# Stochastic Super-resolution of Cosmological Simulations with Denoising Diffusion Models

arXiv: https://arxiv.org/abs/2310.06929 · HTML: https://mlsanity.com/paper/2310.06929/

## Key facts

- Cited by 4 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 5 of its 9 references that are in the map.
- First posted on arXiv 10 Oct 2023.

## Placed in

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

## Builds on (most cited first, 5 of 5)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)

## Built on by (most cited first, 4 of 4)

- [Adaptive Guidance: Training-free Acceleration of Conditional Diffusion Models](https://mlsanity.com/paper/2312.12487/) (2023)
- [CD-TVD: Contrastive Diffusion for 3D Super-Resolution with Scarce High-Resolution Time-Varying Data](https://mlsanity.com/paper/2508.08173/) (2025)
- [Conditional Diffusion-Flow models for generating 3D cosmic density fields: applications to f(R) cosmologies](https://mlsanity.com/paper/2502.17087/) (2025)
- [A Malliavin-Gamma calculus approach to Score Based Diffusion Generative models for random fields](https://mlsanity.com/paper/2505.13189/) (2025)

## Abstract (arXiv)

In recent years, deep learning models have been successfully employed for augmenting low-resolution cosmological simulations with small-scale information, a task known as "super-resolution". So far, these cosmological super-resolution models have relied on generative adversarial networks (GANs), which can achieve highly realistic results, but suffer from various shortcomings (e.g. low sample diversity). We introduce denoising diffusion models as a powerful generative model for super-resolving cosmic large-scale structure predictions (as a first proof-of-concept in two dimensions). To obtain accurate results down to small scales, we develop a new "filter-boosted" training approach that redistributes the importance of different scales in the pixel-wise training objective. We demonstrate that our model not only produces convincing super-resolution images and power spectra consistent at the percent level, but is also able to reproduce the diversity of small-scale features consistent with a given low-resolution simulation. This enables uncertainty quantification for the generated small-scale features, which is critical for the usefulness of such super-resolution models as a viable surrogate model for cosmic structure formation.