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REVIEW 3 major objections 5 minor 114 references

DiRIM draws joint pixel-space posterior samples of the lensed source and foreground mass, fitting realistic simulations down to the noise level.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-01 12:40 UTC pith:UU33OCDC

load-bearing objection DiRIM looks like a real step forward for pixel-space lensing posteriors, but the trained loss and the score identity don't quite match; worth fixing before the 'down to the noise level' claim is taken literally. the 3 major comments →

arxiv 2607.19459 v1 pith:UU33OCDC submitted 2026-07-21 astro-ph.IM astro-ph.COcs.CVstat.ML

Strong Gravitational Lensing Posterior Sampling in Pixel-Space Using Diffusion Models and Recurrent Inference Machines

Guillaume Payeur , Laurence Perreault-Levasseur , Gabriel Missael Barco , Yashar Hezaveh This is my paper
classification astro-ph.IM astro-ph.COcs.CVstat.ML
keywords strong gravitational lensingdiffusion modelsrecurrent inference machinesposterior samplingpixel-space inferencesubhalo detectionscore-based generative modelingBayesian inverse problems
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Galaxy-galaxy strong lensing is usually modeled with low-dimensional parametric profiles for the source and foreground mass, a simplification that biases inference at high resolution and high signal-to-noise. The paper claims to close the open problem of sampling the full joint posterior of a pixelated source image and a pixelated convergence map from one noisy observation, using DiRIM: a conditional diffusion model whose denoising network is refined by a recurrent inference machine before its output is converted into posterior scores and integrated backward through a diffusion SDE. On realistic mock observations built from galaxies drawn from cosmological hydrodynamical simulations, DiRIM fits the data down to the noise level, passes coverage-calibration checks, recovers an injected dark-matter subhalo in all 740 samples — a ≳3σ detection — and samples along the known source-size/mass-slope degeneracy, at about five seconds per posterior sample. Small residual biases remain, most visibly for systems with multiple deflectors.

Core claim

DiRIM's central claim: the joint posterior of a pixelated source image and a pixelated convergence map, given one noisy lens observation, can be sampled directly in pixel space. A U-Net conditioned on the observation, likelihood gradients, and normalized residuals acts as a denoiser for (s, log κ), refined over five recurrent inference iterations. The refined estimate is fed to the score identity ∇_xt log p_t(x_t|y) = (x̂0^(M) − x_t)/σ²(t), and a 1000-step reverse-SDE solve yields posterior samples. The appendix proves the required conditional-mean property only for a loss weighting that supervises the final iteration, not the equal weighting used in training. Empirically, the method fits re

What carries the argument

The carrying mechanism is the DiRIM denoiser: a U-Net (a convolutional encoder-decoder network) g_θ that, at each diffusion time t, receives the noisy pair (s_t, log κ_t), the observation y, likelihood gradients, and normalized residuals, and outputs a refined estimate of the clean pair after M=5 recurrent iterations. The load-bearing identity is the posterior-score formula ∇_xt log p_t(x_t|y) = (x̂0^(M) − x_t)/σ²(t), which turns the refined denoiser output into the score needed to integrate the reverse SDE, replacing the unknown posterior with a trained refinement. The recurrent inference machine is what makes the score accurate enough: with M=1 the method collapses to biased conditional sc

Load-bearing premise

The samples are draws from the true joint posterior only if the five-step refined denoiser is the exact conditional mean the score formula requires — a property proven in Appendix A.2 for a loss weighting that supervises only the final iteration, not the equal weighting over the last four iterations that the model actually trained with (Table 4).

What would settle it

Generate mock lenses from a source and mass distribution distinct from the training set and compare DiRIM's pixel-space credible regions against an independent reference sampler — nested sampling or Hamiltonian Monte Carlo on the same forward model — for the same observations. If empirical coverage leaves the diagonal beyond the bootstrap 2σ band, or if the χ² distribution shifts off the theoretical k-degree-of-freedom curve, the score identity behind the sampler is not holding.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Pixel-space Bayesian lens modeling becomes routine: joint source and convergence-map samples at roughly five seconds each, with no parametric assumptions and no user-supplied source or mass models.
  • The recurrent refinement is what makes it work: with the RIM disabled (M=1), the model leaves structured residuals and a badly shifted χ² distribution, so plain conditional diffusion is insufficient for this problem.
  • Dark-matter substructure is detectable at significance: in the analytic test set all 740 samples retained the injected subhalo, and fitted subhalo mass, position, and concentration posteriors contain the truth.
  • Degeneracies are sampled, not smoothed over: the source-size versus mass-slope degeneracy appears as an elongated posterior ellipse with samples spanning the full range.
  • The method extends beyond its training distribution: it models a convergence map made of two unrelated merged halos and recovers the morphology of an out-of-distribution source, with residuals degrading as expected.

Where Pith is reading between the lines

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

  • The decisive stress test is calibration on conditions outside the training distribution — or on real survey data — since the coverage and χ² checks shown are computed on the same simulation distribution used for training; the paper's own multi-deflector and out-of-distribution examples show small residual biases that would likely grow there.
  • The gap between the proven loss weighting (final iteration only) and the trained one (equal weights on the last four iterations) is a concrete suspect for those biases: annealing the weights toward the proven limit, or directly checking whether the refined denoiser is the conditional mean, would isolate whether the score identity is the bottleneck.
  • Because the method needs only a differentiable forward model, the same recipe should transfer to other nonlinear imaging inverse problems — interferometric lensing, deconvolution, radio imaging — whenever a fast differentiable simulator exists.
  • The planned latent-space version would trade the pixel-space guarantees derived here for resolution and speed; the score identity and the calibration demonstrated in this paper would have to be re-established for the latent representation.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper introduces DiRIM, a method for joint posterior sampling of pixelated source galaxy images and foreground convergence maps in strong gravitational lensing. DiRIM combines a conditional diffusion model with a recurrent inference machine (RIM): the diffusion model provides the score-based sampling framework, while the RIM iteratively refines denoiser outputs before they are converted to posterior scores via Eq. (18). The method is trained on realistic mock observations built from SKIRT-TNG source images, IllustrisTNG convergence maps, and analytic convergence profiles, and is evaluated with residual/p-value checks, TARP calibration, chi-square distributions, subhalo detection, parameter recovery, and out-of-distribution tests. The central claim is that DiRIM can jointly sample the high-dimensional, non-linear posterior p(s,kappa|y) enough to model simulated observations down to the noise level.

Significance. If the central claim holds, DiRIM would close an open problem identified in the introduction: joint pixel-space posterior sampling for strong lensing with non-linear dependence on the foreground mass distribution. The paper's empirical case is substantial and genuinely useful: public code/data, a clean M=1 ablation showing that the RIM component is essential, noise-level residuals on many test examples, near-flat TARP curves, and explicit recovery of a known degeneracy (source size vs. density slope). The method also demonstrates a concrete subhalo-detection use case. However, the theoretical bridge between the trained objective and the posterior score is weaker than the presentation suggests, and the calibration checks are performed on the same simulation distribution used for training. The contribution is significant if that gap is closed or if the method is honestly reframed as an approximate posterior sampler.

major comments (3)
  1. [§2.2.1, Eq. (18), Table 4] Eq. (18) is the only theoretical link between the trained denoiser and the reverse-SDE sampler. Appendix A.2 proves the equivalence between L_DiRIM and L_CDSM only for the iteration weights of Eq. (17) (w_M=1, w_m=0 otherwise). Table 4 states that the actual training weights are {0,1/4,1/4,1/4,1/4}. With shared parameters and iterative refinement, the minimizer of Eq. (16) for these weights is not shown to equal E[x0|xt,y,t], so Eq. (18) is not justified for the trained objective. The TARP and chi-square checks, computed on the same simulator used for training, are empirical substitutes but do not replace the missing proof. I recommend retraining with Eq. (17) weights, proving the score identity for the actual weights, or explicitly reframing DiRIM as an approximate posterior sampler.
  2. [Appendix D, Figure 21] The text states that during training loss gradients are backpropagated through green edges only, and not through orange/red edges. This means the actual training objective is not exactly L_DiRIM in Eq. (16), even setting aside the weight mismatch. Appendix A.2's equivalence argument assumes the minimizer of the unmodified loss. Please state precisely which loss is optimized and whether the theoretical claim applies to it, or train with full backpropagation through the unrolled graph.
  3. [§3.1–§3.2, Figs. 7, 8, 20] Given the score-identity gap, the posterior-sampling claim rests on the empirical calibration evidence. TARP and chi-square are computed on observations drawn from the same simulation distribution used for training, and the paper itself acknowledges small residual biases (Fig. 6, Sec. 4). To make the posterior claim credible, I would like to see at least one validation against an independent posterior—for example, Hamiltonian Monte Carlo or an analytic posterior on a reduced-dimensional or parametric subset of the same forward model. This is a concrete test within the paper's scope and would substantially strengthen the claim.
minor comments (5)
  1. [§2.3.2, Table 1] The text mentions 'EPL, external shear and multipole components' and says the total is 14 parameters, but Table 1 lists no external shear parameters. Please add or remove external shear consistently; as written the dataset description is internally inconsistent.
  2. [Table 4, Fig. 11] For the M=1 ablation, the iteration loss weights are not specified. 'Keeping everything else fixed' is ambiguous because the weight vector dimension changes with M; please state the weights used for the M=1 model.
  3. [Appendix B] The time-weight function W(t) is a heuristic with a free parameter bar_sigma. Since the score-matching minimizer is independent of W(t) only in the infinite-capacity limit, a brief remark or sensitivity check on bar_sigma would clarify the finite-capacity behavior.
  4. [§3.2, Table 2] The statement that 740/740 samples containing the subhalo corresponds to '>~3 sigma detection' should specify the null hypothesis and detection criterion. Without a prior or a no-subhalo reference, the statistical significance is not well defined.
  5. [Figures 5, 6] The p-values in the panels are defined in footnote 8, but the notation 'p = 0.23' could be confused with a model parameter. Consider relabeling as 'p_chi2' or 'p-value' in the figure panels.

Circularity Check

0 steps flagged

No significant circularity: central derivation is self-contained against standard external score-matching results; only minor non-load-bearing self-citations.

full rationale

I walked the derivation chain. The forward model (Eq. 3) and Gaussian likelihood (Eq. 19) define the target posterior; the conditional score is estimated by minimizing the standard conditional denoising score-matching loss (Eqs. 8, 10), whose minimizer equals the posterior score by external results (Vincent 2011; Song et al. 2020; Batzolis et al. 2021). DiRIM's loss (Eq. 16) is shown in Appendix A.2 to have the same minimizer only for the last-iteration-only weights (Eq. 17), and Eq. 18 then follows from the algebraic relation between score and denoiser (Eq. 11/A.1-A.2), not from a quantity fitted to the evaluated posterior. No fitted parameter is renamed as a prediction: TARP (Figs. 7, 20) and chi-square (Fig. 8) are computed on held-out test observations from the same simulator, which is internal validation rather than circular reasoning. Self-citations (Adam et al. 2023 for convergence-map dataset; Lemos et al. 2023 for TARP; Sharief et al. 2026 for motivation) are contextual or tooling citations and are not load-bearing in the derivation. The notable gap is that Table 4 trains with RIM weights {0,1/4,1/4,1/4,1/4}, while Appendix A.2 proves the score identity only for w_M=1 and other weights zero; consequently Eq. 18 is not formally justified for the actual trained objective. This is a soundness/validation concern, not a circularity: the training target is not the posterior itself, and the calibration checks are independent of the identity. Overall the central claim has independent content and is not forced by definition or self-citation.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 1 invented entities

The method leans on standard score-matching theory and on the simulator being a truthful forward model. The free parameters are training hyperparameters (bar_sigma, beta_min/beta_max, c_s/c_kappa, RIM weights, iteration count) tuned by validation performance, not physical constants. No new physical entities are introduced. The main structural caveat is that the score identity in Eq. 18 is tied to a loss weighting (Eq. 17) different from the one actually used (Table 4).

free parameters (5)
  • bar_sigma (time-weight transition in W(t)) = 2e-2 (analytic kappa model), 4e-2 (simulated kappa model)
    Appendix B: W(t) transition point; tuned because the authors 'found that these values perform best empirically'.
  • VP-SDE noise schedule endpoints beta_min, beta_max = 2e-3, 250
    Appendix C: hand-chosen SDE schedule hyperparameters, not derived from data.
  • likelihood-gradient normalization factors c_s, c_kappa = 100, 100
    Appendix D, Eqs. D17-D18: tanh scaling of likelihood gradients; chosen hyperparameters.
  • RIM iteration loss weights w_m = {0, 1/4, 1/4, 1/4, 1/4} for M=5
    Table 4: actual training weights, inconsistent with Eq. 17, which is the basis for the claimed CDSM equivalence.
  • RIM iteration count M = 5 for main models; 1 for ablation
    Table 4: design choice controlling the amount of recurrent score refinement.
axioms (5)
  • standard math Denoising score matching yields the true conditional score in the limit of infinite data and model capacity
    Appendix A and Eq. 8 invoke standard results from Vincent 2011, Song et al. 2020, and Batzolis et al. 2021 to justify Eq. 18.
  • domain assumption The thin-screen ray-tracing forward model with Gaussian PSF and additive Gaussian noise is an exact generator of observations y from (s,kappa)
    Eqs. 1-3 and Eq. 19: all validation data is produced with this simulator, so calibration is internal to the same forward model.
  • domain assumption Training priors (SKIRT-TNG source images and TNG or analytic convergence maps) are representative of real lensing sources and mass distributions
    Section 2.3: the claim of physics realism depends on this; the OOD tests only partially probe mismatch.
  • domain assumption Source images and convergence maps can be treated as independent priors via unpaired shuffling during training
    Appendix D: sources and convergence maps are shuffled every epoch, assuming no physical correlation between source morphology and deflector mass.
  • ad hoc to paper The heuristic time-weight function W(t) preserves unbiased posterior sampling
    Appendix B: W(t) with tuned bar_sigma is motivated by intuition about where the observation dominates, not proven to yield the correct posterior score.
invented entities (1)
  • None no independent evidence
    purpose: No new physical entities are introduced.
    DiRIM is a network architecture and training scheme, not a new particle, force, dimension, or conserved quantity.

pith-pipeline@v1.3.0-alltime-deepseek · 27461 in / 14400 out tokens · 141751 ms · 2026-08-01T12:40:07.596527+00:00 · methodology

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read the original abstract

Modeling galaxy-galaxy strong gravitational lenses to infer the brightness of the source galaxy and the mass distribution of the foreground galaxy is computationally challenging, particularly for high-resolution, high signal-to-noise ratio observations. In this regime, high-dimensional representations of both the source and the foreground mass distribution are necessary to model the data down to the noise level. This inference problem has been challenging for both traditional and machine learning-based methods because of its high dimensionality and its non-linearity in the foreground mass distribution. We present a method to generate joint posterior samples of the source galaxy and foreground mass distribution as pixelated images conditioned on observations. The method combines diffusion-based generative modeling and recurrent inference machines. It can model realistic gravitational lensing simulations with background and foreground galaxies drawn from cosmological hydrodynamical simulations down to the noise level.

Figures

Figures reproduced from arXiv: 2607.19459 by Gabriel Missael Barco, Guillaume Payeur, Laurence Perreault-Levasseur, Yashar Hezaveh.

Figure 1
Figure 1. Figure 1: Graphical representation of DiRIM (Diffusion Recurrent Inference Machine) for strong gravitational lensing. A neural network gθ is trained to denoise noisy source galaxy images st and noisy convergence map images log κt given lens observations y. It iteratively updates its estimate of the denoised source and convergence map (sˆ0, log κˆ0) using the Recurrent Inference Machine (RIM) framework. The dashed li… view at source ↗
Figure 2
Figure 2. Figure 2: Graphical representation of conditional denoising score matching. A neural network gθ is trained to denoise noisy model parameters xt generated by passing prior sam￾ples x0 through the forward SDE Eq.4. The neural network does so given t and observations y generated from x0 by the forward model. It outputs an estimate xˆ0 of x0, and the dashed line represents the loss function Eq.10. where f is the forward… view at source ↗
Figure 4
Figure 4. Figure 4: Graphical representation of DiRIM. A neural network gθ is trained to denoise noisy model parameters xt given t and observations y. It does so by iteratively updating its prediction xˆ0 using the RIM framework. The dashed line represents the loss function Eq.16. This computation graph corresponds to a superimposition of the computation graphs in Figures 2 and 3. the DiRIM loss function LDiRIM in Eq.16 has t… view at source ↗
Figure 5
Figure 5. Figure 5: Lens model for a mock observation from the test set. This example features a convergence map with a single main deflector. We show the true source image, the true convergence map, the mock observation as well as four joint source and convergence map samples, with the reconstructed lensed image and residuals for each. st, log κt, y, ∇sˆ (m) 0 L, ∇κˆ (m) 0 L, δy (m)/σy, sˆ (m) 0 , log κˆ (m) 0 ) are concaten… view at source ↗
Figure 7
Figure 7. Figure 7: Tests of Accuracy with Random Points (TARP) plot computed on the test set. TARP is a necessary and sufficient condition for a posterior estimator to be unbiased. The plot demonstrates the near-perfect calibration of our posterior samples in pixel-space across the test set. parameterized by the Einstein radius RE, the density slope τ and the axis ratio q. In addition, the EPL com￾ponent is rotated by an ang… view at source ↗
Figure 9
Figure 9. Figure 9: Posterior samples for mock observations from the test set, selected and ordered based on their reconstructed image χ 2 percentile ranks. The samples are ordered from top to bottom in order of lowest χ 2 to highest χ 2 . 3.1. Simulated convergence model This section discusses our results on tests done with the DiRIM model trained on the set of simulated conver￾gence maps. The purpose of these tests is to as… view at source ↗
Figure 10
Figure 10. Figure 10: Posterior samples for mock observations from the test set, selected on the basis that their convergence map is highly complex. For each observation, we show one joint source and convergence map sample [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison between our methods and a tra￾ditional inference method for an observation from the test set. The traditional method consists in modeling the fore￾ground mass with a low-dimensional parametric macromodel comprising an EPL main deflector augmented with external shear and m = 3, 4 multipoles. We fix the source to the ground truth and determine the maximum likelihood macro￾model parameters. Even i… view at source ↗
Figure 13
Figure 13. Figure 13: Test of our methods on out-of-distribution (OOD) data. The convergence map is the sum of two ran￾domly selected convergence maps from the test set, assessing the robustness of the model to changes in the physical prop￾erties of the convergence maps. We show four joint posterior samples and the corresponding lensed image reconstruction and residuals. has additional flexibility, which translates into improv… view at source ↗
Figure 14
Figure 14. Figure 14: Lens model for a mock observation from the test set. The convergence map is generated from the analytic pro￾file, and does not contain a subhalo. We show the true source image, the true convergence map, the mock observation, and four joint source and convergence map samples, along with the reconstructed lensed image and residuals for each. the observation and image reconstruction indicate a bias caused by… view at source ↗
Figure 16
Figure 16. Figure 16: Posterior distribution of the macromodel parameters used to generate the analytic convergence maps for a mock observation from the test set. The posterior samples are obtained by performing a least-squares fit on the pixelated convergence map samples obtained with our methods. The true macromodel parameters used to generate the convergence map are shown as black stars and black dotted lines. The dark and … view at source ↗
Figure 18
Figure 18. Figure 18: Coverage of the degeneracy between the size of the source R and the radial slope of the convergence map τ across posterior samples. The blue points and confidence contours are computed from posterior samples for an obser￾vation from the test set. The orange, green and pink points correspond to the samples with the smallest, median, and largest value of R, respectively, and their associated source and conv… view at source ↗
Figure 17
Figure 17. Figure 17: Same as [PITH_FULL_IMAGE:figures/full_fig_p015_17.png] view at source ↗
Figure 20
Figure 20. Figure 20: Tests of Accuracy with Random Points (TARP) plot demonstrating the near-perfect calibration of our poste￾rior samples in pixel-space on the test set. of the source and convergence map is inferred correctly, demonstrating some capacity to generalize to OOD data. To assess the calibration of posterior samples gener￾ated with our methods, we show in [PITH_FULL_IMAGE:figures/full_fig_p016_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Unrolled computation graph of the DiRIM. During training, loss gradients with respect to the weights are back￾propagated through the green edges only. The orange edges do not contribute to the gradient of the loss function with respect to model parameters. Gradients are not backpropagated through the red edges to avoid instabilities from log-domain backprop￾agation [PITH_FULL_IMAGE:figures/full_fig_p023_… view at source ↗
Figure 22
Figure 22. Figure 22: Same as [PITH_FULL_IMAGE:figures/full_fig_p024_22.png] view at source ↗
Figure 24
Figure 24. Figure 24: Same as [PITH_FULL_IMAGE:figures/full_fig_p025_24.png] view at source ↗
Figure 26
Figure 26. Figure 26: Same as [PITH_FULL_IMAGE:figures/full_fig_p026_26.png] view at source ↗
Figure 28
Figure 28. Figure 28: Same as [PITH_FULL_IMAGE:figures/full_fig_p027_28.png] view at source ↗
Figure 30
Figure 30. Figure 30: Same as [PITH_FULL_IMAGE:figures/full_fig_p028_30.png] view at source ↗
Figure 32
Figure 32. Figure 32 [PITH_FULL_IMAGE:figures/full_fig_p029_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: Same as [PITH_FULL_IMAGE:figures/full_fig_p030_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: Same as [PITH_FULL_IMAGE:figures/full_fig_p031_34.png] view at source ↗

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Reference graph

Works this paper leans on

114 extracted references · 25 canonical work pages · 10 internal anchors

  1. [1]

    The Astrophysical Journal , author=

    Pixelated Reconstruction of Foreground Density and Background Surface Brightness in Gravitational Lensing Systems Using Recurrent Inference Machines , volume=. The Astrophysical Journal , author=. 2023 , month=july, pages=. doi:10.3847/1538-4357/accf84 , abstractNote=

    work page doi:10.3847/1538-4357/accf84 2023

  2. [2]

    arXiv e-prints , author=

    Score-Based Generative Modeling through Stochastic Differential Equations , url=. arXiv e-prints , author=. 2020 , month=nov, pages=. doi:10.48550/arXiv.2011.13456 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2011.13456 2020

  3. [3]

    Introduction to Gravitational Lensing: With Python Examples , author=

    Introduction to Gravitational Lensing: With Python Examples , url=. Introduction to Gravitational Lensing: With Python Examples , author=. 2022 , language=

    2022

  4. [4]

    Journal of Open Source Software , author=

    Caustics: A Python Package for Accelerated Strong Gravitational Lensing Simulations , volume=. Journal of Open Source Software , author=. 2024 , month=nov, pages=. doi:10.21105/joss.07081 , abstractNote=

    doi:10.21105/joss.07081 2024

  5. [5]

    Stochastic Processes and their Applications , author=

    Reverse-time diffusion equation models , volume=. Stochastic Processes and their Applications , author=. 1982 , month=may, pages=. doi:10.1016/0304-4149(82)90051-5 , number=

    doi:10.1016/0304-4149(82)90051-5 1982

  6. [6]

    Conditional Image Generation with Score-Based Diffusion Models , url=

    Batzolis, Georgios and Stanczuk, Jan and Schönlieb, Carola-Bibiane and Etmann, Christian , year=. Conditional Image Generation with Score-Based Diffusion Models , url=. doi:10.48550/arXiv.2111.13606 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2111.13606

  7. [7]

    The Principles of Diffusion Models , url=

    Lai, Chieh-Hsin and Song, Yang and Kim, Dongjun and Mitsufuji, Yuki and Ermon, Stefano , year=. The Principles of Diffusion Models , url=. doi:10.48550/arXiv.2510.21890 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2510.21890

  8. [8]

    Recurrent Inference Machines for Solving Inverse Problems

    Putzky, Patrick and Welling, Max , year=. Recurrent Inference Machines for Solving Inverse Problems , url=. doi:10.48550/arXiv.1706.04008 , abstractNote=

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1706.04008

  9. [9]

    Estimation of Non-Normalized Statistical Models by Score Matching , author=. J. Mach. Learn. Res. , year=

  10. [10]

    Neural Computation , author=

    A Connection Between Score Matching and Denoising Autoencoders , volume=. Neural Computation , author=. 2011 , month=july, pages=. doi:10.1162/NECO_a_00142 , abstractNote=

    doi:10.1162/neco_a_00142 2011

  11. [11]

    Monthly Notices of the Royal Astronomical Society: Letters , author=

    Posterior sampling of the initial conditions of the universe from non-linear large scale structures using score-based generative models , volume=. Monthly Notices of the Royal Astronomical Society: Letters , author=. 2023 , month=oct, pages=. doi:10.1093/mnrasl/slad152 , abstractNote=

    doi:10.1093/mnrasl/slad152 2023

  12. [12]

    and Norouzi, Mohammad and Chan, William , year=

    Chen, Nanxin and Zhang, Yu and Zen, Heiga and Weiss, Ron J. and Norouzi, Mohammad and Chan, William , year=. WaveGrad: Estimating Gradients for Waveform Generation , url=. doi:10.48550/arXiv.2009.00713 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2009.00713 2009

  13. [13]

    and Norouzi, Mohammad , year=

    Saharia, Chitwan and Ho, Jonathan and Chan, William and Salimans, Tim and Fleet, David J. and Norouzi, Mohammad , year=. Image Super-Resolution via Iterative Refinement , url=. doi:10.48550/arXiv.2104.07636 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2104.07636

  14. [14]

    and Ho, Jonathan and Salimans, Tim and Fleet, David J

    Saharia, Chitwan and Chan, William and Chang, Huiwen and Lee, Chris A. and Ho, Jonathan and Salimans, Tim and Fleet, David J. and Norouzi, Mohammad , year=. Palette: Image-to-Image Diffusion Models , url=. doi:10.48550/arXiv.2111.05826 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2111.05826

  15. [15]

    U-Net: Convolutional Networks for Biomedical Image Segmentation , url=

    Ronneberger, Olaf and Fischer, Philipp and Brox, Thomas , year=. U-Net: Convolutional Networks for Biomedical Image Segmentation , url=. doi:10.48550/arXiv.1505.04597 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.1505.04597

  16. [16]

    Elucidating the Design Space of Diffusion-Based Generative Models , url=

    Karras, Tero and Aittala, Miika and Aila, Timo and Laine, Samuli , year=. Elucidating the Design Space of Diffusion-Based Generative Models , url=. doi:10.48550/arXiv.2206.00364 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2206.00364

  17. [17]

    Medical Image Analysis , author =

    Recurrent inference machines for reconstructing heterogeneous. Medical Image Analysis , author =. 2019 , pmid =. doi:10.1016/j.media.2019.01.005 , abstract =

    work page doi:10.1016/j.media.2019.01.005 2019

  18. [18]

    The Astrophysical Journal , author =

    Data-driven. The Astrophysical Journal , author =. 2019 , pages =. doi:10.3847/1538-4357/ab35d7 , abstract =

    doi:10.3847/1538-4357/ab35d7 2019

  19. [19]

    Deconvolving X-ray Galaxy Cluster Spectra Using a Recurrent Inference Machine

    Rhea, Carter and Hlavacek-Larrondo, Julie and Adam, Alexandre and Kraft, Ralph and Bogdan, Akos and Perreault-Levasseur, Laurence and Prunier, Marine , month = sep, year =. Deconvolving. doi:10.48550/arXiv.2409.10711 , abstract =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2409.10711

  20. [20]

    and Hezaveh, Yashar D

    Morningstar, Warren R. and Hezaveh, Yashar D. and Levasseur, Laurence Perreault and Blandford, Roger D. and Marshall, Philip J. and Putzky, Patrick and Wechsler, Risa H. , month = jul, year =. Analyzing interferometric observations of strong gravitational lenses with recurrent and convolutional neural networks , url =. doi:10.48550/arXiv.1808.00011 , abstract =

    Pith/arXiv arXiv doi:10.48550/arxiv.1808.00011

  21. [21]

    Medical Image Analysis , author =

    Recurrent inference machines as inverse problem solvers for. Medical Image Analysis , author =. 2021 , pages =. doi:10.1016/j.media.2021.102220 , language =

    arXiv 2021

  22. [22]

    PyTorch: An Imperative Style, High-Performance Deep Learning Library , url=

    Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen, Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca and Desmaison, Alban and Köpf, Andreas and Yang, Edward and DeVito, Zach and Raison, Martin and Tejani, Alykhan and Chilamkurthy, Sasank and Steiner, Benoit and Fang, Lu and B...

    Pith/arXiv arXiv doi:10.48550/arxiv.1912.01703 1912

  23. [23]

    Colvin, Samuel and Jolibois, Eric and Ramezani, Hasan and Garcia Badaracco, Adrian and Dorsey, Terrence and Montague, David and Matveenko, Serge and Trylesinski, Marcelo and Runkle, Sydney and Hewitt, David and Hall, Alex and Plot, Victorien , license =

  24. [24]

    and Millman, K

    Harris, Charles R. and Millman, K. Jarrod and Walt, Stéfan J. van der and Gommers, Ralf and Virtanen, Pauli and Cournapeau, David and Wieser, Eric and Taylor, Julian and Berg, Sebastian and Smith, Nathaniel J. and Kern, Robert and Picus, Matti and Hoyer, Stephan and Kerkwijk, Marten H. van and Brett, Matthew and Haldane, Allan and Río, Jaime Fernández del...

    Pith/arXiv arXiv doi:10.48550/arxiv.2006.10256 2006

  25. [25]

    Computing in Science & Engineering , author=

    Matplotlib: A 2D Graphics Environment , volume=. Computing in Science & Engineering , author=. 2007 , pages=. doi:10.1109/MCSE.2007.55 , number=

    doi:10.1109/mcse.2007.55 2007

  26. [26]

    2023 , month=nov, pages=

    Monthly Notices of the Royal Astronomical Society , author=. 2023 , month=nov, pages=. doi:10.1093/mnras/stad2971 , abstractNote=

    doi:10.1093/mnras/stad2971 2023

  27. [27]

    and Baes, M

    Camps, P. and Baes, M. , year=. SKIRT 9: Redesigning an advanced dust radiative transfer code to allow kinematics, line transfer and polarization by aligned dust grains , volume=. doi:10.1016/j.ascom.2020.100381 , journal=

    arXiv 2020

  28. [28]

    Computational Astrophysics and Cosmology , author=

    The IllustrisTNG simulations: public data release , volume=. Computational Astrophysics and Cosmology , author=. 2019 , month=dec, pages=. doi:10.1186/s40668-019-0028-x , abstractNote=

    doi:10.1186/s40668-019-0028-x 2019

  29. [29]

    The Astrophysical Journal , author=

    Fast Calculation of a Family of Elliptical Gravitational Lens Models , volume=. The Astrophysical Journal , author=. 1998 , month=aug, pages=. doi:10.1086/305950 , number=

    doi:10.1086/305950 1998

  30. [30]

    The Astrophysical Journal , author=

    A Universal Density Profile from Hierarchical Clustering , volume=. The Astrophysical Journal , author=. 1997 , month=dec, pages=. doi:10.1086/304888 , number=

    doi:10.1086/304888 1997

  31. [31]

    Rendiconti del Circolo Matematico di Palermo , volume =

    Continuous Markov processes and stochastic equations , author =. Rendiconti del Circolo Matematico di Palermo , volume =. 1955 , doi =

    1955

  32. [32]

    1992 , doi =

    Numerical Solution of Stochastic Differential Equations , author =. 1992 , doi =

    1992

  33. [33]

    Sampling-Based Accuracy Testing of Posterior Estimators for General Inference , url=

    Lemos, Pablo and Coogan, Adam and Hezaveh, Yashar and Perreault-Levasseur, Laurence , year=. Sampling-Based Accuracy Testing of Posterior Estimators for General Inference , url=. doi:10.48550/arXiv.2302.03026 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2302.03026

  34. [34]

    Nature Astronomy , author=

    The revolution in strong lensing discoveries from Euclid , volume=. Nature Astronomy , author=. 2025 , month=aug, pages=. doi:10.1038/s41550-025-02616-5 , abstractNote=

    work page doi:10.1038/s41550-025-02616-5 2025

  35. [35]

    Rubin Observatory , volume=

    Strong gravitational lenses from the Vera C. Rubin Observatory , volume=. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences , author=. 2025 , month=may, pages=. doi:10.1098/rsta.2024.0117 , abstractNote=

    arXiv 2025

  36. [36]

    and Perreault-Levasseur, Laurence , year=

    Modi, Chirag and Lanusse, François and Seljak, Uroš and Spergel, David N. and Perreault-Levasseur, Laurence , year=. CosmicRIM: Reconstructing Early Universe by Combining Differentiable Simulations with Recurrent Inference Machines , rights=. doi:10.48550/ARXIV.2104.12864 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2104.12864

  37. [37]

    Inpainting Galaxy Counts onto N-Body Simulations over Multiple Cosmologies and Astrophysics

    Bourdin, Antoine and Legin, Ronan and Ho, Matthew and Adam, Alexandre and Hezaveh, Yashar and Perreault-Levasseur, Laurence , year=. Inpainting Galaxy Counts onto N-Body Simulations over Multiple Cosmologies and Astrophysics , url=. doi:10.48550/arXiv.2408.00839 , abstractNote=

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2408.00839

  38. [38]

    Posterior samples of source galaxies in strong gravitational lenses with score-based priors , rights=

    Adam, Alexandre and Coogan, Adam and Malkin, Nikolay and Legin, Ronan and Perreault-Levasseur, Laurence and Hezaveh, Yashar and Bengio, Yoshua , year=. Posterior samples of source galaxies in strong gravitational lenses with score-based priors , rights=. doi:10.48550/ARXIV.2211.03812 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2211.03812

  39. [39]

    The Astronomical Journal , author=

    Echoes in the Noise: Posterior Samples of Faint Galaxy Surface Brightness Profiles with Score-based Likelihoods and Priors , volume=. The Astronomical Journal , author=. 2025 , month=may, pages=. doi:10.3847/1538-3881/adb039 , abstractNote=

    work page doi:10.3847/1538-3881/adb039 2025

  40. [40]

    Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation , url=

    Andry, Gérôme and Lewin, Sacha and Rozet, François and Rochman, Omer and Mangeleer, Victor and Pirlet, Matthias and Faulx, Elise and Grégoire, Marilaure and Louppe, Gilles , year=. Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation , url=. doi:10.48550/arXiv.2504.18720 , abstractNote=

    doi:10.48550/arxiv.2504.18720

  41. [41]

    The Astrophysical Journal , author=

    Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-dimensional Data-driven Priors for Inverse Problems , volume=. The Astrophysical Journal , author=. 2025 , month=feb, pages=. doi:10.3847/1538-4357/ad9b92 , abstractNote=

    doi:10.3847/1538-4357/ad9b92 2025

  42. [42]

    Blind Strong Gravitational Lensing Inversion: Joint Inference of Source and Lens Mass with Score-Based Models , rights=

    Barco, Gabriel Missael and Legin, Ronan and Stone, Connor and Hezaveh, Yashar and Perreault-Levasseur, Laurence , year=. Blind Strong Gravitational Lensing Inversion: Joint Inference of Source and Lens Mass with Score-Based Models , rights=. doi:10.48550/ARXIV.2511.04792 , abstractNote=

    doi:10.48550/arxiv.2511.04792

  43. [43]

    Physical Review D , author=

    Diffusion-based mass map reconstruction from weak lensing data , volume=. Physical Review D , author=. 2025 , month=apr, pages=. doi:10.1103/PhysRevD.111.083542 , number=

    doi:10.1103/physrevd.111.083542 2025

  44. [44]

    A point cloud approach to generative modeling for galaxy surveys at the field level , url=

    Cuesta-Lazaro, Carolina and Mishra-Sharma, Siddharth , year=. A point cloud approach to generative modeling for galaxy surveys at the field level , url=. doi:10.48550/arXiv.2311.17141 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2311.17141

  45. [45]

    Dia, Noe and Yantovski-Barth, M. J. and Adam, Alexandre and Bowles, Micah and Lemos, Pablo and Scaife, Anna M. M. and Hezaveh, Yashar and Perreault-Levasseur, Laurence , year=. Bayesian Imaging for Radio Interferometry with Score-Based Priors , url=. doi:10.48550/arXiv.2311.18012 , abstractNote=

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2311.18012

  46. [46]

    Diffusion Models for Medical Image Analysis: A Comprehensive Survey , rights=

    Kazerouni, Amirhossein and Aghdam, Ehsan Khodapanah and Heidari, Moein and Azad, Reza and Fayyaz, Mohsen and Hacihaliloglu, Ilker and Merhof, Dorit , year=. Diffusion Models for Medical Image Analysis: A Comprehensive Survey , rights=. doi:10.48550/ARXIV.2211.07804 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2211.07804

  47. [47]

    Mind the Information Gap: Unveiling Detailed Morphologies of z 0.5-1.0 Galaxies with SLACS Strong Lenses and Data-Driven Analysis , rights=

    Legin, Ronan and Stone, Connor and Adam, Alexandre and Barco, Gabriel Missael and Coogan, Adam and Malkin, Nikolay and Perreault-Levasseur, Laurence and Hezaveh, Yashar , year=. Mind the Information Gap: Unveiling Detailed Morphologies of z 0.5-1.0 Galaxies with SLACS Strong Lenses and Data-Driven Analysis , rights=. doi:10.48550/ARXIV.2511.19595 , abstractNote=

    doi:10.48550/arxiv.2511.19595

  48. [48]

    Astronomy & Astrophysics , author=

    Probabilistic mass-mapping with neural score estimation , volume=. Astronomy & Astrophysics , author=. 2023 , month=apr, pages=. doi:10.1051/0004-6361/202243054 , abstractNote=

    doi:10.1051/0004-6361/202243054 2023

  49. [49]

    Machine Learning: Science and Technology , author=

    Conditional Diffusion-Flow models for generating 3D cosmic density fields: applications to f ( R ) cosmologies , volume=. Machine Learning: Science and Technology , author=. 2025 , month=sept, pages=. doi:10.1088/2632-2153/adf8b1 , abstractNote=

    doi:10.1088/2632-2153/adf8b1 2025

  50. [50]

    Learning Diffusion Priors from Observations by Expectation Maximization , url=

    Rozet, François and Andry, Gérôme and Lanusse, François and Louppe, Gilles , year=. Learning Diffusion Priors from Observations by Expectation Maximization , url=. doi:10.48550/arXiv.2405.13712 , abstractNote=

    doi:10.48550/arxiv.2405.13712

  51. [51]

    Pixellated Posterior Sampling of Point Spread Functions in Astronomical Images , rights=

    Stone, Connor and Legin, Ronan and Adam, Alexandre and Malkin, Nikolay and Barco, Gabriel Missael and Perreault-Levasseur, Laurence and Hezaveh, Yashar , year=. Pixellated Posterior Sampling of Point Spread Functions in Astronomical Images , rights=. doi:10.48550/ARXIV.2511.19594 , abstractNote=

    work page doi:10.48550/arxiv.2511.19594

  52. [52]

    Wu, Zihui and Sun, Yu and Chen, Yifan and Zhang, Bingliang and Yue, Yisong and Bouman, Katherine L. , year=. Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors , url=. doi:10.48550/arXiv.2405.18782 , abstractNote=

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2405.18782

  53. [53]

    Diffusion Models for Probabilistic Deconvolution of Galaxy Images

    Xue, Zhiwei and Li, Yuhang and Patel, Yash and Regier, Jeffrey , year=. Diffusion Models for Probabilistic Deconvolution of Galaxy Images , rights=. doi:10.48550/ARXIV.2307.11122 , abstractNote=

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2307.11122

  54. [54]

    Solving Inverse Problems in Medical Imaging with Score-Based Generative Models , rights=

    Song, Yang and Shen, Liyue and Xing, Lei and Ermon, Stefano , year=. Solving Inverse Problems in Medical Imaging with Score-Based Generative Models , rights=. doi:10.48550/ARXIV.2111.08005 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2111.08005

  55. [55]

    Denoising Diffusion Probabilistic Models , rights=

    Ho, Jonathan and Jain, Ajay and Abbeel, Pieter , year=. Denoising Diffusion Probabilistic Models , rights=. doi:10.48550/ARXIV.2006.11239 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.2006.11239 2006

  56. [56]

    Generative Modeling by Estimating Gradients of the Data Distribution , rights=

    Song, Yang and Ermon, Stefano , year=. Generative Modeling by Estimating Gradients of the Data Distribution , rights=. doi:10.48550/ARXIV.1907.05600 , abstractNote=

    Pith/arXiv arXiv doi:10.48550/arxiv.1907.05600 1907

  57. [57]

    Space Science Reviews , author=

    Time-Delay Cosmography: Measuring the Hubble Constant and Other Cosmological Parameters with Strong Gravitational Lensing , volume=. Space Science Reviews , author=. 2024 , month=aug, pages=. doi:10.1007/s11214-024-01079-w , abstractNote=

    doi:10.1007/s11214-024-01079-w 2024

  58. [58]

    The European Physical Journal C , author=

    A joint analysis of strong lensing and type Ia supernovae to determine the Hubble constant , volume=. The European Physical Journal C , author=. 2025 , month=may, pages=. doi:10.1140/epjc/s10052-025-14315-6 , abstractNote=

    work page doi:10.1140/epjc/s10052-025-14315-6 2025

  59. [59]

    Monthly Notices of the Royal Astronomical Society , author=

    Measurements of the Hubble constant and cosmic curvature with quasars: ultracompact radio structure and strong gravitational lensing , volume=. Monthly Notices of the Royal Astronomical Society , author=. 2021 , month=mar, pages=. doi:10.1093/mnras/stab638 , abstractNote=

    work page doi:10.1093/mnras/stab638 2021

  60. [60]

    Monthly Notices of the Royal Astronomical Society , author=

    STRIDES: a 3.9 per cent measurement of the Hubble constant from the strong lens system DES J0408-5354 , volume=. Monthly Notices of the Royal Astronomical Society , author=. 2020 , month=june, pages=. doi:10.1093/mnras/staa828 , abstractNote=

    doi:10.1093/mnras/staa828 2020

  61. [61]

    A 2.4 per cent measurement of H0 from lensed quasars: 5.3 tension between early- and late-Universe probes , volume=

    H0LiCOW – XIII. A 2.4 per cent measurement of H0 from lensed quasars: 5.3 tension between early- and late-Universe probes , volume=. Monthly Notices of the Royal Astronomical Society , author=. 2020 , month=oct, pages=. doi:10.1093/mnras/stz3094 , abstractNote=

    doi:10.1093/mnras/stz3094 2020

  62. [62]

    Improved Hubble constant measurement from lensing time delays using spatially resolved stellar kinematics of the lens galaxy , volume=

    TDCOSMO: XII. Improved Hubble constant measurement from lensing time delays using spatially resolved stellar kinematics of the lens galaxy , volume=. Astronomy & Astrophysics , author=. 2023 , month=may, pages=. doi:10.1051/0004-6361/202345878 , abstractNote=

    doi:10.1051/0004-6361/202345878 2023

  63. [63]

    Monthly Notices of the Royal Astronomical Society , author=

    The low-mass end of the fundamental relation for gravitationally lensed star-forming galaxies at 1 < z < 6: Low-mass lensed galaxies , volume=. Monthly Notices of the Royal Astronomical Society , author=. 2012 , month=dec, pages=. doi:10.1111/j.1365-2966.2012.22006.x , number=

    arXiv 2012

  64. [64]

    The Astrophysical Journal , author=

    CLASH: THREE STRONGLY LENSED IMAGES OF A CANDIDATE z ≈ 11 GALAXY , volume=. The Astrophysical Journal , author=. 2013 , month=jan, pages=. doi:10.1088/0004-637X/762/1/32 , number=

    doi:10.1088/0004-637x/762/1/32 2013

  65. [65]

    The Astrophysical Journal Letters , author=

    The Discovery of a Gravitationally Lensed Quasar at z = 6.51 , volume=. The Astrophysical Journal Letters , author=. 2019 , month=jan, pages=. doi:10.3847/2041-8213/aaeffe , abstractNote=

    doi:10.3847/2041-8213/aaeffe 2019

  66. [66]

    Monthly Notices of the Royal Astronomical Society , author=

    Finding high-redshift strong lenses in DES using convolutional neural networks , volume=. Monthly Notices of the Royal Astronomical Society , author=. 2019 , month=apr, pages=. doi:10.1093/mnras/stz272 , number=

    doi:10.1093/mnras/stz272 2019

  67. [67]

    Monthly Notices of the Royal Astronomical Society , author=

    Rest-frame UV properties of luminous strong gravitationally lensed Ly emitters from the BELLS GALLERY Survey , volume=. Monthly Notices of the Royal Astronomical Society , author=. 2020 , month=feb, pages=. doi:10.1093/mnras/stz3500 , abstractNote=

    work page doi:10.1093/mnras/stz3500 2020

  68. [68]

    The Astrophysical Journal , author=

    The Strong Gravitationally Lensed Herschel Galaxy HLock01: Optical Spectroscopy Reveals a Close Galaxy Merger with Evidence of Inflowing Gas , volume=. The Astrophysical Journal , author=. 2018 , month=feb, pages=. doi:10.3847/1538-4357/aaabb7 , abstractNote=

    doi:10.3847/1538-4357/aaabb7 2018

  69. [69]

    The Astrophysical Journal Letters , author=

    Discovery of a Very Bright and Intrinsically Very Luminous, Strongly Lensed Ly Emitting Galaxy at z = 2.82 in the BOSS Emission-Line Lens Survey* , volume=. The Astrophysical Journal Letters , author=. 2017 , month=jan, pages=. doi:10.3847/2041-8213/834/2/L18 , abstractNote=

    doi:10.3847/2041-8213/834/2/l18 2017

  70. [70]

    The COSMOS-Web Lens Survey (COWLS) I: Discovery of >100 high redshift strong lenses in contiguous JWST imaging

    Nightingale, James and Mahler, Guillaume and McCleary, Jacqueline and He, Qiuhan and Hogg, Natalie B. and Amvrosiadis, Aristeidis and Gozaliasl, Ghassem and Mercier, Wilfried and Scognamiglio, Diana and Berman, Edward and Leroy, Gavin and Liu, Daizhong and Massey, Richard J. and Shuntov, Marko and von Wietersheim-Kramsta, Maximilian and Franco, Maximilien...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2503.08777

  71. [71]

    The Astrophysical Journal , author=

    A Census of Optically Dark Massive Galaxies in the Early Universe from Magnification by Lensing Galaxy Clusters , volume=. The Astrophysical Journal , author=. 2022 , month=feb, pages=. doi:10.3847/1538-4357/ac3de5 , abstractNote=

    work page doi:10.3847/1538-4357/ac3de5 2022

  72. [72]

    High-redshift, strong-lens search in the Hyper Suprime-Cam Subaru Strategic Program , volume=

    HOLISMOKES: VIII. High-redshift, strong-lens search in the Hyper Suprime-Cam Subaru Strategic Program , volume=. Astronomy & Astrophysics , author=. 2022 , month=june, pages=. doi:10.1051/0004-6361/202243203 , abstractNote=

    work page doi:10.1051/0004-6361/202243203 2022

  73. [73]

    Monthly Notices of the Royal Astronomical Society , author=

    Spectroscopic detection of C iv 1548 in a galaxy at z = 7.045: implications for the ionizing spectra of reionization-era galaxies , volume=. Monthly Notices of the Royal Astronomical Society , author=. 2015 , month=dec, pages=. doi:10.1093/mnras/stv1907 , number=

    doi:10.1093/mnras/stv1907 2015

  74. [74]

    The Astrophysical Journal , author=

    CLASH: DISCOVERY OF A BRIGHT z ≃ 6.2 DWARF GALAXY QUADRUPLY LENSED BY MACS J0329.6-0211 , volume=. The Astrophysical Journal , author=. 2012 , month=mar, pages=. doi:10.1088/2041-8205/747/1/L9 , number=

    doi:10.1088/2041-8205/747/1/l9 2012

  75. [75]

    Space Science Reviews , author=

    Strong Lensing by Galaxies , volume=. Space Science Reviews , author=. 2024 , month=nov, pages=. doi:10.1007/s11214-024-01105-x , abstractNote=

    doi:10.1007/s11214-024-01105-x 2024

  76. [76]

    Space Science Reviews , author=

    Strong Gravitational Lensing as a Probe of Dark Matter , volume=. Space Science Reviews , author=. 2024 , month=aug, pages=. doi:10.1007/s11214-024-01087-w , abstractNote=

    doi:10.1007/s11214-024-01087-w 2024

  77. [77]

    Monthly Notices of the Royal Astronomical Society , author=

    Estimating the warm dark matter mass from strong lensing images with truncated marginal neural ratio estimation , volume=. Monthly Notices of the Royal Astronomical Society , author=. 2022 , month=nov, pages=. doi:10.1093/mnras/stac3215 , abstractNote=

    work page doi:10.1093/mnras/stac3215 2022

  78. [78]

    Monthly Notices of the Royal Astronomical Society , author=

    Gravitational imaging through a triple source plane lens: revisiting the CDM-defying dark subhalo in SDSSJ0946+1006 , volume=. Monthly Notices of the Royal Astronomical Society , author=. 2024 , month=feb, pages=. doi:10.1093/mnras/stae514 , abstractNote=

    doi:10.1093/mnras/stae514 2024

  79. [79]

    Probing sub-galactic mass structure with the power spectrum of surface-brightness anomalies in high-resolution observations of galaxy–galaxy strong gravitational lenses. II. Observational constraints on the subgalactic matter power spectrum , volume=. Monthly Notices of the Royal Astronomical Society , author=. 2023 , month=may, pages=. doi:10.1093/mnras/...

    work page doi:10.1093/mnras/stad1402 2023

  80. [80]

    Power-spectrum measurement and feasibility study , volume=

    Probing sub-galactic mass structure with the power spectrum of surface-brightness anomalies in high-resolution observations of galaxy-galaxy strong gravitational lenses – I. Power-spectrum measurement and feasibility study , volume=. Monthly Notices of the Royal Astronomical Society , author=. 2023 , month=may, pages=. doi:10.1093/mnras/stad1403 , abstractNote=

    work page doi:10.1093/mnras/stad1403 2023

Showing first 80 references.