A Unified View of Dark Matter and Cosmology: Diffusion Models in Gravitational Lensing ✛ ✦
Context
Modern sky surveys like LSST collect vast amounts of data on the shapes of billions of galaxies. The weak gravitational lensing effect, predicted by Einstein within general relativity, manifests as coherent distortions of these shapes due to the gravity of dark matter. Extracting cosmological information from these data traditionally relies on compressing them into correlation functions, but this loses much of the information encoded in non-Gaussian features of the matter distribution. Moving to field-level analysis promises a radical improvement in precision, but requires simultaneously solving two tasks: reconstructing the hidden mass maps and estimating cosmological parameters—which is exactly what this work accomplishes.
Methods
The authors proposed JADE, based on diffusion models—generative neural networks that learn to turn noise into realistic data samples. Unlike traditional approaches, here the model is trained directly on simulations of log-normal convergence fields that reproduce the non-linear clumping of matter and depend on six cosmological parameters of the wCDM model: densities of dark matter, dark energy, fluctuation amplitude, and others. The architecture uses a transformer that processes patches of the map flattened into tokens together with cosmological parameters as a single sequence, allowing mutual interactions to be captured. At inference time, the trained model, given an observed shear field, generates joint posterior samples of convergence maps and parameters by solving a stochastic differential equation.
Results
The JADE model, tested on simulated LSST Y10 data (5×5 degree field, 128×128 pixels, 5 tomographic bins with redshift), showed excellent agreement with classical MCMC sampling. The cosmological posterior distributions for parameters Ωc, σ8, w0, and others matched NUTS chains, and the calibration metric MIRA reached 0.635±0.017 (ideal 2/3). The recovered convergence maps not only reproduce two-point correlations (power spectrum with relative error of 6.7%), but also correctly capture non-Gaussian statistics, including one-point distributions with relative error of 5.2%. Importantly, all checks were performed frame-by-frame: for each sample, an independent simulation was generated at the corresponding parameters, confirming the internal consistency of the joint posterior.
Implications
The work demonstrates that deep learning can unify field-level and parameter inference in a single Bayesian scheme, eliminating the need for a differentiable forward model—which has long been a bottleneck for such analyses. This means that arbitrarily complex simulators, including full N-body and hydrodynamical codes, can now be used without sacrificing the ability to perform faithful Bayesian inference. The method lays the foundation for data analysis that retains all non-Gaussian information, which is especially valuable at small scales where non-linear structure formation generates a rich higher-order correlation structure.
Future development
Future development of the method includes transferring it to more realistic N-body simulations and extending it to curved celestial spheres rather than the flat-sky approximation. An important direction will be incorporating gradients of the forward model into training, if available, to improve the efficiency of using expensive simulations. Moreover, the architecture could be adapted for joint reconstruction of the initial conditions of the Universe, enabling tests of cosmological models through prediction of unobserved fields.
Impact
The proposed approach will impact extragalactic astronomy and cosmology by providing a tool to extract maximum information from upcoming surveys. It can also be used in other tasks requiring joint reconstruction of fields and global parameters, such as high-energy astrophysics or the physics of the expansion of the Universe.
Next steps
The immediate next steps include applying JADE to more realistic simulations, accounting for masking and systematic effects, and exploring the possibility of multi-probe analysis combining lensing with other cosmological observables.
Key open problems
The method is directly connected to the problems of dark matter and dark energy, allowing more precise measurement of the parameters governing the evolution of the Universe. It also brings us closer to fully utilizing the information contained in the large-scale structure, which is one of the key challenges of modern cosmology.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors introduced JADE, a diffusion model for joint inference of convergence maps and cosmological parameters from weak lensing data. The model is trained on simulations of log-normal fields and shows agreement with MCMC on posterior distributions of parameters, while also recovering non-Gaussian statistics of the fields.
Where its strength is
JADE combines field-level and parametric inference in a unified Bayesian framework without the need for a differentiable forward model, removing a key limitation of previous approaches.
Where it could go next
- It might be interesting to see how JADE could be adapted to strong lensing analysis, where one needs to recover lens parameters from a limited number of images. In our archive, there is a related paper where a neural network recovers gravitational lens parameters from just four image points.based on: Neural Network Sculptor: Reading a Gravitational Lens from Four Points arXiv:2607.22812v1
- One could consider applying JADE to gravitational wave data as an additional probe of dark matter and dark energy. The archive has a quick review of a paper where gravitational sirens are used to refine cosmological parameters.based on: Gravitational Sirens: Where to Find the Key to the Dark Universe arXiv:2605.27357
- Another direction is to study systematic effects and calibrate the model on realistic simulations. Nearby, there is a full review of another neural network method for weak lensing analysis, which discusses issues of accuracy and reliability in detail.based on: Neural Networks vs. Dark Matter: A New Method for Analyzing Weak Lensing arXiv:2607.09867
Worth trying
- Test how robust JADE is to realistic noise and masks, using approaches from work 2607.09867.
- Explore the possibility of using JADE for fast generation of synthetic convergence maps with specified cosmological parameters.
- Assess how incorporating information from gravitational waves could improve constraints on dark energy parameters.
Why this may matter
Combining field-level and parametric inference opens the way to more fully exploiting the information in weak lensing data, which is critical for future surveys such as LSST and could lead to tighter constraints on the nature of dark matter and dark energy.
Nearby works in our archive
- How to See the Invisible Web of the Cosmossimilarity 0.72
- Gravitational Waves to Put New Theory to the Testsimilarity 0.65
- Neural Network Sculptor: Reading a Gravitational Lens from Four Pointssimilarity 0.65
- The Universe's Memory of Gravitational Wavessimilarity 0.65
- Gravitational Sirens: Where to Find the Key to the Dark Universesimilarity 0.64
- Sentinel with a Map: Hunting Free-Floating Planetssimilarity 0.64
- Neural Networks vs. Dark Matter: A New Method for Analyzing Weak Lensingsimilarity 0.63
The archive is crowded around this work: 3 reviews nearby, closest at 0.72. This ground is well walked — and there is plenty to compare against.
Original abstract
as written by the authors arXiv:2606.31988
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.
Training the model required only 100,000 simulations, while a single MCMC run for one observation typically needs about a million calls to the simulator. Moreover, generating one posterior sample takes just 0.2 seconds.
In science fiction, the idea of mapping invisible structures by their gravitational influence was explored in Peter Watts' novel 'Blindsight,' where alien ships are disguised but betrayed by background distortions.
Key numbers
- Number of simulations for training: 100 000
- Field size: 5×5 degrees
- Time to generate one sample: 0.2 seconds
- MIRA metric: 0.635±0.017
- Relative error of power spectrum: 6.7%