# Conditional Diffusion-Flow models for generating 3D cosmic density fields: applications to f(R) cosmologies

arXiv: https://arxiv.org/abs/2502.17087 · HTML: https://mlsanity.com/paper/2502.17087/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 12 of 12)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (2024)
- [Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2304.03322/) (2023)
- [On Memorization in Probabilistic Deep Generative Models](https://mlsanity.com/paper/2106.03216/) (2021)
- [Can denoising diffusion probabilistic models generate realistic astrophysical fields?](https://mlsanity.com/paper/2211.12444/) (2022)
- [Stochastic Super-resolution of Cosmological Simulations with Denoising Diffusion Models](https://mlsanity.com/paper/2310.06929/) (2023)
- [A Brief Introduction to Generative Models](https://mlsanity.com/paper/2103.00265/) (2021)
- [Cosmological Field Emulation and Parameter Inference with Diffusion Models](https://mlsanity.com/paper/2312.07534/) (2023)

## Built on by (most cited first, 2 of 2)

- [Cosmo3DFlow: Wavelet Flow Matching for Spatial-to-Spectral Compression in Reconstructing the Early Universe](https://mlsanity.com/paper/2602.10172/) (2026)
- [Score Matching on Large Geometric Graphs for Cosmology Generation](https://mlsanity.com/paper/2508.16990/) (2025)

## Abstract (arXiv)

Next-generation galaxy surveys promise unprecedented precision in testing gravity at cosmological scales. However, realising this potential requires accurately modelling the non-linear cosmic web. We address this challenge by exploring conditional generative modelling to create 3D dark matter density fields via score-based (diffusion) and flow-based methods. Our results demonstrate the power of diffusion models to accurately reproduce the matter power spectra and bispectra, even for unseen configurations. They also offer a significant speed-up with slightly reduced accuracy, when flow-based reconstructing the probability distribution function, but they struggle with higher-order statistics. To improve conditional generation, we introduce a novel multi-output model to develop feature representations of the cosmological parameters. Our findings offer a powerful tool for exploring deviations from standard gravity, combining high precision with reduced computational cost, thus paving the way for more comprehensive and efficient cosmological analyses