**Carol Cuesta-Lazaro (IAIFI Fellow)**

**in collaboration with Siddarth Mishra-Sharma and Tess Smidt**

# Diffusion Models for Cosmology

Bridging simulations and observations of the Universe

**Initial Conditions of the Universe**

**Laws of gravity**

**3-D distribution of galaxies**

*Which are the ICs of OUR Universe?*

*What is the origin of these fluctuations?*

*Probe Inflation*

**Galaxy formation**

**3-D distribution of dark matter **

*Is GR modified on large scales?*

*How do galaxies form?*

**ML for Large Scale Structure:**

**A wish list**

**Generative models**

**Learn p(x)**

Evaluate the likelihood of a 3D map, as a function of the parameters of interest

**1**

Combine different galaxy properties (such as velocities and positions)

**2**

Sample 3D maps from the posterior distribution

**3**

Reverse diffusion: Denoise previous step

Forward diffusion: Add Gaussian noise (fixed)

**Diffusion models**

*A person half Yoda half Gandalf*

**Diffusion on 6D coordinates**

Reverse diffusion: Denoise previous step

Forward diffusion: Add Gaussian noise (fixed)

*Cosmology*

Tractable likelihood!

**Setting tight constraints with only 5000 galaxies**

**All learnable functions**

*Equivariant functions*

**Data constraints**

Credit: Adapted from Tess Smidt

**Equivariant diffusion**

Implications for robustness and interpretability?

*+ Galaxy formation*

*+ Observational systematics (Cut-sky, Fiber collisions)*

**Forward Model**

**N-body simulations**

**Observations**

https://arxiv.org/pdf/1611.08606.pdf

**Is the model robust to systematic errors?**

**How are simulations and data different?**

#### deck

By carol cuesta

# deck

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