Uncovering Physical Drivers of Dark Matter Halo Structures with Auxiliary-Variable-Guided Generative Models

Arkaprabha Ganguli; Anirban Samaddar; Florian Kéruzoré; Nesar Ramachandra; Julie Bessac; Sandeep Madireddy; Emil Constantinescu

stat.MLFeb 26, 2026

Uncovering Physical Drivers of Dark Matter Halo Structures with Auxiliary-Variable-Guided Generative Models

Authors: Arkaprabha Ganguli, Anirban Samaddar, Florian Kéruzoré, Nesar Ramachandra, Julie Bessac, Sandeep Madireddy, Emil Constantinescu

Organizations: Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL 60439 · High Energy Physics Division, Argonne National Laboratory, Lemont, IL 60439, USA · Computational Science Division, Argonne National Laboratory, Lemont, IL 60439 · Computational Science Center, Data, Analysis and Visualization Group, National Renewable Energy Laboratory, Golden, CO, USA

Abstract

Deep generative models (DGMs) compress high-dimensional data but often entangle distinct physical factors in their latent spaces. We present an auxiliary-variable-guided framework for disentangling representations of thermal Sunyaev-Zel'dovich (tSZ) maps of dark matter halos. We introduce halo mass and concentration as auxiliary variables and apply a lightweight alignment penalty to encourage latent dimensions to reflect these physical quantities. To generate sharp and realistic samples, we extend latent conditional flow matching (LCFM), a state-of-the-art generative model, to enforce disentanglement in the latent space. Our Disentangled Latent-CFM (DL-CFM) model recovers the established mass-concentration scaling relation and identifies latent space outliers that may correspond to unusual halo formation histories. By linking latent coordinates to interpretable astrophysical properties, our method transforms the latent space into a diagnostic tool for cosmological structure. This work demonstrates that auxiliary guidance preserves generative flexibility while yielding physically meaningful, disentangled embeddings, providing a generalizable pathway for uncovering independent factors in complex astronomical datasets.

Figures & tables

Methods	# Params.	Sinkhorn ( $\downarrow$ )	Energy ( $\downarrow$ )	Gaussian ( $\downarrow$ )	Laplacian ( $\downarrow$ )
ICFM	34.42M	4564.03 $\pm$ 37.883	84.073 $\pm$ 0.797	0.00813 $\pm$ 0.00020	0.00693 $\pm$ 0.00011
DL-CFM	38.06M	4819.211 $\pm$ 32.718	83.148 $\pm$ 0.767	0.00813 $\pm$ 0.00014	0.00678 $\pm$ 0.00012

Table 1: Table shows the generation quality for ICFM and DL-CFM in terms of different distance metrics (mean

\pm

Sd). In terms of most metrics, the two approaches show similar generation quality.

Panel of Figure 3 — Figure 3: Generating samples from the center (top) and tail (bottom) of the reconstruction-focused latents $z_{\mathrm{rec}}$ , with the first two auxiliary-guided coordinates fixed at $(z_{1},z_{2})=(0.001,0.001)$ .

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A.1: Schematic of the DL-CFM inference. Given a training sample, we fix the sampled latent from the disentangled latent space. The latent variable is used in the vector field network to evolve the source samples to the data distribution. For demonstration, we show two snapshots of the iterative reverse process at $t=0.5$ (left) and $t=1$ (right) using the vector field U-Net.

Hyperparameters	tSZ data
Train set size	10,142
# steps	240K
Training batch size	128
Optimizer	Adam
Learning rate	2e-4
Latent dimension	256

Appendix

Table A.1: Hyperparameter settings used for DL-CFM model training on the tSZ dataset.

Figure A.2: Generating samples from the center of the reconstruction-focused latents $z_{\mathrm{rec}}$ , with the first two auxiliary-guided coordinates fixed at $(z_{1},z_{2})=(0.001,0.9)$ - low-mass high-concentration setting .

Figure A.3: Generating samples from the tail of the reconstruction-focused latents $z_{\mathrm{rec}}$ , with the first two auxiliary-guided coordinates fixed at $(z_{1},z_{2})=(0.001,0.9)$ - low-mass high-concentration setting .

Figure A.4: Generating samples from the center of the reconstruction-focused latents $z_{\mathrm{rec}}$ , with the first two auxiliary-guided coordinates fixed at $(z_{1},z_{2})=(0.9,0.001)$ - high-mass low-concentration setting .

Figure A.5: Generating samples from the tail of the reconstruction-focused latents $z_{\mathrm{rec}}$ , with the first two auxiliary-guided coordinates fixed at $(z_{1},z_{2})=(0.9,0.001)$ - high-mass low-concentration setting .

Figure A.6: The auxiliary-guided latents maintain the inter-dependency between halo mass and concentration, yielding consistent $M_{200c}$ – $c_{200c}$ dependency structure.

Disentangled Representation Learning

Disentangled representation learning separates distinct factors of variation so models can interpret, control, and generalize their predictions.

See all 231 papers

Mapping Dark-Matter Clusters via Physics-Guided Diffusion Models
Mar 15, 2026Diego Royo, Brandon Zhao, Adolfo Muñoz +2Astrophysics Diffusion-Based Inverse Problems
Universidad de Zaragoza–I3A, Spain · California Institute of Technology, USA
Generative Diffusion Priors for 3D Mapping of the Dark Universe
May 30, 2026Brandon Zhao, Diana Scognamiglio, Olivier Doré +13D Reconstruction Bayesian Inverse Problems
Department of Computing and Mathematical Sciences, California Institute of Technology · Jet Propulsion Laboratory, California Institute of Technology · Department of Physics, Duke University +1
Compositional Generative Modeling from Decentralized Data
Jun 8, 2026Mashrur M. Morshed, Vishnu Naresh BoddetiFlow Matching Decentralized Learning
Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, USA.

Mar 15, 2026J/K move · Enter open · S save

Mapping Dark-Matter Clusters via Physics-Guided Diffusion Models

Diego Royo, Brandon Zhao, Adolfo Muñoz, Diego Gutierrez+1

Universidad de Zaragoza–I3A, Spain · California Institute of Technology, USA

Astrophysics Diffusion-Based Inverse Problems Physics-Informed Diffusion Models

Open paper AskPDF arXiv

Galaxy clusters are powerful probes of astrophysics and cosmology through gravitational lensing: the clusters' mass, dominated by 85% dark matter, distorts background light. Yet, mass reconstruction lacks the scalability and large-scale benchmarks to process the hundreds of thousands of clusters expected from forthcoming wide-field surveys. We introduce a fully automated method to reconstruct cluster surface mass density from photometry and gravitational lensing observables. Central to our approach is DarkClusters-15k, our new dataset of 15,000 simulated clusters with paired mass and photometry maps, the largest benchmark to date, spanning multiple redshifts and simulation frameworks. We train a plug-and-play diffusion prior on DarkClusters-15k that learns the statistical relationship between mass and light, and draw posterior samples constrained by weak- and strong-lensing observables; this yields principled reconstructions driven by explicit physics, alongside well-calibrated uncertainties. Our approach requires no expert tuning, runs in minutes rather than hours, achieves higher accuracy, and matches expertly-tuned reconstructions of the MACS 1206 cluster. We release our method and DarkClusters-15k to support development and benchmarking for upcoming wide-field cosmological surveys.

Abstract

Disentangled Representation Learning

Explore similar work

Mapping Dark-Matter Clusters via Physics-Guided Diffusion Models

Generative Diffusion Priors for 3D Mapping of the Dark Universe

Compositional Generative Modeling from Decentralized Data