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arxiv: 2606.31988 · v1 · pith:BTSLXR26new · submitted 2026-06-30 · 🌌 astro-ph.CO · astro-ph.IM

Joint inference of weak lensing convergence map and cosmology with diffusion models

Benjamin Remy , Chihway Chang , Rebecca Willett This is my paper

Pith reviewed 2026-07-01 03:22 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.IM
keywords weak lensingconvergence mapsdiffusion modelscosmological inferenceimplicit inferencefield-level analysisshear observations
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The pith

Diffusion models learn to jointly sample convergence maps and cosmological parameters from weak lensing shear fields.

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

The paper develops a method to infer both the dark matter convergence map and the cosmological parameters at the same time from weak lensing observations. It trains a diffusion model on simulations to capture the joint distribution of maps and parameters without needing an explicit differentiable forward model. The architecture processes the pixel data and parameters together in one network. A reader would care because this removes a major barrier to field-level cosmological inference with realistic simulators. On the simulated log-normal fields the recovered maps and parameter posteriors match results from standard sampling methods.

Core claim

The central claim is that implicit inference via diffusion models can generate accurate posterior samples of both convergence maps and cosmological parameters conditioned on observed noisy shear, with the samples reproducing correct two-point and non-Gaussian one-point statistics and yielding posteriors consistent with those from traditional MCMC.

What carries the argument

A transformer-based diffusion model that treats the convergence field in pixel space and cosmological parameters as tokens in a single sequence for joint multimodal processing.

If this is right

  • The inferred convergence maps reproduce the correct two-point statistics as well as the one-point distribution of the true fields.
  • Cosmological parameter posteriors match those obtained from traditional MCMC sampling on the same data.
  • The approach works without requiring a differentiable forward model for gradient-based sampling.
  • Full field-level joint inference becomes feasible for simulators that cannot be differentiated.

Where Pith is reading between the lines

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

  • The same trained network could be applied directly to real weak lensing survey data once the training simulations are upgraded to include more realistic effects.
  • The method could be extended to condition on additional observables such as galaxy positions or other probes within the same sequence architecture.
  • Similar diffusion-based implicit inference might reduce the computational cost of field-level analyses in other high-dimensional cosmological settings.

Load-bearing premise

The log-normal fields in a wCDM cosmology used to generate the training simulations are representative of the data the model will later see.

What would settle it

Running the trained model on shear fields generated from a different simulation suite that includes baryonic physics or a different cosmology and checking whether the output maps and parameter posteriors remain statistically consistent with the input truth.

Figures

Figures reproduced from arXiv: 2606.31988 by Benjamin Remy, Chihway Chang, Rebecca Willett.

Figure 1
Figure 1. Figure 1: Joint field and cosmological denoising transformer architecture inputs a noisy convergence map, noisy cosmological parameters, and observed shear field, and outputs denoised field and cosmology (hat denotes estimated variable). Fields are first patched and then linearly projected into embedding vectors, and summed to their positional encoding. Time embedding modulates each transformer block. The flow match… view at source ↗
Figure 2
Figure 2. Figure 2: The first row shows the 5 bins of the observed convergence 𝜅obs = FPF−1𝛾obs, i.e. the Kaiser-Squires transformation of the observed shear field. The second row shows ground truth convergence and cosmology behind the noise. The third and fourth rows show posterior cosmology and convergence field, jointly sampled with our conditional diffusion model ( 𝜃, 𝜅 ) ∼ 𝑝𝜑 ( 𝜃, 𝜅 | 𝛾obs). Both the MIRA and TARP diagno… view at source ↗
Figure 3
Figure 3. Figure 3: Auto- and cross-power spectra Cℓ of the convergence field for all tomographic bin combinations. For each posterior draw (𝜃 (𝑖) , 𝜅 (𝑖) ), the black curves show the spectra of an independent simulation drawn at the sampled cosmology 𝜃 (𝑖) , while the corresponding posterior samples 𝜅 (𝑖) are shown in blue. The solid blue line indicates the mean over posterior samples, and the shaded region denotes the sampl… view at source ↗
Figure 4
Figure 4. Figure 4: TARP coverage test of the marginal posterior 𝑝( 𝜃 | 𝛾obs) inferred with the amortized model, showing mean and error bars with 𝜎 ∈ [1, 2, 3] computed with bootstrap. sistent with the jointly inferred cosmology, as verified through power spectra and one-point PDF comparisons. The marginal cosmolog￾ical posterior is in excellent agreement with NUTS-based MCMC chains and is well calibrated as assessed by the T… view at source ↗
read the original abstract

We present a method for joint inference of cosmological parameters and convergence maps from weak lensing observations, targeting the full posterior conditioned on the observed shear field. Our approach uses implicit inference with diffusion models, learning the joint distribution from simulations, without the need to have an explicit and differentiable forward model for gradient-based MCMC sampling. We introduce a transformer-based architecture that operates in pixel space and treats cosmological parameters as additional tokens in a unified sequence, enabling efficient multimodal processing within a single network. At inference time, the trained model generates posterior samples of joint convergence maps and cosmological parameters conditioned on observed noisy shear fields. We demonstrate the method on simulated weak lensing data generated from log-normal fields in a wcdm cosmology. The model accurately reconstructs convergence maps and recovers cosmological posteriors that agree with traditional MCMC, while remaining well calibrated across the prior, with a MIRA calibration score of $0.635 \pm 0.017$ on the joint posterior (where $0.667$ is optimal). The inferred fields reproduce the correct two-point statistics as well as non-Gaussian statistics such as the one-point distribution. This work establishes diffusion-based implicit inference as a viable route toward full field-level cosmological analyses, paving the way for applications to more realistic, non-differentiable simulators.

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 / 1 minor

Summary. The manuscript presents a diffusion-model approach to implicit inference for jointly sampling weak-lensing convergence maps and cosmological parameters conditioned on noisy shear observations. A transformer architecture processes pixel-space shear data together with cosmological-parameter tokens; the model is trained on log-normal wCDM simulations and is shown to produce posterior samples whose marginals agree with MCMC, achieve a MIRA calibration score of 0.635 ± 0.017, and reproduce both two-point and one-point statistics of the convergence field.

Significance. If the reported agreement and calibration hold under more realistic forward models, the method would constitute a practical route to field-level cosmological inference for simulators that are neither differentiable nor analytically tractable, which is a recognized bottleneck for Stage-IV surveys.

major comments (2)
  1. [Abstract] Abstract: the claim that the inferred posteriors 'agree with traditional MCMC' is not accompanied by any quantitative measure (e.g., posterior mean offsets, credible-interval coverage, or KL divergence) beyond the single MIRA scalar; without these numbers it is impossible to judge whether the agreement is sufficient to support the central methodological claim.
  2. [Abstract] Abstract and methods description: no information is supplied on training-set size, convergence diagnostics, or regularization against the log-normal approximation used to generate the training fields; because the learned joint distribution is defined entirely by these simulations, the absence of such details leaves open the possibility that reported performance is tied to the specific generative model rather than to the diffusion architecture itself.
minor comments (1)
  1. [Abstract] The acronym 'wcdm' appears in lowercase in the abstract while 'wCDM' is conventional; consistent capitalization would aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments and positive recommendation for minor revision. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the inferred posteriors 'agree with traditional MCMC' is not accompanied by any quantitative measure (e.g., posterior mean offsets, credible-interval coverage, or KL divergence) beyond the single MIRA scalar; without these numbers it is impossible to judge whether the agreement is sufficient to support the central methodological claim.

    Authors: We agree that the abstract would benefit from additional quantitative measures of agreement beyond the MIRA calibration score. In the revised manuscript we will add explicit metrics such as posterior mean offsets and credible-interval coverage probabilities (computed from the existing MCMC comparison runs) to provide a more rigorous quantification of the agreement. revision: yes

  2. Referee: [Abstract] Abstract and methods description: no information is supplied on training-set size, convergence diagnostics, or regularization against the log-normal approximation used to generate the training fields; because the learned joint distribution is defined entirely by these simulations, the absence of such details leaves open the possibility that reported performance is tied to the specific generative model rather than to the diffusion architecture itself.

    Authors: We agree that these details should be stated explicitly. In the revised manuscript we will expand the methods section to report the training-set size, training convergence diagnostics, and a brief discussion of the log-normal approximation and its implications for the reported results. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper trains a diffusion model on external simulations (log-normal wCDM fields) to learn the joint posterior over maps and parameters, then evaluates reconstruction accuracy, posterior agreement with MCMC, and calibration (MIRA score) on held-out simulations from the same distribution. No load-bearing step reduces by the paper's equations to a fitted quantity renamed as prediction, a self-definitional relation, or a self-citation chain. The reported results are direct empirical outcomes of the trained network on the simulation test set; the forward-looking caveat about representativeness for real data is explicitly separated from the internal validity claims.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that log-normal fields adequately represent the statistics needed for training; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Weak lensing convergence fields can be approximated by log-normal random fields in a wCDM cosmology for the purpose of generating training simulations.
    All reported results are obtained on data generated from this approximation.

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Reference graph

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