Dark matter forms invisible filaments that weave through the cosmos. On them, like beads on a string, hang galaxy. To understand the laws of the Universe, astronomers compare maps of real galaxies with thousands of simulated ones. In the past, each model required elaborate numerical simulation — virtual universes with gas, stars, and black holes. Those calculations took months on supercomputers.

The new approach works like instant embroidery. It takes a rough 3D sketch — a low-resolution density map of dark matter (blurry, like a drawing on wax paper). A Machine Learning network, trained on accurate examples, turns this draft into a detailed canvas in seconds: placing hundreds of galaxies, indicating their stellar masses and star formation rate. For this, it uses a transformers architecture with elements of Convolutional Neural Networks — each future galaxy 'looks' at the others, achieving overall harmony. Essentially, it's a Diffusion Models — it learns to remove noise from a random set of points until an ordered pattern emerges from chaos.

Training was done on data from the IllustrisTNG project: the machine processed 90 thousand training patches to learn to reconstruct large-scale structure — a web of filaments and clumps. After that, one cube with side length 151 megaparsecs (nearly half a billion light-years) is filled in 10 seconds on an ordinary gaming graphics card. Such a generator directly connects invisible mass with observed objects, bypassing a long chain of intermediate calculations. This accelerates analysis for future sky surveys DESI and Euclid and will help more precisely extract the signal of cosmological parameters — for example, redshift, which tells about the expansion of the Universe. The dark canvas is no longer a mystery: the swift stitches of the neural network reveal the map of the cosmos on it.