# Cosmological Field Emulation and Parameter Inference with Diffusion Models

arXiv: https://arxiv.org/abs/2312.07534 · HTML: https://mlsanity.com/paper/2312.07534/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 12 Dec 2023.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Efficient Attention: Attention with Linear Complexities](https://mlsanity.com/paper/1812.01243/) (2018)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [The CAMELS Multifield Dataset: Learning the Universe's Fundamental Parameters with Artificial Intelligence](https://mlsanity.com/paper/2109.10915/) (2021)
- [CosmoGAN: creating high-fidelity weak lensing convergence maps using Generative Adversarial Networks](https://mlsanity.com/paper/1706.02390/) (2017)
- [Multifield Cosmology with Artificial Intelligence](https://mlsanity.com/paper/2109.09747/) (2021)
- [Multiscale Flow for Robust and Optimal Cosmological Analysis](https://mlsanity.com/paper/2306.04689/) (2023)

## Built on by (most cited first, 3 of 3)

- [Diffusion models recover accurate mixture weights despite score function insensitivity](https://mlsanity.com/paper/2607.15485/) (2026)
- [Conditional Diffusion-Flow models for generating 3D cosmic density fields: applications to f(R) cosmologies](https://mlsanity.com/paper/2502.17087/) (2025)
- [Generative Diffusion Priors for 3D Mapping of the Dark Universe](https://mlsanity.com/paper/2606.00803/) (2026)

## Abstract (arXiv)

Cosmological simulations play a crucial role in elucidating the effect of physical parameters on the statistics of fields and on constraining parameters given information on density fields. We leverage diffusion generative models to address two tasks of importance to cosmology -- as an emulator for cold dark matter density fields conditional on input cosmological parameters Omegam and σ8, and as a parameter inference model that can return constraints on the cosmological parameters of an input field. We show that the model is able to generate fields with power spectra that are consistent with those of the simulated target distribution, and capture the subtle effect of each parameter on modulations in the power spectrum. We additionally explore their utility as parameter inference models and find that we can obtain tight constraints on cosmological parameters.