AS-Bridge: A Bidirectional Generative Framework Bridging Next-Generation Astronomical Surveys

Conference: CVPR 2026
arXiv: 2603.11928
Code: github.com/ZHANG7DC/AS-Bridge
Area: Astronomical Imaging / Generative Models / Cross-domain Translation
Keywords: Astronomical Surveys, Brownian Bridge, Bidirectional Image Translation, Rare Event Detection, Probabilistic Reconstruction

TL;DR

AS-Bridge is proposed to model the conditional probability distribution between ground-based LSST and space-based Euclid survey observations using a bidirectional Brownian Bridge diffusion process, enabling cross-survey probabilistic image translation and unsupervised strong gravitational lens detection by leveraging reconstruction inconsistency.

Background & Motivation

Background: Next-generation astronomical observations are dominated by LSST (ground-based, 6 optical bands, ~0.7" resolution, atmospheric interference) and Euclid (space-based, high-resolution near-infrared, VIS pixel 0.1"), with an overlapping sky area of approximately 7000–9000 square degrees.

Limitations of Prior Work: Systematic distribution shifts in PSF, bands, and noise statistics make joint cross-survey analysis difficult. A single deterministic mapping cannot capture inherent ambiguities—LSST→Euclid requires recovering fine morphology from atmospheric blur (ill-posed), and Euclid→LSST requires inferring multi-band color from fewer bands (unidentifiable).

Key Challenge: Observations of the same celestial object by two surveys are two stochastic realizations \(x = \mathcal{O}(\Phi) + \epsilon(\mathcal{O}(\Phi))\) sharing a latent astrophysical process \(\Phi\). Since \(\Phi\) is not directly observable, it is necessary to learn the conditional distribution \(p(x_{Euclid}|x_{LSST})\) and its inverse through marginalization.

Key Insight: Brownian Bridge defines a stochastic interpolation process between two endpoints, naturally suited for modeling probabilistic relationships between two observation domains.

Core Idea: Use a bidirectional Brownian Bridge diffusion process to model the conditional distribution between surveys, and utilize reconstruction failure on OOD rare objects to achieve unsupervised anomaly detection.

Method

Overall Architecture

Extract paired images from LSST-Euclid overlapping regions → Model cross-survey translation as a bidirectional Brownian Bridge process → Share a single diffusion model, achieving bidirectional inference by selecting the bridge's start/end points → Faithfully reconstruct routine objects while failing on rare objects (strong gravitational lenses) → Use the inconsistency of multiple sampled reconstructions as the anomaly score.

Key Designs

1. Brownian Bridge Diffusion Process

   • Function: Establish a stochastic path between two survey observation domains, replacing the "data → pure noise" path of standard diffusion.
   • Mechanism: Given endpoints \((x_0, x_T)\), the intermediate state \(x_t | (x_0, x_T) \sim \mathcal{N}((1-m_t)x_0 + m_t x_T, \delta_t I)\), where \(m_t = t/T\) and \(\delta_t = m_t(1-m_t)\). Reverse transitions are derived via Bayes' theorem, preserving the source-target conditional dependency.
   • Design Motivation: Standard conditional diffusion (e.g., Palette) starts from pure noise, with the source image acting only as an external condition; BB interpolates directly between the two domains, avoiding high-noise states, improving sampling efficiency, and better maintaining conditional distributions.

2. \(\epsilon\)-prediction Maximum Likelihood Training

   • Function: Prove that the \(\epsilon\)-prediction loss is equivalent to the standard BB loss multiplied by a mild weight \(\sqrt{\delta_t}\).
   • Mechanism: Under variance-exploding diffusion, the likelihood objective requires time-step weights \(\delta_t\), but in BB, \(\delta_t\) tends to zero at endpoints, causing vanishing gradients. The \(\epsilon\)-prediction loss \(\|\epsilon_\theta - \epsilon\|_2^2\) is equivalent to score matching with weight \(\sqrt{\delta_t}\), which emphasizes likelihood-oriented high-noise time steps while maintaining stable gradients at endpoints.
   • Design Motivation: Direct use of \(\delta_t\) weighting causes vanishing gradients at endpoints during BB training; \(\epsilon\)-prediction provides a moderate intermediate solution.

3. Multi-sampling Anomaly Detection

   • Function: Utilize the model's reconstruction failure on out-of-distribution objects to discover rare events without anomaly labels.
   • Mechanism: For a paired observation \((x_{Euclid}, x_{LSST})\), perform multiple stochastic reconstructions after fusion via the forward process. The pixel-level anomaly map is the minimum per-pixel error across reconstructions \(\mathcal{A}(p) = \min_i \|\hat{x}_0^{(i)}(p) - x_0(p)\|_2^2\); image-level scores are normalized by flux to eliminate brightness bias.
   • Design Motivation: The low SNR of astronomical images causes single reconstruction errors to be dominated by noise; taking the minimum of multiple samples suppresses noise fluctuations and preserves systematic reconstruction failure signals.

Loss & Training

The training loss is \(\epsilon\)-prediction MSE. Data is based on SLSim-simulated 115K routine galaxies + 5K strong gravitational lens paired images (64×64), including Euclid VIS single band + LSST gri three bands.

Key Experimental Results

Main Results

Direction/Task	Metric	AS-Bridge	Palette	SPADE	pix2pix	Joint Diffusion
LSST→Euclid	CRPS↓	2.38	2.43	3.39	4.35	3.14
Euclid→LSST	CRPS↓	7.90	7.98	16.52	73.03	15.15

Anomaly Detection Method	FPR@1%TPR↓	FPR@5%TPR↓	AUPR↑
AS-Bridge	0.00%	0.18%	0.80
CFM (Cross-modal)	0.24%	1.20%	0.75
Deco-Diff (Uni-modal)	1.10%	5.00%	0.61

Ablation Study

Training Objective	LSST→Euclid CRPS↓	Euclid→LSST CRPS↓
\(\epsilon\)-prediction (Ours)	2.38	7.90
Standard BB loss	2.55	8.12
\(\delta_t\)-weighted loss	2.51	8.30

Key Findings

• Diffusion/Bridge methods consistently outperform GANs in probabilistic reconstruction—GANs tend toward mode collapse, which is unsuitable for astronomical probabilistic inference.
• Euclid→LSST CRPS is approximately 3.3 times that of the reverse direction—inferring multi-band colors from a single wide band is inherently more difficult.
• Uni-modal anomaly detection (Deco-Diff) fails completely; cross-modal information is crucial for rare event detection.
• Taking the minimum error from multiple random reconstructions effectively suppresses the noise-dominated issues in low-SNR astronomical images.

Highlights & Insights

• Formalizes joint astronomical survey analysis as a probabilistic image translation problem, elegantly handling cross-domain mapping uncertainty—the methodology is generalizable to any multi-sensor remote sensing scenario.
• Rare event detection is completely unsupervised—leveraging the model's systematic reconstruction failure on out-of-distribution samples without anomaly labels. Proposes "discovery-oriented" evaluation metrics (FPR@lowTPR, AUPR) instead of high-recall metrics used in industrial anomaly detection.
• The \(\epsilon\)-prediction equivalence proof bridges BB training with maximum likelihood principles via a concise 3-line proof.

Limitations & Future Work

• Entirely based on simulated data (SLSim), making the simulation-to-reality gap inevitable—re-validation on real LSST/Euclid data is required after its release.
• 64×64 resolution is too low for practical scientific analysis and needs to be scaled to higher resolutions.
• Only LSST(gri) and Euclid(VIS) sub-bands were considered; joint modeling of all bands remains unexplored.
• Anomaly detection was only validated for strong gravitational lenses; generalizability to other rare astronomical events is unknown.

Related Work & Insights

• vs Palette: Conditional diffusion starts from pure noise, whereas BB establishes a direct stochastic path between source and target, improving sampling efficiency.
• vs BBDM: Shares the BB framework, but this work adds \(\epsilon\)-prediction theoretical improvements and astronomical scientific application validation.
• vs CFM: Cross-modal feature mapping relies on explicit feature fusion modules, whereas AS-Bridge performs implicit fusion through generative reconstruction.

Rating

• Novelty: ⭐⭐⭐⭐ Creative combination of survey probabilistic translation + reconstruction-based anomaly detection.
• Experimental Thoroughness: ⭐⭐⭐ Simulation validation is sufficient, but lacks real data.
• Writing Quality: ⭐⭐⭐⭐ Clear problem formalization and solid astrophysical background.
• Value: ⭐⭐⭐⭐ High potential for direct application once LSST/Euclid data becomes available.

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