🤖 AI Summary
This work addresses cosmological parameter inference by introducing the first unified diffusion-based emulator and inverse inference framework for cosmic density fields. Methodologically, it employs a single diffusion model to generate high-fidelity cold dark matter density fields (forward emulation), while proposing Diffusion-HMC—a novel Hamiltonian Monte Carlo sampler driven by a differentiable, tractable likelihood approximation derived from the diffusion model—to enable robust, high-precision posterior inference of cosmological parameters. Under rigorous statistical consistency evaluation, the framework accurately reproduces key statistics—including power spectra and configuration-space structures—of target N-body simulations. It yields tight, well-calibrated parameter constraints on test samples and demonstrates significantly improved noise robustness compared to state-of-the-art discriminative networks. The core contribution lies in the first simultaneous application of diffusion models to both forward density-field modeling and inverse Bayesian inference, establishing a differentiable, sampleable likelihood approximation paradigm for cosmological inference.
📝 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.