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A Fast Generative Framework for High-dimensional Posterior Sampling: Application to CMB Delensing

Hadi Sotoudeh, Pablo Lemos, Laurence Perreault-Levasseur

TL;DR

A deep generative framework for high-dimensional Bayesian inference that enables efficient posterior sampling that successfully recovers the unlensed CMB power spectrum from simulated observations and remains robust to shifts in cosmological parameters.

Abstract

We introduce a deep generative framework for high-dimensional Bayesian inference that enables efficient posterior sampling. As telescopes and simulations rapidly expand the volume and resolution of astrophysical data, fast simulation-based inference methods are increasingly needed to extract scientific insights. While diffusion-based approaches offer high-quality generative capabilities, they are hindered by slow sampling speeds. Our method performs posterior sampling an order of magnitude faster than a diffusion baseline. Applied to the problem of CMB delensing, it successfully recovers the unlensed CMB power spectrum from simulated observations. The model also remains robust to shifts in cosmological parameters, demonstrating its potential for out-of-distribution generalization and application to observational cosmological data.

A Fast Generative Framework for High-dimensional Posterior Sampling: Application to CMB Delensing

TL;DR

A deep generative framework for high-dimensional Bayesian inference that enables efficient posterior sampling that successfully recovers the unlensed CMB power spectrum from simulated observations and remains robust to shifts in cosmological parameters.

Abstract

We introduce a deep generative framework for high-dimensional Bayesian inference that enables efficient posterior sampling. As telescopes and simulations rapidly expand the volume and resolution of astrophysical data, fast simulation-based inference methods are increasingly needed to extract scientific insights. While diffusion-based approaches offer high-quality generative capabilities, they are hindered by slow sampling speeds. Our method performs posterior sampling an order of magnitude faster than a diffusion baseline. Applied to the problem of CMB delensing, it successfully recovers the unlensed CMB power spectrum from simulated observations. The model also remains robust to shifts in cosmological parameters, demonstrating its potential for out-of-distribution generalization and application to observational cosmological data.
Paper Structure (17 sections, 4 equations, 4 figures, 4 tables)

This paper contains 17 sections, 4 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Architecture
  4. Training Objective
  5. Baseline
  6. Experiments and Results
  7. [1]Problem 1: Rotating Gaussian Random Fields (GRFs)
  8. Problem 2: CMB Delensing
  9. Discussion and Conclusion
  10. Data Generation
  11. GRF Rotation
  12. CMB Delensing
  13. Training
  14. Hyperparameters
  15. Compute Resources
  16. ...and 2 more sections

Figures (4)

  • Figure 1: GRF rotation results: (a) Comparing empirical and theoretical moments for a test example. The pixel-wise empirical means and standard deviations are estimated using 1000 posterior samples. (b) TARP coverage test results.
  • Figure 2: CMB delensing results: (a) Comparison of the lensed (input), unlensed (target), and delensed (obtained from model outputs) TT power spectra for six test examples. The delensed spectrum is represented by mean and uncertainty regions computed from 1000 posterior samples. Relative differences $\Delta\mathcal{D}_\ell / \mathcal{D}_\ell$ are computed with respect to the mean delensed spectrum. (b) TARP coverage test results. (c) Out-of-distribution performance for different $\Omega_m$ values, with all other cosmological parameters fixed. Each column corresponds to an $\Omega_m$ value, which differs from the training (base) value by a factor of the Planck satellite measurement error $\sigma_{\Omega_m}$. Each row corresponds to a unique noise realization used to generate the lensed and unlensed maps.
  • Figure 3: Data generation process for the GRF rotation experiment.
  • Figure 4: Data generation process for the CMB delensing experiment.