Cosmo3DFlow: Wavelet Flow Matching for Spatial-to-Spectral Compression in Reconstructing the Early Universe

• URL: http://arxiv.org/abs/2602.10172v1
• Date: Tue, 10 Feb 2026 15:47:18 GMT
• Title: Cosmo3DFlow: Wavelet Flow Matching for Spatial-to-Spectral Compression in Reconstructing the Early Universe
• Abstract summary: We devise a novel generative framework, Cosmo3DFlow, designed to address dimensionality and sparsity.<n>Wavelet Transform addresses the void problem'' by translating spatial emptiness into spectral sparsity.
• Score: 11.574480297424428
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reconstructing the early Universe from the evolved present-day Universe is a challenging and computationally demanding problem in modern astrophysics. We devise a novel generative framework, Cosmo3DFlow, designed to address dimensionality and sparsity, the critical bottlenecks inherent in current state-of-the-art methods for cosmological inference. By integrating 3D Discrete Wavelet Transform (DWT) with flow matching, we effectively represent high-dimensional cosmological structures. The Wavelet Transform addresses the ``void problem'' by translating spatial emptiness into spectral sparsity. It decouples high-frequency details from low-frequency structures through spatial compression, and wavelet-space velocity fields facilitate stable ordinary differential equation (ODE) solvers with large step sizes. Using large-scale cosmological $N$-body simulations, at $128^3$ resolution, we achieve up to $50\times$ faster sampling than diffusion models, combining a $10\times$ reduction in integration steps with lower per-step computational cost from wavelet compression. Our results enable initial conditions to be sampled in seconds, compared to minutes for previous methods.

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