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

Abstract

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.

Published in ApJ, Updated with the accepted version

References in corpus (13)

• Simulating Galaxy Formation with the IllustrisTNG Model
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking
• The CAMELS project: Cosmology and Astrophysics with MachinE Learning Simulations
• The Coyote Universe II: Cosmological Models and Precision Emulation of the Nonlinear Matter Power Spectrum
• Constraints on Cosmology and Gravity from the Dynamics of Voids
• CosmoGAN: creating high-fidelity weak lensing convergence maps using Generative Adversarial Networks
• The CAMELS Multifield Dataset: Learning the Universe's Fundamental Parameters with Artificial Intelligence
• Going Beyond the Galaxy Power Spectrum: an Analysis of BOSS Data with Wavelet Scattering Transforms
• Probabilistic Mass Mapping with Neural Score Estimation
• Precise Cosmological Constraints from BOSS Galaxy Clustering with a Simulation-Based Emulator of the Wavelet Scattering Transform
• A comparative study of cosmological constraints from weak lensing using Convolutional Neural Networks
• Generative Models of Multi-channel Data from a Single Example -- Application to Dust Emission

Cited by in corpus (5)

• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-Dimensional Data-Driven Priors for Inverse Problems
• Detecting Modeling Bias with Continuous Time Flow Models on Weak Lensing Maps
• nuGAN: Generative Adversarial Emulator for Cosmic Web with Neutrinos
• Fast Sampling of Cosmological Initial Conditions with Gaussian Neural Posterior Estimation