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arxiv: 2509.20430 · v2 · pith:ZE3OYOBYnew · submitted 2025-09-24 · 🌌 astro-ph.GA · astro-ph.CO

pop-cosmos: Star formation over 12 Gyr from generative modelling of a deep infrared-selected galaxy catalogue

Sinan Deger , Hiranya V. Peiris , Stephen Thorp , Daniel J. Mortlock , Gurjeet Jagwani , Justin Alsing , Boris Leistedt , Joel Leja This is my paper

Pith reviewed 2026-05-18 13:59 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords star formation rate densitygalaxy quenchinggenerative modelingstellar population synthesisCOSMOS surveyAGN feedbackcosmic star formation historynon-parametric star formation histories
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The pith

A generative model trained on 420,000 infrared-selected galaxies shows the cosmic star formation rate density peaked at redshift 1.3 and maps distinct star-formation histories for star-forming versus quiescent systems.

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

The paper applies a score-based diffusion model called pop-cosmos to 26-band photometry of a deep IRAC-selected sample from COSMOS2020. It directly integrates recovered star-formation rates to trace the cosmic star-formation rate density back to redshift 3.5. The work then extracts non-parametric star-formation histories and separates star-forming from quiescent galaxies using specific star-formation rate. This separation reveals gradually decorrelating activity in star-forming galaxies and abrupt quenching transitions in quiescent ones. The model also links peak AGN infrared output to the moment massive galaxies cross from star-forming to quiescent states.

Core claim

The central claim is that a score-based diffusion generative model, trained to match the joint distribution of 16 stellar population synthesis parameters on 420,000 IRAC-selected COSMOS2020 galaxies, recovers individual star-formation rates sufficiently well to compute the star-formation rate density by direct summation. This yields a peak at z = 1.3 ± 0.1 of 0.08 ± 0.01 M⊙ yr⁻¹ Mpc⁻³. Non-parametric histories show star-forming galaxies with star-formation-rate correlations that fall from near unity to zero over 13 Gyr, while quiescent galaxies maintain full recent correlation followed by sharp decorrelation on roughly 1 Gyr timescales for systems above 10¹⁰ M⊙. Infrared AGN luminosity is at

What carries the argument

pop-cosmos, a score-based diffusion generative model that learns the joint posterior distribution over 16 stellar population synthesis parameters directly from 26-band photometry of an IRAC Ch.1 < 26 selected sample of 420,000 COSMOS2020 galaxies.

If this is right

  • The star-formation rate density reaches a maximum of 0.08 M⊙ yr⁻¹ Mpc⁻³ at redshift 1.3 and declines both toward the present and toward earlier epochs.
  • Star-forming galaxies exhibit star-formation-rate correlations that decrease smoothly from r ≈ 1 at recent times to r ≈ 0 at lookback times of 13 Gyr.
  • Quiescent galaxies display full correlation over the most recent 300 Myr followed by abrupt decorrelation, indicating quenching transitions on ~1 Gyr timescales for galaxies with stellar masses between 10¹⁰ and 10¹¹ M⊙.
  • Infrared AGN luminosity reaches its highest values in massive galaxies precisely as they approach the star-forming to quiescent transition and drops once quiescence is established.

Where Pith is reading between the lines

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

  • If the recovered quenching timescale of ~1 Gyr holds in larger samples, semi-analytic models and hydrodynamical simulations will need to incorporate feedback mechanisms that operate on that specific duration rather than instantaneous or multi-Gyr processes.
  • The finding that AGN infrared output peaks only during the transition phase suggests future multi-wavelength surveys could test whether black-hole accretion is causally required for quenching by searching for similar timing offsets in independent AGN indicators.
  • Extending the same generative approach to wider-area or deeper infrared surveys could test whether the reported absence of low-mass quiescent galaxies at z ~ 1 persists or is an artifact of the current sample depth.

Load-bearing premise

The diffusion model recovers the true joint posterior over the 16 stellar population parameters without substantial selection biases or misspecification that would distort integrated star-formation rate densities or the derived correlations in star-formation histories.

What would settle it

An independent analysis of the same COSMOS2020 sample using spectroscopic redshifts and alternative SED-fitting codes that returns a star-formation rate density peak redshift differing by more than 0.3 or a quiescent fraction at z ~ 1 that differs by more than 15 percent would falsify the central results.

Figures

Figures reproduced from arXiv: 2509.20430 by Boris Leistedt, Daniel J. Mortlock, Gurjeet Jagwani, Hiranya V. Peiris, Joel Leja, Justin Alsing, Sinan Deger, Stephen Thorp.

Figure 1
Figure 1. Figure 1: The pop-cosmos cosmic SFRD in bins of width Δ𝑧 = 0.2. Dark- and light-red shaded regions show, respectively, our COSMOS2020- and model￾thresholded estimates. Black curve is from Madau & Dickinson (2014). Gray and orange curves are from Behroozi et al. (2019). Blue markers show the literature compilation assembled by Behroozi et al. (2019) and updated in this paper. Black and purple markers highlight result… view at source ↗
Figure 2
Figure 2. Figure 2: Rest-frame 𝑁𝑈𝑉𝑟 𝐽 colour–colour diagrams. Cells are shaded based on the median sSFR, and are only shaded when they contain 𝑁 > 5 galaxies. The orange line shows the SF/Q boundary from Weaver et al. (2023b). In our colour-based analysis, Q galaxies are those to the upper left of the boundary. The sSFR range on the colourbar is limited to [10−11 , 10−8.5 ] yr−1 . 0.0-0.5 0.5-0.8 0.8-1.0 1.0-1.1 1.1-1.3 1.3-1… view at source ↗
Figure 3
Figure 3. Figure 3: Left: Contaminant fraction – i.e. false discovery rate, FP/(TP + FP) – for Q galaxies identified via 𝑁𝑈𝑉𝑟 𝐽, in bins of redshift and stellar mass above our mass-completeness limit. Cells above the mass-completeness threshold are populated if they contain at least 1000 galaxies. Right: Same as left panel, but with bins shaded based on the median log10(sSFR) of the galaxies in the bin. Each redshift (column)… view at source ↗
Figure 4
Figure 4. Figure 4: Quenched fraction as a function of stellar mass in bins of redshift. Each redshift bin contains 10 percent of the sample. Left: SF/Q selection based on 𝑁𝑈𝑉𝑟 𝐽 diagram. Right: SF/Q selection based on an sSFR threshold of 10−11 yr−1 . 0 1 2 3 redshift 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 quenched fraction log10(sSFR) < 11.0 [yr 1 ] log10(M* / M ) [7.2, 8.8) [8.8, 9.0) [9.0, 9.2) [9.2, 9.3) [9.3, 9.5) [9.5, 9.7) [… view at source ↗
Figure 5
Figure 5. Figure 5: The quenched fraction as a function of redshift in bins of stellar mass. Each stellar mass bin contains 10 percent of the sample, except for the two most-massive bins, which contain 10 percent between them. Left: SF/Q selection based on 𝑁𝑈𝑉𝑟 𝐽 diagram. Right: SF/Q selection based on an sSFR threshold of 10−11 yr−1 . Estimated cosmic variance for a COSMOS-sized field is shown as a shaded region for the most… view at source ↗
Figure 6
Figure 6. Figure 6: The stellar mass distribution of the full (left), star-forming (middle), and quiescent galaxies from pop-cosmos. Cells are shaded by number of galaxies. Only galaxies above our mass completeness threshold (red curve, left panel) are included. Faisst et al. 2017; Ellison et al. 2024; Heckman et al. 2024), nor extremely gradual (e.g. starvation of gas; Bekki et al. 2002; Van Den Bosch et al. 2008; Peng et al… view at source ↗
Figure 7
Figure 7. Figure 7: The SMF of the full (left), star-forming (middle), and the quiescent galaxies (right) in bins of redshift. Shaded regions show uncertainty due to cosmic variance and Poisson noise. We overplot the Schechter functions from Weaver et al. (2023b), including their reported uncertainty due to Poisson noise, cosmic variance, and stellar mass uncertainty from SED fitting. Redshift bins are from Weaver et al. (202… view at source ↗
Figure 8
Figure 8. Figure 8: The redshift-binned SMF of the full (left), star-forming (middle), and quiescent (right) samples. Redshift bins contain 10 percent of the full sample. Shaded regions show uncertainty due to cosmic variance and Poisson noise. Only galaxies above our mass-completeness threshold (see Section 2.4) are included. Matharu et al. 2021; Alberts & Noble 2022). We observe a minor increase of 0.5 dex in the peak mass … view at source ↗
Figure 9
Figure 9. Figure 9: Star formation and stellar mass assembly history of the SF sample at 1.0 < 𝑧 < 1.4, with 10 < log10 (𝑀∗/M⊙ ) < 11 and log10 (sSFR/yr−1 ) > −11. Top left: Correlation matrix between the SFH bins of this sample. Colourbar range is fixed to [0, 1]. Top right: The SFR distributions in the 7 SFH bins. Bottom left: Median SFR and standard deviation per SFH bin for this sample (black), and representative SFHs for… view at source ↗
Figure 10
Figure 10. Figure 10: Same as [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Distributions of SFR ratios between the SFH bins for all the galaxies in 1.0 < 𝑧 < 1.4. SFH bins 𝑛 = 1 and 𝑛 = 7, respectively correspond to the most recent and earliest epochs of the SFH. The SFR ratio plotted is therefore the ratio of a more recent bin to the immediately preceding bin. The dashed vertical line shows an SFR ratio of one. The black histogram shows the Student’s 𝑡 continuity prior from Lej… view at source ↗
Figure 12
Figure 12. Figure 12: Mass dependent contribution to the SFRD, with the same redshift binning as [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Stellar mass doubling time-scale (inverse sSFR; see, e.g. Bower et al. 2017) vs. stellar mass in bins of redshift. Left: Cells shaded based on galaxy count. Right: Cells shaded based on median AGN bolometric luminosity fraction, 𝑓AGN. The dashed gray line indicates a doubling time of 100 Gyr, equivalent to our SF/Q boundary of sSFR = 10−11 yr−1 . The vertical dashed lines show the mass completeness limit … view at source ↗
read the original abstract

We study star formation over 12 Gyr using pop-cosmos, a generative model trained on 26-band photometry of 420,000 COSMOS2020 galaxies (IRAC Ch.1 $<26$). The model learns distributions over 16 SPS parameters via score-based diffusion, matching observed colours and magnitudes. We compute the star formation rate density (SFRD) to $z=3.5$ by directly integrating individual galaxy SFRs. The SFRD peaks at $z=1.3\pm0.1$, with peak value $0.08\pm0.01$ M$_{\odot}$ yr$^{-1}$ Mpc$^{-3}$. We classify star-forming (SF) and quiescent (Q) galaxies using specific SFR $<10^{-11}$ yr$^{-1}$, comparing with $NUVrJ$ colour selection. The sSFR criterion yields up to 20% smaller quiescent fractions across $0<z<3.5$, with $NUVrJ$-selected samples contaminated by galaxies with sSFR up to $10^{-9}$ yr$^{-1}$. Our sSFR-selected stellar mass function shows a negligible number density of low-mass ($<10^{9.5}$ M$_\odot$) Q galaxies at $z\sim1$, where colour-selection shows a prominent increase. Non-parametric star formation histories around the SFRD peak reveal distinct patterns: SF galaxies show gradually decreasing SFR correlations with lookback time ($r\sim1$ to $r\sim0$ over 13 Gyr), implying increasingly stochastic star formation toward early epochs. Q galaxies exhibit full correlation ($r>0.95$) during the most recent $\sim$300 Myr, then sharp decorrelation with earlier star-forming epochs, marking clear quenching transitions. Massive ($10<\log_{10}(M_*/$M$_{\odot})<11$) galaxies quench on a time-scale of $\sim1$ Gyr, with mass assembly concentrated in their first 3.5 Gyr. Finally, AGN activity (infrared luminosity) peaks as massive ($\sim10^{10.5}$ M$_\odot$) galaxies approach the transition between star-forming and quiescent states, declining sharply once quiescence is established. This provides evidence that AGN feedback operates in a critical regime during the $\sim1$ Gyr quenching transition.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces pop-cosmos, a score-based diffusion generative model trained on 26-band photometry for 420,000 IRAC Ch.1<26 selected galaxies from COSMOS2020. The model learns the joint distribution over 16 SPS parameters. SFRD is computed by direct integration of individual galaxy SFRs drawn from the model, yielding a peak at z=1.3±0.1 with value 0.08±0.01 M⊙ yr⁻¹ Mpc⁻³. Galaxies are classified as star-forming or quiescent using an sSFR<10^{-11} yr^{-1} threshold (compared to NUVrJ colour selection), revealing up to 20% differences in quiescent fractions and a negligible low-mass quiescent population at z~1. Non-parametric SFHs are analysed via correlation matrices, showing gradual decorrelation for SF galaxies and sharp ~1 Gyr quenching transitions for Q galaxies. AGN IR luminosity is shown to peak as massive galaxies approach the SF-to-Q transition.

Significance. If the diffusion model recovers unbiased joint posteriors, the work provides a statistically powerful, data-driven view of star formation over 12 Gyr with concrete, falsifiable results on SFRD evolution, SFH stochasticity, quenching timescales, and AGN feedback timing. The direct integration approach and correlation-matrix analysis of non-parametric histories offer a useful complement to traditional parametric SFH fitting and could inform quenching models.

major comments (2)
  1. [§3.3 and §4.1] §3.3 and §4.1: The validation of the score-based diffusion model (e.g., recovery of held-out photometry, posterior calibration on mocks, or explicit marginalisation over the IRAC Ch.1<26 selection function) is not described in sufficient detail. Since all quantitative results (SFRD, quiescent fractions, SFH correlations, AGN timing) rest on the accuracy of the inferred 16-dimensional SPS posteriors, this validation is load-bearing and must be strengthened to rule out selection biases or misspecification for low-mass/high-z galaxies.
  2. [§5.2, Figure 7] §5.2, Figure 7: The reported ~1 Gyr quenching timescale and mass-assembly concentration in the first 3.5 Gyr for 10<log M*/M⊙<11 galaxies are derived from the correlation matrices of the non-parametric SFHs. It is unclear how sensitive these timescales are to the choice of SFH basis or time binning; an explicit test with an alternative basis would be needed to confirm the result is not an artifact of the representation.
minor comments (2)
  1. [Abstract and §2] The abstract and §2 should explicitly state the number of diffusion steps, noise schedule, and any conditioning on redshift or magnitude used during training.
  2. [Table 1 or §4.3] Table 1 or §4.3: The comparison of quiescent fractions between sSFR and NUVrJ selections would benefit from a quantitative breakdown by stellar mass and redshift bin rather than the current summary statement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed report. We address each major comment below and indicate the revisions that will be incorporated in the next version of the manuscript.

read point-by-point responses

  1. Referee: [§3.3 and §4.1] §3.3 and §4.1: The validation of the score-based diffusion model (e.g., recovery of held-out photometry, posterior calibration on mocks, or explicit marginalisation over the IRAC Ch.1<26 selection function) is not described in sufficient detail. Since all quantitative results (SFRD, quiescent fractions, SFH correlations, AGN timing) rest on the accuracy of the inferred 16-dimensional SPS posteriors, this validation is load-bearing and must be strengthened to rule out selection biases or misspecification for low-mass/high-z galaxies.

    Authors: We agree that the validation of the generative model requires a more explicit and comprehensive presentation. In the revised manuscript we have substantially expanded §3.3 to include quantitative recovery statistics for held-out photometry across the full redshift and stellar-mass range, together with posterior calibration tests performed on mock catalogues that explicitly incorporate the IRAC Ch.1<26 selection function. A new subsection in §4.1 now reports bias and coverage diagnostics specifically for the low-mass and high-redshift regimes, demonstrating that any residual selection-induced biases remain well within the quoted uncertainties on the derived quantities. These additions directly strengthen the load-bearing validation. revision: yes

  2. Referee: [§5.2, Figure 7] §5.2, Figure 7: The reported ~1 Gyr quenching timescale and mass-assembly concentration in the first 3.5 Gyr for 10<log M*/M⊙<11 galaxies are derived from the correlation matrices of the non-parametric SFHs. It is unclear how sensitive these timescales are to the choice of SFH basis or time binning; an explicit test with an alternative basis would be needed to confirm the result is not an artifact of the representation.

    Authors: We acknowledge that robustness to the choice of non-parametric basis and time binning should be demonstrated explicitly. In the revised version we have added an alternative SFH representation that uses a different set of time bins (finer sampling in the most recent 2 Gyr). The corresponding correlation matrices are shown in a new panel of Figure 7 and discussed in §5.2. The ~1 Gyr quenching timescale and the concentration of mass assembly within the first 3.5 Gyr remain consistent to within 10 percent, confirming that the reported features are not artifacts of the original basis choice. revision: yes

Circularity Check

0 steps flagged

Generative diffusion model yields downstream SFRD and SFH statistics without definitional reduction to training inputs

full rationale

The paper trains a score-based diffusion model to match the joint distribution of 16 SPS parameters to the observed 26-band photometry of the IRAC-selected COSMOS2020 sample. SFRD is obtained by integrating the SFR values drawn from the learned generative distribution; SF/Q classifications and correlation matrices are computed directly on the inferred non-parametric SFHs. These quantities are downstream inferences from the fitted model rather than quantities defined by construction from the same parameters used in training. No load-bearing step reduces an output to an input via self-definition, fitted-parameter renaming, or a self-citation chain that lacks independent verification. Minor self-citation of prior diffusion-model methodology is present but not central to the reported SFRD peak or quenching timescales. The derivation remains self-contained against external photometric benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the assumption that the diffusion model faithfully represents the underlying galaxy population and that the chosen sSFR threshold cleanly separates physical states; no new particles or forces are introduced.

axioms (2)
  • domain assumption The sSFR < 10^{-11} yr^{-1} threshold provides a physically meaningful separation between star-forming and quiescent galaxies that is less contaminated than NUVrJ color selection.
    Used to derive quiescent fractions and stellar mass functions that differ from color-based results.
  • domain assumption The 26-band photometry and IRAC magnitude limit allow the generative model to recover unbiased distributions over the 16 SPS parameters across the redshift range studied.
    Underlies the training and subsequent integration to obtain SFRD and SFHs.

pith-pipeline@v0.9.0 · 6008 in / 1728 out tokens · 52257 ms · 2026-05-18T13:59:07.820268+00:00 · methodology

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Reference graph

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