# Diffusion-HMC: Parameter Inference with Diffusion-model-driven Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/2405.05255 · HTML: https://mlsanity.com/paper/2405.05255/

## 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 7 of its 23 references that are in the map.
- First posted on arXiv 8 May 2024.

## Placed in

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

## Builds on (most cited first, 7 of 7)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [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)
- [Probabilistic Mass Mapping with Neural Score Estimation](https://mlsanity.com/paper/2201.05561/) (2022)
- [Learning cosmology and clustering with cosmic graphs](https://mlsanity.com/paper/2204.13713/) (2022)
- [Multiscale Flow for Robust and Optimal Cosmological Analysis](https://mlsanity.com/paper/2306.04689/) (2023)

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

- [Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-Dimensional Data-Driven Priors for Inverse Problems](https://mlsanity.com/paper/2407.17667/) (2024)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [Generative Diffusion Priors for 3D Mapping of the Dark Universe](https://mlsanity.com/paper/2606.00803/) (2026)

## Abstract (arXiv)

Diffusion generative models have excelled at diverse image generation and reconstruction tasks across fields. A less explored avenue is their application to discriminative tasks involving regression or classification problems. The cornerstone of modern cosmology is the ability to generate predictions for observed astrophysical fields from theory and constrain physical models from observations using these predictions. This work uses a single diffusion generative model to address these interlinked objectives -- as a surrogate model or emulator for cold dark matter density fields conditional on input cosmological parameters, and as a parameter inference model that solves the inverse problem of constraining the cosmological parameters of an input field. The model is able to emulate fields with summary statistics consistent with those of the simulated target distribution. We then leverage the approximate likelihood of the diffusion generative model to derive tight constraints on cosmology by using the Hamiltonian Monte Carlo method to sample the posterior on cosmological parameters for a given test image. Finally, we demonstrate that this parameter inference approach is more robust to small perturbations of noise to the field than baseline parameter inference networks.