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From Dark Matter to Galaxies: Halo-Free Mock Generation via Conditional Point-Cloud Diffusion

This paper introduces a diffusion-based generative model that directly synthesizes realistic galaxy point clouds from dark matter density fields without relying on halo finding, achieving high-fidelity reproduction of galaxy properties and spatial distributions in seconds to facilitate large-scale mock catalog generation for upcoming cosmological surveys.

Original authors: Kana Moriwaki, Ken Osato, Naoki Yoshida

Published 2026-07-23

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CC BY 4.0

Original authors: Kana Moriwaki, Ken Osato, Naoki Yoshida

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, invisible ocean made of dark matter. We can't see this ocean directly, but we know it's there because it acts like a cosmic mold, shaping where the stars and galaxies form. Just as water flows into the deepest valleys of a landscape, galaxies tend to gather in the dense, clumpy regions of this dark matter ocean. Astronomers want to understand how the universe works by studying these galaxies, but looking at the real sky is slow and expensive. To speed things up, scientists build "mock" universes—computer simulations that act like practice runs for real telescopes. The big challenge has always been figuring out how to turn the smooth, invisible map of dark matter into a detailed list of individual galaxies with their own unique personalities, like how fast they are forming stars or how heavy they are.

Traditionally, scientists tried to solve this by first finding the "houses" (dark matter halos) where galaxies live, and then painting galaxies onto them. But this is like trying to describe a bustling city by only looking at the street addresses of the buildings; you miss the people walking between them and the complex relationships that exist in the spaces in between. A new paper by Kana Moriwaki and colleagues suggests a smarter, faster way to do this. They have built a digital artist that skips the "house-hunting" step entirely. Instead of looking for specific dark matter clumps, their model looks at the whole dark matter map and instantly "dreams" up a cloud of individual galaxies, complete with their positions and physical traits, directly from the density of the invisible ocean.

The team trained their artificial intelligence on a massive, realistic simulation called IllustrisTNG, which is like a high-definition movie of how the universe evolved. They taught the model to take a low-resolution, blurry map of dark matter and generate a sharp, detailed list of galaxies that match the real physics. The result is a "halo-free" generator. It doesn't need to identify the dark matter clumps first; it just looks at the density of the universe and says, "Okay, here is where a galaxy should be, and here is how much star formation it should have."

The paper finds that this new method is incredibly effective. The galaxies it creates look just like the ones in the real simulation: they cluster in the right places, follow the cosmic web of filaments, and have the correct mix of star formation rates and masses. Crucially, the model can even generate galaxies that are smaller or fainter than the resolution of the input map would normally allow. It does this by "marginalizing" over the missing details—essentially using probability to guess the existence of small structures that the blurry map can't see, rather than ignoring them.

In terms of speed, the results are staggering. The team managed to generate a full catalog of galaxies for a cube of space measuring (151.3 Mpc)³ in just about 10 seconds on a single graphics card. This is a massive leap forward compared to traditional methods, which can take hours or days to produce similar amounts of data. The authors show that their generated catalogs reproduce the statistical patterns of the real universe, including how galaxies cluster together and how they correlate with the dark matter beneath them. While the model doesn't predict the exact location of every single galaxy (because galaxy formation has a random, chaotic element), it perfectly captures the overall statistical behavior. This suggests that conditional point-cloud diffusion is a powerful new tool for creating the massive libraries of mock data needed for upcoming giant sky surveys, allowing astronomers to test their theories against the universe without waiting for the next generation of supercomputers to finish the heavy lifting.

Technical Summary: From Dark Matter to Galaxies via Conditional Point-Cloud Diffusion

Problem Statement
Generating realistic mock galaxy catalogues is essential for the statistical analysis of upcoming large-scale galaxy redshift surveys and line-intensity mapping experiments. While hydrodynamical simulations (e.g., IllustrisTNG) provide the most reliable mocks, they are computationally prohibitive for producing the large ensembles required for modern statistical inference. Alternative "halo-based" approaches, which map baryonic properties onto dark matter (DM) haloes identified in cheaper DM-only simulations, face two primary limitations: they rely on abstracted summary statistics that fail to capture complex environmental effects, and they struggle to model correlations between galaxies across different haloes. Furthermore, these methods are inherently limited by the resolution of the halo finder; galaxies hosted by sub-resolution haloes cannot be generated. Conversely, "map-to-map" approaches that generate galaxy density fields often suffer from inefficiency, as they require extremely high spatial resolution to separate individual galaxies, leading to wasted computational resources on empty pixels.

Methodology
The authors propose a diffusion-based generative model that constructs galaxy catalogues directly from three-dimensional dark matter density fields, bypassing the need for halo identification.

Framework: The model utilizes the Elucidated Diffusion Model (EDM) framework, which reformulates diffusion processes in terms of a continuous noise scale. The model learns to reverse a noise-addition process, transforming a noisy point cloud into a realistic galaxy distribution conditioned on the input DM density.
Architecture: A transformer-based network is employed to model the point-wise features of galaxies. The architecture consists of:
- A 3D Vision Transformer encoder that processes the conditioning DM density cube (voxelized) into patch tokens.
- A decoder that treats the galaxy point cloud as a set of unordered points. It updates point features via self-attention and cross-attention to the conditioning DM sequence.
- Adaptive Layer Normalization (AdaLN) injects noise-level embeddings into every decoder layer.
Data and Training: The model is trained on the IllustrisTNG suite (specifically TNG300-1 for target galaxies and TNG300-3-Dark for input fields).
- Input: Low-resolution DM density fields are constructed by downsampling the TNG300-3-Dark particle data (selecting 1/10th of particles), resulting in a particle mass of $4.5 \times 10^{10} h^{-1} M_\odot$ . This corresponds to a voxel size of $(1.2 \text{ Mpc})^3$ .
- Target: Galaxies with Star Formation Rates (SFR) $> 1 M_\odot/\text{yr}$ from the high-resolution TNG300-1.
- Patch-based Generation: To manage computational costs and capture local environmental effects, the simulation volume is divided into non-overlapping patches of side length $l_{patch} = 18.9$ Mpc ( $16^3$ voxels). The model generates galaxy point clouds for each patch independently.
- Feature Vector: Each galaxy is represented by a 5-dimensional vector (3D position, SFR, stellar mass) plus a flag distinguishing real galaxies from padded dummy samples.
Sampling: Generation proceeds via a second-order Heun method sampling schedule. The authors optimized this schedule to achieve stable generation quality in $\ge 20$ steps.

Key Contributions

Halo-Free Generation: The model generates galaxies directly as a point cloud conditioned on the DM density field, eliminating the need for halo finding algorithms (e.g., Friends-of-Friends or SubFind).
Sub-Resolution Generation: By marginalizing over unresolved small-scale structures rather than relying on resolved haloes, the model successfully generates galaxies associated with structures below the nominal resolution limit of the input DM field (i.e., haloes with masses $< 4.5 \times 10^{12} h^{-1} M_\odot$ ).
Scalability and Efficiency: The patch-based approach allows for the generation of large volumes with low computational cost. The authors demonstrate that a full catalogue over a $(151.3 \text{ Mpc})^3$ volume can be generated in approximately 10 seconds on a single NVIDIA RTX 6000 Ada GPU.
Flexibility: The point-cloud representation avoids the inefficiencies of map-to-map methods (where most pixels are empty) and allows for continuous output coordinates, facilitating post-processing for various survey geometries.

Results
The authors validate the model against the true TNG galaxy distribution using several statistical metrics:

Visual Inspection: Generated galaxies preferentially populate high-density regions and filamentary structures, matching the spatial correspondence of the underlying DM field.
Property Distributions: The model accurately reproduces the one-dimensional distributions of SFR and stellar mass, as well as their joint two-dimensional distribution. It captures the population of low-SFR and low-mass galaxies that would be missed by a halo-based approach limited to resolved haloes.
Clustering Statistics:
- The galaxy auto-power spectrum is reproduced over a wide range of scales.
- The galaxy–DM cross-power spectrum matches the TNG results, confirming correct correlation with the matter distribution.
- The cross-correlation coefficient between TNG and generated distributions remains close to unity on large scales and stays positive on small scales, indicating the model captures both large-scale structure and stochastic small-scale variations.
Boundary Effects: The patch-based assembly does not introduce significant artifacts at patch boundaries for two-point statistics, suggesting that explicit information from neighboring patches is not strictly required for these metrics.

Significance and Claims
The paper claims that this method provides a practical engine for producing large mock ensembles for upcoming surveys (e.g., Euclid, DESI, LSST) and line-intensity mapping experiments. By bypassing halo finding, the model offers a path toward simulation-based inference that directly connects field-level dark matter statistics to observable galaxy populations. The authors emphasize that the model does not aim to reproduce the exact realization of a specific simulation galaxy-by-galaxy (due to the stochastic nature of star formation), but rather to generate statistically consistent realizations conditioned on the dark matter field. The framework is presented as extensible, capable of incorporating additional galaxy properties (e.g., velocities, metallicities) by increasing feature vector dimensionality without significantly increasing computational cost, and adaptable to different redshifts or cosmological models via global conditioning.

Technical Summary: From Dark Matter to Galaxies via Conditional Point-Cloud Diffusion

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