🔭 astrophysics

From DESI to Euclid: A Generative Bridge to Unbiased Galaxy Structures

This paper introduces a generative model that translates ground-based DESI imaging into space-like Euclid VIS images, significantly improving resolution and effectively removing size-dependent biases in galaxy structural parameters to create a validated dataset for the Euclid DR1 footprint.

Original authors: Renhao Ye, Shiyin Shen

Published 2026-07-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Renhao Ye, Shiyin Shen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to study the architecture of a city, but you are forced to look at it through a thick, foggy window. From this blurry view, small buildings look like indistinct blobs, and you can't tell if a structure is a single tower or a cluster of smaller ones. This is the problem astronomers face when studying galaxies from Earth. Our atmosphere acts like that foggy window (called "seeing"), blurring the sharp details of distant galaxies.

To get a clear picture, astronomers usually need to send telescopes into space, like the European Space Agency's Euclid mission. However, Euclid has only mapped a tiny fraction of the sky so far. Meanwhile, a powerful ground-based telescope called DESI has mapped a huge area, but its images are too blurry to measure the true shapes of many small galaxies.

This paper presents a clever solution: a "Generative Bridge" that uses artificial intelligence to turn the blurry DESI images into sharp, space-quality images, filling the gap until Euclid maps the whole sky.

Here is how they did it and what they found, explained simply:

1. The Problem: The "Foggy Window"

When you look at a galaxy through DESI's ground-based camera, the atmosphere smears the light.

The Consequence: If a galaxy is small or compact, the blur swallows its details. It's like trying to read the fine print on a contract through a frosted glass pane.
The Old Way: Astronomers used to try to mathematically "un-blur" these images. But there's a limit: once the light is smeared too much, the central details are gone forever. You can't invent information that isn't there.

2. The Solution: The "AI Translator"

Instead of just trying to un-blur the image, the authors built an AI model called an Image-to-Image Schrödinger Bridge. Think of this model as a master translator who has studied both the "foggy language" (DESI images) and the "clear language" (Euclid images).

How it works: The AI learned from a small overlap where both telescopes looked at the same patch of sky. It learned the "joint distribution"—essentially, the rules of how a galaxy looks when it is blurry versus how it looks when it is sharp.
The Magic: When the AI sees a blurry DESI image, it doesn't just guess randomly. It uses the specific details in the blurry image to "translate" it into what that galaxy would look like if it were taken by Euclid. It's like a skilled artist who can look at a rough sketch and confidently fill in the missing details because they understand the subject perfectly.

3. The Test: Did the AI "Hallucinate"?

A major worry with AI is that it might just make things up (hallucinate) because it has seen millions of galaxies before. The authors had to prove two things:

Is the detail real? Did the AI invent new spiral arms that weren't there?
Is the measurement fair? Does the AI help us measure the galaxy's size correctly?

The Results:

The "Trust Scale": They used a frequency test (like checking the static on a radio) to see how much detail was real. The AI successfully recovered structures down to a size of 0.37 arcseconds.
- Analogy: DESI could only see details larger than a basketball from a mile away. Euclid can see a tennis ball. The AI managed to recover details down to the size of a soccer ball. It didn't reach the full sharpness of Euclid (the tennis ball), but it was a massive improvement over the original blurry view.
No Invention: Crucially, the details the AI added were phase-coherent. This means the AI didn't just paste random patterns; the new details lined up perfectly with the actual data. It was constrained by the real galaxy, not just the AI's imagination.

4. The Payoff: Fixing the Measurements

The ultimate goal was to measure galaxy properties accurately.

Before (DESI): Because of the blur, the AI (and previous methods) thought small galaxies were much larger and rounder than they really were. It was like measuring a small pebble and thinking it's a boulder because the fog made it look big.
After (The AI Bridge): The new "Euclid-resolution" images fixed these errors.
- The bias in measuring the radius (size) dropped from a huge error to almost zero.
- The bias in measuring the shape (how concentrated the light is) was also nearly eliminated.

5. The Outcome: E-BGS

The authors have released these new, sharpened images for the entire area covered by Euclid's first data release. They call this dataset E-BGS (Euclid-resolution Bright Galaxy Survey).

In summary:
This paper doesn't claim the AI can see everything Euclid sees (it can't reach the absolute sharpest limit yet). However, it successfully built a bridge that turns blurry ground-based photos into sharp enough images to measure galaxy sizes and shapes without the systematic errors caused by Earth's atmosphere. This allows astronomers to study the "population" of galaxies accurately right now, without waiting for the full Euclid sky map to be finished.

What they explicitly did not claim:

They did not claim this works for any type of image (only galaxies in this specific survey).
They did not claim the scatter (random noise) was removed; the measurements are still a bit "fuzzy" around the edges, but the average result is now correct.
They did not claim this solves all astronomy problems; it specifically targets the bias in structural parameters for the Bright Galaxy Survey.

Technical Summary: From DESI to Euclid: A Generative Bridge to Unbiased Galaxy Structures

Problem Statement
Ground-based imaging, such as that provided by the Dark Energy Spectroscopic Instrument (DESI) Bright Galaxy Survey (BGS), suffers from atmospheric seeing that imposes a size-dependent systematic bias on galaxy structural parameters. Approximately 25% of BGS galaxies have $r$ -band half-light radii smaller than the median Point Spread Function (PSF) Full Width at Half Maximum (FWHM $\approx 1.3''$ ), rendering them under-resolved. In this regime, traditional correction methods (analytic prescriptions, forward modeling, or empirical calibration) fail to restore central light profiles overwhelmed by the PSF, leading to collapsed concentration measurements and persistent biases in structural parameters like the S'ersic index. While space-based imaging (e.g., Euclid VIS) offers the necessary resolution ( $0.16''$ FWHM) for unbiased measurements, it currently covers only a tiny fraction of the BGS footprint, leaving the vast majority of galaxies without high-resolution data.

Methodology
The authors propose a generative approach using an Image-to-Image Schr"odinger Bridge (I2SB) to translate DESI imaging into Euclid-resolution images.

Data: The model is trained on 82,830 paired images from the DESI Legacy Imaging Surveys (using $r$ and $z$ bands) and the Euclid Quick Data Release 1 (Q1) VIS band over a $63.1 \text{ deg}^2$ overlap. The dataset is split into training, validation, and spatially disjoint test sets.
Model Architecture: The I2SB defines a stochastic bridge between two fixed endpoints: the Euclid VIS image ( $x_0$ ) and the DESI $r$ -band image ( $x_1$ ). The forward process gradually blurs the Euclid image into its DESI counterpart. A UNet ( $\epsilon_\theta$ ) is trained to reverse this process, predicting the score (correction) to move from a noisy intermediate state $x_t$ back toward the Euclid endpoint.
Conditioning: To ensure the reconstruction is constrained by the input data rather than purely by a learned prior, the DESI $z$ -band is concatenated as a conditional input channel ( $c = \text{DESI}_z$ ) alongside the intermediate image. This provides structural information not present in the $r$ -band alone.
Training Objective: The network minimizes a masked mean squared error loss, predicting the noise component required to recover the Euclid structure from the blurred DESI input.

Key Results
The study validates the model against two criteria: whether the recovered structure is data-constrained and whether the resulting structural parameters are unbiased.

Resolution and Fidelity: Fourier-domain analysis reveals that the model recovers structural details down to a scale of $0.37''$ , a $\sim 3.8\times$ improvement over the DESI $r$ -band baseline ( $1.41''$ ). While this does not reach the native Euclid VIS resolution ( $0.16''$ ), the Fourier Ring Correlation (FRC) confirms that the recovered structure is phase-coherent with the ground truth (GT) and not an artifact of the generative prior.
Bias Correction: The translation significantly reduces systematic biases in structural parameters relative to the DESI $r$ $r$ -band measurements:
- Petrosian Radius ( $R_{Pet}$ ): Bias reduced from $-0.870''$ to $+0.075''$ , effectively decoupling the measurement from galaxy size.
- S'ersic Effective Radius ( $R_e$ ): Bias reduced from $-0.322''$ to $-0.018''$ .
- S'ersic Index ( $n$ ): Bias reduced from $+0.262$ to $+0.093$ , removing the value-dependent bias where DESI underestimates high- $n$ galaxies.
Scatter: The model does not reduce the scatter (noise) in the measurements; for the S'ersic index, scatter remains high ($0.609$) because the model predicts a plausible solution for unresolved central profiles rather than a unique truth. However, the authors note that for population-level studies (e.g., the mass–size relation), correcting the systematic bias is more critical than reducing the scatter.

Significance and Claims
The paper claims to have successfully closed the gap between ground-based and space-based structural measurements for the BGS. By releasing the "Euclid-resolution BGS" (E-BGS) dataset over the Euclid DR1 footprint, the authors provide a resource for population-level studies of galaxy structure at high resolution ahead of the full Euclid data release. The primary significance lies in demonstrating that a generative model can recover unbiased structural parameters from under-resolved data, provided the recovery is strictly constrained by the input data (verified via FRC) and does not rely on "invented" priors. The E-BGS predictions are positioned as a blind testable advance, ready for validation once the full Euclid DR1 becomes public in November 2026.

1. The Problem: The "Foggy Window"

2. The Solution: The "AI Translator"

3. The Test: Did the AI "Hallucinate"?

4. The Payoff: Fixing the Measurements

5. The Outcome: E-BGS

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