Galaxies Without Halos: A Diffusion Model Generates Catalogs Directly from Dark Matter ✛
Context
Upcoming spectroscopic surveys DESI, Euclid, and LSST will collect coordinates of tens of millions of galaxy. To separate the cosmological signal from astrophysical uncertainties, statistical analysis requires thousands of plausible synthetic catalogs. Direct numerical simulation are too expensive, and the traditional 'painting' of dark matter halos with galaxies hits resolution limits and fails to account for environmental influences between different halos. A workaround is needed.
Methods
The researchers chose a Diffusion Models Elucidated Diffusion Model (EDM). During training, the network learns to remove noise from corrupted data: Gaussian noise of varying strength is added to each real point cloud of galaxies, and the neural network 'restorer' predicts the original clean coordinates and properties. The condition is a 3D cube of dark matter density, obtained from the TNG300 simulation with deliberately degraded resolution—only 1/10 of the particles. The network architecture is a transformers: the cube is encoded by a Convolutional Neural Networks Vision Transformer, and each galaxy-point interacts with all others through self-attention and cross-attention mechanisms with the density field. The model was trained on 90 000 patch-cubes of size 18,9 Mpc, reserving up to 200 galaxies per patch (with a dummy flag if there are fewer).
Results
After 10 000 epochs, the network generates catalogs that are indistinguishable from the reference: in random patches, galaxies lie along the filaments and nodes of the cosmic web. Histograms of star formation rates and stellar masses—both marginal and joint—match the true ones within statistics over 100 realizations. large-scale structure power spectra of galaxy autocorrelations and cross-correlations with dark matter are reproduced from scales of a few megaparsecs up to the full volume, without artifacts at patch boundaries. A key result: the model produces galaxies even in structures absent from the input dark matter field due to low resolution. In effect, it 'guesses' the galaxy population in unresolved subhalos, marginalizing over small-scale fluctuations. The full volume (151,3 Mpc)^3 takes 10 seconds on a GPU.
Implications
The method proves that diffusion models can serve as a universal emulator of the dark matter–galaxy connection. Instead of the chain 'simulation → halo finding → galaxy occupation', an end-to-end generator emerges that directly translates the density field into observable objects. This reduces systematic errors and simplifies Machine Learning Bayesian inference of cosmology and star formation parameters.
Future development
Currently, the model is trained on a single redshift z=2 and one simulation. By adding a global parameter to the condition—redshift, cosmology, or feedback recipes—one can obtain a generator for different epochs and physical scenarios. Extending the property vector to velocities, metallicity, and gas masses will provide catalogs for multiple surveys simultaneously.
Impact
Direct benefit for the DESI, Euclid, Subaru PFS, LSST collaborations and line intensity mapping (LIM) experiments. Rapid generation of thousands of independent mocks will speed up covariance matrix estimation and hypothesis testing.
Next steps
Optimization of patch size and encoder architecture for even higher resolution; validation on observational data, not just simulations.
Key open problems
The work directly links nonlinear gravitational clustering of dark matter with the baryonic physics of galaxies, bypassing the subgrid model problem—a step toward extracting cosmological information from small-scale clustering, where the lion's share of the signal hides.
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 paper proposes a diffusion model that directly generates galaxy catalogs from the three-dimensional dark matter density field of the TNG300 simulation, bypassing the halo identification step. The model is trained on patches with coarse resolution and reproduces the spatial distribution, stellar masses, and star formation rates, as well as predicts galaxies in unresolved subhalos.
Where its strength is
The end-to-end generator 'dark matter density → galaxy catalog' eliminates intermediate steps and their associated systematics, and the ability to recover the galaxy population below the resolution limit of the input field paves the way for emulating expensive hydrodynamical simulations over large volumes.
Where it could go next
- It might be interesting to see how the approach applies to alternative dark matter models: in our archive, there is an analysis of simulations with vector dark matter where invisible stars form, and a diffusion emulator could quickly generate catalogs of such objects for comparison with data.based on: Triple Thread: How Vector Dark Matter Gives Birth to Invisible Stars arXiv:2607.18025v1
- Another direction is accelerating direct hydrodynamical simulations: there is a paper in the archive where a neural network learns to spawn galaxies in one step, and your end-to-end generator could be extended into a fast initial condition sampler or a baryonic physics emulator.based on: How to Assemble a Galaxy in One Step arXiv:2605.17546
- Also, one could consider testing the model on observational data: there is a paper where a neural network removes gravitational lensing, and a similar technique would allow applying your generator to real lensing-reconstructed dark matter maps to predict galaxy distributions for comparison with DESI or Euclid surveys.based on: Neural Network Clears the Gravitational Lens from Ancient Light arXiv:2603.04535
Worth trying
- Test catalog generation for simulations with vector dark matter by training the model on corresponding data.
- Investigate whether the diffusion model can serve as an emulator of baryonic physics paired with a fast initial condition sampler.
- Use weak-lensing-reconstructed density fields as conditioning to directly compare synthetic catalogs with photometric surveys.
Why this may matter
Such an emulator could radically accelerate Bayesian inference of cosmological and astrophysical parameters, allowing thousands of realizations to be generated in seconds and thus enabling full comparison of dark matter and galaxy formation models with petascale data from upcoming surveys.
Nearby works in our archive
- Neural Network Learns to See Dark Mattersimilarity 0.65
- How to See the Invisible Web of the Cosmossimilarity 0.64
- Neural Network Fast-Tracks Galaxy Formationsimilarity 0.63
- Dark Matter Without Fine-Tuningsimilarity 0.61
- Invisible Conductors of Galactic Diskssimilarity 0.61
- Triple Thread: How Vector Dark Matter Gives Birth to Invisible Starssimilarity 0.61
- How to Assemble a Galaxy in One Stepsimilarity 0.61
- Neural Network Clears the Gravitational Lens from Ancient Lightsimilarity 0.60
The closest work in the archive sits at 0.65 by meaning — the usual level for our corpus.
Original abstract
as written by the authors arXiv:2607.19808v1
We present a diffusion-based generative model for constructing realistic galaxy catalogues from dark matter density fields. The model takes a three-dimensional dark matter density field as input and generates galaxies directly as a point cloud with positions and physical properties, including star formation rate (SFR), without identifying dark matter haloes or subhaloes. We train the model on galaxy catalogues from the IllustrisTNG hydrodynamical simulation. The generated catalogues reproduce the spatial correspondence between galaxies and the underlying dark matter field, preferentially populating dense regions and filamentary structures. They also accurately reproduce the one- and two-dimensional distributions of SFR and stellar mass, the galaxy auto-power spectrum, and the galaxy--dark matter cross-power spectrum. The model generates galaxies associated with structures below the nominal resolution of the input density field by marginalising over unresolved small-scale structure rather than relying on a resolved halo catalogue. With an optimised diffusion sampling schedule, it generates a catalogue with SFR $$> 1 ~\rm M_\odot/yr$$ over a $$(151.3 ~\rm Mpc)^3$$ volume in approximately 10 seconds on a single GPU. Our model therefore provides a practical engine for producing large mock ensembles for upcoming galaxy redshift surveys and line-intensity mapping experiments, and offers a path toward simulation-based inference that bypasses halo finding and directly connects field-level dark matter statistics to observable galaxy populations.
A patch 18,9 Mpc across is about 500 billion cubic light-years, yet the network 'sees' it as a whole and places up to 200 galaxies within it, never once 'thinking' about neighboring cubes.
Key numbers
- cube volume: (151.3 Mpc)^3
- generation time: ~10 s
- patch size: 18.9 Mpc
- SFR threshold: >1 M☉/yr
- input dark matter resolution: 1.2 Mpc/voxel