Reconstructing the Projected Dark Matter Field across 0.1-100 Mpc Scales from the SDSS Survey

Dark matter sets the gravitational environment in which galaxies form and evolve, but cannot be observed directly. We present a conditional diffusion model that reconstructs the projected dark matter density field from the galaxy stellar-mass density field for direct application to galaxy surveys. The model is trained on CAMELS and validated on the independent IllustrisTNG300-1 simulation. Halo masses inferred from the reconstructed projected-aperture measurements agree well with the corresponding true values, with a scatter below 0.2 dex. On 100 kpc scales, reconstructed surface densities show a typical scatter of 0.3 dex in the regime most relevant for observations. We apply the model to SDSS galaxies with M 10 9,M in a contiguous low-redshift region. Averaging over 100 stochastic realizations, we reconstruct and publicly release a projected dark matter field covering 90 times90,(h-1 Mpc) squared with a pixel size of 0.097,h-1 Mpc. This pixel area corresponds to the characteristic projected area of halos with masses of 10 10.6,h-1,M. The map reveals the multiscale projected cosmic web, including cluster-scale overdensities, filaments and voids. Projected-aperture masses are statistically consistent with SDSS group-catalog masses, while the derived halo mass function broadly matches mock-catalog expectations. The reconstructed projected potential places Coma in one of the deepest wells and near a convergence region of the inferred projected acceleration field, suggesting that the reconstruction retains both local overdensities and coherent large-scale projected gravitational structure. This work shows that diffusion-based dark matter reconstruction can be applied to real galaxy surveys, enabling halo-mass- and spatially resolved dark-matter-environment-based studies of galaxy evolution in SDSS and future wide-area surveys.