claim is partially by construction. The separate concern that validation cutouts may overlap training cutouts is a data-split validity threat, not a circularity of the derivation chain, and is therefore not scored here.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The model is almost entirely fitted to the Agora training set. The only substantive new construction is the scale-dependent hybrid prior, but its finest-scale component is built from the target power spectra, which reduces the independence of the two-point validation. The paper's scientific value depends on the unverified transfer of Agora-based statistics to the real sky.

free parameters (4)
  • CC prior covariance matrices Sigma(ell) at finest wavelet scale = not tabulated; computed from training data power and cross-spectra
    Used in the HCC prior for level 8; encodes the target two-point statistics directly, so small-scale power-spectrum recovery is partly by construction.
  • Input standardization mean and standard deviation per component = computed over training set
    Applied to kappa and transformed CIB; these data-derived values are not reported numerically.
  • Amplitude of Gaussian noise added to kappa beyond Nyquist frequency = not specified in text
    Ad hoc addition to improve high-frequency training convergence; the paper claims it does not affect analysis scales.
  • Flow network weights (Glow blocks per scale) = trained by maximum likelihood; not enumerated
    The core fitted parameters of the generative model.
assumptions (5)
  • standard math The change-of-variables formula and unit Jacobian for orthonormal Haar wavelets hold.
    Used in Sections 3.1 to 3.3 to write the target density as a product over wavelet scales.
  • domain assumption Agora simulations provide a sufficiently accurate model of real kappa and CIB fields.
    The entire training and validation set comes from Agora; Section 2 argues the fields trace the same large-scale structure.
  • domain assumption Held-out cutouts from the same simulation are a valid test of the generative model's ability to support CMB analyses.
    No independent simulation or real-data validation is performed.
  • ad hoc to paper Adding Gaussian noise to kappa beyond the Nyquist frequency does not affect scientifically relevant scales.
    Stated in Section 4.1; no quantitative test is shown.
  • domain assumption Two-degree cutouts and a 7-level Haar decomposition capture the field statistics relevant for current experiments.
    The paper acknowledges map size limits and proposes tiling or outpainting as future work.

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Cite this review

Pith. "Pith review of Wavelet Flow For Extragalactic Foreground Simulations." pith.science (2026). https://pith.science/paper/I2MVP2E4

@misc{pith2026250521220,
  author       = {Pith},
  title        = {Pith review of: Wavelet Flow For Extragalactic Foreground Simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I2MVP2E4}},
  note         = {Machine review of arXiv:2505.21220}
}
abstract

Extragalactic foregrounds in cosmic microwave background (CMB) observations are both a source of cosmological and astrophysical information and a nuisance to the CMB. Effective field-level modeling that captures their non-Gaussian statistical distributions is increasingly important for optimal information extraction, particularly given the precise and low-noise observations from current and upcoming experiments. We explore the use of Wavelet Flow (WF) models to tackle the novel task of modeling the field-level probability distributions of multi-component CMB secondaries and foreground. Specifically, we jointly train correlated CMB lensing convergence ($\kappa$) and cosmic infrared background (CIB) maps with a WF model and obtain a network that statistically recovers the input to high accuracy -- the trained network generates samples of $\kappa$ and CIB fields whose average power spectra are within a few percent of the inputs across all scales, and whose Minkowski functionals are similarly accurate compared to the inputs. Leveraging the multiscale architecture of these models, we fine-tune both the model parameters and the priors at each scale independently, optimizing performance across different resolutions. These results demonstrate that WF models can accurately simulate correlated components of CMB secondaries, supporting improved analysis of cosmological data. Our code and trained models can be found here (https://github.com/matiwosm/HybridPriorWavletFlow.git).

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Forward citations

Cited by 2 Pith papers

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

  1. Cosmo3DFlow: Wavelet Flow Matching for Spatial-to-Spectral Compression in Reconstructing the Early Universe

    astro-ph.IM 2026-02 conditional novelty 6.0 of 10

    Wavelet-space flow matching reconstructs cosmological initial conditions from z=0 density fields roughly 50x faster than score-based diffusion with comparable or better fidelity.

  2. Learning Correlated Astrophysical Foregrounds with Denoising Diffusion Probabilistic Models

    astro-ph.CO 2025-06 conditional novelty 6.0 of 10

    A denoising diffusion model trained on Agora simulations generates correlated CIB and tSZ foreground patches that reproduce 2-, 3-, and 4-point statistics, histograms, and Minkowski functionals.

Reference graph

Works this paper leans on

88 extracted references · 31 canonical work pages · cited by 2 Pith papers

  1. [1]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, M. Ashdown et al.,Planck 2013 results. XVI. Cosmological parameters,A&A571(2014) A16 [1303.5076]

    arXiv 2014

  2. [2]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont et al., Planck 2015 results. XIII. Cosmological parameters,A&A594(2016) A13 [1502.01589]

    arXiv 2016

  3. [3]

    Aghanim, Y

    Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi et al., Planck 2018 results. VI. Cosmological parameters,A&A641(2020) A6 [1807.06209]

    arXiv 2020

  4. [4]

    Lewis and A

    A. Lewis and A. Challinor,Weak gravitational lensing of the CMB,Phys. Rep.429(2006) 1 [astro-ph/0601594]

    arXiv 2006

  5. [5]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, M. Ashdown et al.,Planck 2013 results. XVII. Gravitational lensing by large-scale structure,A&A571 (2014) A17 [1303.5077]

    arXiv 2014

  6. [6]

    Aghanim, Y

    Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi et al., Planck 2018 results. VIII. Gravitational lensing,A&A641(2020) A8 [1807.06210]

    arXiv 2020

  7. [7]

    Bocquet, J.P

    S. Bocquet, J.P. Dietrich, T. Schrabback, L.E. Bleem, M. Klein, S.W. Allen et al.,Cluster Cosmology Constraints from the 2500 deg 2 SPT-SZ Survey: Inclusion of Weak Gravitational Lensing Data from Magellan and the Hubble Space Telescope,ApJ878(2019) 55 [1812.01679]

    arXiv 2019

  8. [8]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont et al., Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts,A&A594 (2016) A24 [1502.01597]

    arXiv 2016

Show all 88 references
  1. [9]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, M. Ashdown et al.,Planck 2013 results. XXX. Cosmic infrared background measurements and implications for star formation,A&A571(2014) A30 [1309.0382]

    2014 arXiv

  2. [10]

    Osborne, D

    S.J. Osborne, D. Hanson and O. Dor´ e,Extragalactic foreground contamination in temperature-based CMB lens reconstruction,JCAP2014(2014) 024 [1310.7547]. – 16 –

    2014 arXiv

  3. [11]

    van Engelen, S

    A. van Engelen, S. Bhattacharya, N. Sehgal, G.P. Holder, O. Zahn and D. Nagai,CMB Lensing Power Spectrum Biases from Galaxies and Clusters Using High-angular Resolution Temperature Maps,ApJ786(2014) 13 [1310.7023]

    2014 arXiv

  4. [12]

    Shirasaki,Impact of radio sources and cosmic infrared background on thermal Sunyaev-Zel’dovich - gravitational lensing cross-correlation,MNRAS483(2019) 342 [1807.09412]

    M. Shirasaki,Impact of radio sources and cosmic infrared background on thermal Sunyaev-Zel’dovich - gravitational lensing cross-correlation,MNRAS483(2019) 342 [1807.09412]

    2019 arXiv

  5. [13]

    Sunyaev and Y.B

    R.A. Sunyaev and Y.B. Zeldovich,The Observations of Relic Radiation as a Test of the Nature of X-Ray Radiation from the Clusters of Galaxies,Comments on Astrophysics and Space Physics4(1972) 173

    1972

  6. [14]

    Puget, A

    J.L. Puget, A. Abergel, J.P. Bernard, F. Boulanger, W.B. Burton, F.X. Desert et al.,Tentative detection of a cosmic far-infrared background with COBE.,A&A308(1996) L5

    1996

  7. [15]

    Hauser and E

    M.G. Hauser and E. Dwek,The cosmic infrared background: measurements and implications, Ann. Rev. Astron. Astrophys.39(2001) 249 [astro-ph/0105539]

    2001 arXiv

  8. [16]

    de Zotti, M

    G. de Zotti, M. Massardi, M. Negrello and J. Wall,Radio and millimeter continuum surveys and their astrophysical implications,A&ARv18(2010) 1 [0908.1896]

    2010 arXiv

  9. [17]

    Madhavacheril, F.J

    M.S. Madhavacheril, F.J. Qu, B.D. Sherwin, N. MacCrann, Y. Li, I. Abril-Cabezas et al.,The Atacama Cosmology Telescope: DR6 Gravitational Lensing Map and Cosmological Parameters, ApJ962(2024) 113 [2304.05203]

    2024 arXiv

  10. [18]

    Planck Collaboration, Ade, P. A. R., Aghanim, N., Armitage-Caplan, C., Arnaud, M., Ashdown, M. et al.,Planck 2013 results. xviii. the gravitational lensing-infrared background correlation,A&A571(2014) A18

    2014

  11. [19]

    Hill and E

    J.C. Hill and E. Pajer,Cosmology from the thermal Sunyaev-Zel’dovich power spectrum: Primordial non-Gaussianity and massive neutrinos,Phys. Rev. D88(2013) 063526 [1303.4726]

    2013 arXiv

  12. [20]

    Vavagiakis, P.A

    E.M. Vavagiakis, P.A. Gallardo, V. Calafut, S. Amodeo, S. Aiola, J.E. Austermann et al.,The Atacama Cosmology Telescope: Probing the baryon content of SDSS DR15 galaxies with the thermal and kinematic Sunyaev-Zel’dovich effects,Phys. Rev. D104(2021) 043503 [2101.08373]

    2021 arXiv

  13. [21]

    S´ anchez, Y

    J. S´ anchez, Y. Omori, C. Chang, L.E. Bleem, T. Crawford, A. Drlica-Wagner et al.,Mapping gas around massive galaxies: cross-correlation of DES Y3 galaxies and Compton-y maps from SPT and Planck,MNRAS522(2023) 3163 [2210.08633]

    2023 arXiv

  14. [22]

    Stein, M.A

    G. Stein, M.A. Alvarez, J.R. Bond, A. van Engelen and N. Battaglia,The Websky extragalactic CMB simulations,JCAP2020(2020) 012 [2001.08787]

    2020 arXiv

  15. [23]

    Omori,AGORA: Multicomponent simulation for cross-survey science,MNRAS530(2024) 5030 [2212.07420]

    Y. Omori,AGORA: Multicomponent simulation for cross-survey science,MNRAS530(2024) 5030 [2212.07420]

    2024 arXiv

  16. [24]

    Bayer, Y

    A.E. Bayer, Y. Zhong, Z. Li, J. DeRose, Y. Feng and J. Liu,The HalfDome Multi-Survey Cosmological Simulations: N-body Simulations,arXiv e-prints(2024) arXiv:2407.17462 [2407.17462]

    2024 arXiv

  17. [25]

    Dai and U

    B. Dai and U. Seljak,Learning effective physical laws for generating cosmological hydrodynamics with Lagrangian deep learning,Proceedings of the National Academy of Science 118(2021) e2020324118 [2010.02926]

    2021 arXiv

  18. [26]

    L. Dinh, D. Krueger and Y. Bengio,Nice: Non-linear independent components estimation, arXiv: Learning(2014)

    2014

  19. [27]

    Papamakarios, E

    G. Papamakarios, E. Nalisnick, D. Jimenez Rezende, S. Mohamed and B. Lakshminarayanan, Normalizing Flows for Probabilistic Modeling and Inference,arXiv e-prints(2019) arXiv:1912.02762 [1912.02762]. – 17 –

    2019 arXiv

  20. [28]

    Dinh, J.N

    L. Dinh, J.N. Sohl-Dickstein and S. Bengio,Density estimation using real nvp,ArXiv abs/1605.08803(2016)

    2016 arXiv

  21. [29]

    Rezende and S

    D.J. Rezende and S. Mohamed,Variational inference with normalizing flows,ArXiv abs/1505.05770(2015)

    2015 arXiv

  22. [30]

    Kingma and P

    D.P. Kingma and P. Dhariwal,Glow: Generative flow with invertible 1x1 convolutions,ArXiv abs/1807.03039(2018)

    2018 arXiv

  23. [31]

    Rouhiainen, U

    A. Rouhiainen, U. Giri and M. Munchmeyer,Normalizing flows for random fields in cosmology, 2021, https://api.semanticscholar.org/CorpusID:235186898

    2021

  24. [32]

    Dai and U

    B. Dai and U. Seljak,Translation and rotation equivariant normalizing flow (TRENF) for optimal cosmological analysis,MNRAS516(2022) 2363 [2202.05282]

    2022 arXiv

  25. [33]

    Lovell, S

    C. Lovell, S. Hassan, D. Angl´ es-Alc´ azar, G. Bryan, G. Fabbian, S. Genel et al.,A hierarchy of normalizing flows for modelling the galaxy-halo relationship, June, 2023, DOI

    2023

  26. [34]

    Hassan, F

    S. Hassan, F. Villaescusa-Navarro, B.D. Wandelt, D.N. Spergel, D. Angl’es-Alc’azar, S. Genel et al.,Hiflow: Generating diverse hi maps and inferring cosmology while marginalizing over astrophysics using normalizing flows,The Astrophysical Journal937(2021)

    2021

  27. [35]

    Stachurski, C

    F. Stachurski, C. Messenger and M.A. Hendry,Cosmological inference using gravitational waves and normalizing flows,Physical Review D(2023)

    2023

  28. [36]

    J.J. Yu, K.G. Derpanis and M.A. Brubaker,Wavelet Flow: Fast Training of High Resolution Normalizing Flows,arXiv e-prints(2020) arXiv:2010.13821 [2010.13821]

    2020 arXiv

  29. [37]

    Dai and U

    B. Dai and U. Seljak,Multiscale Flow for robust and optimal cosmological analysis,Proceedings of the National Academy of Science121(2024) e2309624121

    2024

  30. [38]

    D. Han, N. Sehgal and F. Villaescusa-Navarro,Deep learning simulations of the microwave sky, Phys. Rev. D104(2021) 123521 [2105.11444]

    2021 arXiv

  31. [39]

    Stimper, B

    V. Stimper, B. Scholkopf and J.M. Hern´ andez-Lobato,Resampling base distributions of normalizing flows,ArXivabs/2110.15828(2021)

    2021 arXiv

  32. [40]

    Crenshaw, J

    J.F. Crenshaw, J. Kalmbach, A. Gagliano, Z. Yan, A.J. Connolly, A.I. Malz et al.,Probabilistic forward modeling of galaxy catalogs with normalizing flows,The Astronomical Journal(2024)

    2024

  33. [41]

    Papamakarios, I

    G. Papamakarios, I. Murray and T. Pavlakou,Masked autoregressive flow for density estimation,ArXivabs/1705.07057(2017)

    2017 arXiv

  34. [42]

    F. Ge, M. Millea, E. Camphuis, C. Daley, N. Huang, Y. Omori et al.,Cosmology from CMB lensing and delensed E power spectra using 2019-2020 SPT-3G polarization data,Phys. Rev. D 111(2025) 083534 [2411.06000]

    2025 arXiv

  35. [43]

    Huterer,Growth of cosmic structure,The Astronomy and Astrophysics Review31(2023)

    D. Huterer,Growth of cosmic structure,The Astronomy and Astrophysics Review31(2023)

    2023

  36. [44]

    Horowitz and U

    B. Horowitz and U. Seljak,Cosmological constraints from thermal Sunyaev-Zeldovich power spectrum revisited,MNRAS469(2017) 394 [1609.01850]

    2017 arXiv

  37. [45]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont et al., Planck 2015 results. XXI. The integrated Sachs-Wolfe effect,A&A594(2016) A21 [1502.01595]

    2016 arXiv

  38. [46]

    Everett, L

    W.B. Everett, L. Zhang, T.M. Crawford, J.D. Vieira, M. Aravena, M.A. Archipley et al., Millimeter-wave Point Sources from the 2500 Square Degree SPT-SZ Survey: Catalog and Population Statistics,ApJ900(2020) 55 [2003.03431]

    2020 arXiv

  39. [47]

    Datta, S

    R. Datta, S. Aiola, S.K. Choi, M. Devlin, J. Dunkley, R. D¨ unner et al.,The Atacama Cosmology Telescope: two-season ACTPol extragalactic point sources and their polarization properties,MNRAS486(2019) 5239 [1811.01854]. – 18 –

    2019 arXiv

  40. [48]

    Hu and T

    W. Hu and T. Okamoto,Mass reconstruction with cmb polarization,Astrophys. J.574(2002) 566 [astro-ph/0111606]

    2002 arXiv

  41. [49]

    Das and P

    S. Das and P. Bode,A Large Sky Simulation of the Gravitational Lensing of the Cosmic Microwave Background,ApJ682(2008) 1 [0711.3793]

    2008 arXiv

  42. [50]

    Bartelmann and P

    M. Bartelmann and P. Schneider,Weak gravitational lensing,Phys. Rept.340(2001) 291 [astro-ph/9912508]

    2001 arXiv

  43. [51]

    Fl¨ oss, W.R

    T. Fl¨ oss, W.R. Coulton, A.J. Duivenvoorden, F. Villaescusa-Navarro and B.D. Wandelt, Denoising diffusion delensing: reconstructing the non-Gaussian CMB lensing potential with diffusion models,MNRAS533(2024) 423 [2405.05598]

    2024 arXiv

  44. [52]

    Casey, D

    C.M. Casey, D. Narayanan and A. Cooray,Dusty star-forming galaxies at high redshift,Physics Reports541(2014) 45

    2014

  45. [53]

    Maniyar, M

    A. Maniyar, M. B´ ethermin and G. Lagache,Simple halo model formalism for the cosmic infrared background and its correlation with the thermal Sunyaev-Zel’dovich effect,A&A645 (2021) A40 [2006.16329]

    2021 arXiv

  46. [54]

    Lagache, J.-L

    G. Lagache, J.-L. Puget and H. Dole,Dusty infrared galaxies: Sources of the cosmic infrared background,Ann. Rev. Astron. Astrophys.43(2005) 727 [astro-ph/0507298]

    2005 arXiv

  47. [55]

    Y.-S. Song, A. Cooray, L. Knox and M. Zaldarriaga,The far-infrared background correlation with cosmic microwave background lensing,The Astrophysical Journal590(2003) 664

    2003

  48. [56]

    Z. Pan, F. Bianchini, W.L.K. Wu, P.A.R. Ade, Z. Ahmed, E. Anderes et al.,Measurement of gravitational lensing of the cosmic microwave background using SPT-3G 2018 data, Phys. Rev. D108(2023) 122005 [2308.11608]

    2023 arXiv

  49. [57]

    Ravenni, M

    A. Ravenni, M. Rizzato, S. Radinovi´ c, M. Liguori, F. Lacasa and E. Sellentin,Breaking degeneracies with the Sunyaev-Zeldovich full bispectrum,JCAP2021(2021) 026 [2008.12947]

    2021 arXiv

  50. [58]

    Crawford, K.K

    T.M. Crawford, K.K. Schaffer, S. Bhattacharya, K.A. Aird, B.A. Benson, L.E. Bleem et al.,A Measurement of the Secondary-CMB and Millimeter-wave-foreground Bispectrum using 800 deg2 of South Pole Telescope Data,ApJ784(2014) 143 [1303.3535]

    2014 arXiv

  51. [59]

    Lacasa, A

    F. Lacasa, A. P´ enin and N. Aghanim,Non-Gaussianity of the cosmic infrared background anisotropies - I. Diagrammatic formalism and application to the angular bispectrum,MNRAS 439(2014) 123 [1312.1251]

    2014 arXiv

  52. [60]

    Haar,Zur theorie der orthogonalen funktionensysteme

    A. Haar,Zur theorie der orthogonalen funktionensysteme. (erste mitteilung).,Mathematische Annalen69(1910) 331

    1910

  53. [61]

    Klypin, G

    A. Klypin, G. Yepes, S. Gottl¨ ober, F. Prada and S. Heß,MultiDark simulations: the story of dark matter halo concentrations and density profiles,MNRAS457(2016) 4340 [1411.4001]

    2016 arXiv

  54. [62]

    Behroozi, R.H

    P. Behroozi, R.H. Wechsler, A.P. Hearin and C. Conroy,Universemachine: The correlation between galaxy growth and dark matter halo assembly fromz= 0−10,Monthly Notices of the Royal Astronomical Society488(2019) 3143 [https://academic.oup.com/mnras/article-pdf/488/3/3143/2901613...

    2019

  55. [63]

    Valiuddin, C.G.A

    M.M.A. Valiuddin, C.G.A. Viviers, R. van Sloun, P.H.N. de With and F. van der Sommen, Efficient out-of-distribution detection of melanoma with wavelet-based normalizing flows,ArXiv abs/2208.04639(2022)

    2022 arXiv

  56. [64]

    F.J. Qu, F. Ge, W.L. Kimmy Wu, I. Abril-Cabezas, M.S. Madhavacheril, M. Millea et al., Unified and consistent structure growth measurements from joint ACT, SPT and{Planck} CMB lensing,arXiv e-prints(2025) arXiv:2504.20038 [2504.20038]

    2025

  57. [65]

    Prabhu, S

    K. Prabhu, S. Raghunathan, E.B. Anderes and L.E. Knox,Learning Correlated Astrophysical Foregrounds with Denoising Diffusion Probabilistic Models, . – 19 –

  58. [66]

    Fowler, V

    J.W. Fowler, V. Acquaviva, P.A.R. Ade, P. Aguirre, M. Amiri, J.W. Appel et al.,The Atacama Cosmology Telescope: A Measurement of the 600 ¡ ell ¡ 8000 Cosmic Microwave Background Power Spectrum at 148 GHz,ApJ722(2010) 1148 [1001.2934]

    2010 arXiv

  59. [67]

    Benson, P.A.R

    B.A. Benson, P.A.R. Ade, Z. Ahmed, S.W. Allen, K. Arnold, J.E. Austermann et al.,SPT-3G: a next-generation cosmic microwave background polarization experiment on the South Pole telescope, inMillimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy...

    2014 arXiv

  60. [68]

    Hensley, S.E

    B.S. Hensley, S.E. Clark, V. Fanfani, N. Krachmalnicoff, G. Fabbian, D. Poletti et al.,The Simons Observatory: Galactic Science Goals and Forecasts,ApJ929(2022) 166 [2111.02425]

    2022 arXiv

  61. [69]

    Abazajian, G

    K. Abazajian, G. Addison, P. Adshead, Z. Ahmed, S.W. Allen, D. Alonso et al.,CMB-S4 Science Case, Reference Design, and Project Plan,arXiv e-prints(2019) arXiv:1907.04473 [1907.04473]

    2019 arXiv

  62. [70]

    Rouhiainen and M

    A. Rouhiainen and M. M¨ unchmeyer,De-noising non-Gaussian fields in cosmology with normalizing flows, in36th Conference on Neural Information Processing Systems: Workshop on Machine Learning and the Physical Sciences, 11, 2022 [2211.15161]

    2022 arXiv

  63. [71]

    Rouhiainen, M

    A. Rouhiainen, M. M¨ unchmeyer, G. Shiu, M. Gira and K. Lee,Superresolution emulation of large cosmological fields with a 3D conditional diffusion model,Phys. Rev. D109(2024) 123536 [2311.05217]

    2024 arXiv

  64. [72]

    Durkan, A

    C. Durkan, A. Bekasov, I. Murray and G. Papamakarios,Neural Spline Flows,arXiv e-prints (2019) arXiv:1906.04032 [1906.04032]

    2019 arXiv

  65. [73]

    Millea, E

    M. Millea, E. Anderes and B.D. Wandelt,Sampling-based inference of the primordial CMB and gravitational lensing,Phys. Rev. D102(2020) 123542 [2002.00965]

    2020 arXiv

  66. [74]

    Doohan, M

    M. Doohan, M. Millea, S. Raghunathan, F. Ge, L. Knox, K. Prabhu et al.,Quantifying Bias due to non-Gaussian Foregrounds in an Optimal Reconstruction of CMB Lensing and Temperature Power Spectra,arXiv e-prints(2025) arXiv:2502.20801 [2502.20801]

    2025 arXiv

  67. [75]

    Chiang,Corrected SFD: A More Accurate Galactic Dust Map with Minimal Extragalactic Contamination,ApJ958(2023) 118 [2306.03926]

    Y.-K. Chiang,Corrected SFD: A More Accurate Galactic Dust Map with Minimal Extragalactic Contamination,ApJ958(2023) 118 [2306.03926]

    2023 arXiv

  68. [76]

    McCarthy,Large-scale galactic-dust-cleaned cosmic infrared background maps from{Planck} PR4 and HI4PI with{pyilc},arXiv e-prints(2024) arXiv:2405.13470 [2405.13470]

    F. McCarthy,Large-scale galactic-dust-cleaned cosmic infrared background maps from{Planck} PR4 and HI4PI with{pyilc},arXiv e-prints(2024) arXiv:2405.13470 [2405.13470]

    2024 arXiv

  69. [77]

    D. Lenz, O. Dor´ e and G. Lagache,Large-scale Maps of the Cosmic Infrared Background from Planck,ApJ883(2019) 75 [1905.00426]

    2019 arXiv

  70. [78]

    Hunter,Matplotlib: A 2d graphics environment,Computing in Science & Engineering9 (2007) 90

    J.D. Hunter,Matplotlib: A 2d graphics environment,Computing in Science & Engineering9 (2007) 90

    2007

  71. [79]

    Harris, K.J

    C.R. Harris, K.J. Millman, S.J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau et al., Array programming with NumPy,Nature585(2020) 357–362

    2020

  72. [80]

    McKinney et al.,Data structures for statistical computing in python, inProceedings of the 9th Python in Science Conference, vol

    W. McKinney et al.,Data structures for statistical computing in python, inProceedings of the 9th Python in Science Conference, vol. 445, pp. 51–56, Austin, TX, 2010

    2010

  73. [81]

    Boelens and H.A

    A.M. Boelens and H.A. Tchelepi,Quantimpy: Minkowski functionals and functions with python,SoftwareX16(2021) 100823

    2021

  74. [82]

    van der Walt, J.L

    S. van der Walt, J.L. Sch¨ onberger, J. Nunez-Iglesias, F. Boulogne, J.D. Warner, N. Yager et al.,scikit-image: image processing in Python,PeerJ2(2014) e453

    2014

  75. [83]

    Virtanen, R

    P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau et al., SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python,Nature Methods17 (2020) 261. – 20 –

    2020

  76. [84]

    Waskom,seaborn: statistical data visualization,Journal of Open Source Software6(2021) 3021

    M.L. Waskom,seaborn: statistical data visualization,Journal of Open Source Software6(2021) 3021

    2021

  77. [85]

    lightning

    Jnwatson,Github - jnwatson/py-lmdb: Universal python binding for the lmdb “lightning” database, 2025

    2025

  78. [86]

    Paszke, S

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan et al.,Pytorch: An imperative style, high-performance deep learning library, inAdvances in Neural Information Processing Systems 32, pp. 8024–8035, Curran Associates, Inc. (2019), http://papers.neurips.cc/paper/90...

    2019

  79. [87]

    Cotter,Uses of Complex Wavelets in Deep Convolutional Neural Networks, Ph.D

    F. Cotter,Uses of Complex Wavelets in Deep Convolutional Neural Networks, Ph.D. thesis, Apollo - University of Cambridge Repository, 2019. 10.17863/CAM.53748

    2019 doi

  80. [88]

    G.R. Lee, R. Gommers, F. Waselewski, K. Wohlfahrt and A. O’Leary,Pywavelets: A python package for wavelet analysis,Journal of Open Source Software4(2019) 1237. – 21 –

    2019

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