The Galactic Center Excess (GCE) may yet herald the discovery of annihilating dark matter. Weighing against that conclusion are analyses showing evidence for dim point sources within the spatial structure of the emission. Because of technical limitations these analyses are purely spatial with all spectral information that could disentangle the excess from astrophysical backgrounds discarded. Here, we demonstrate that a neural network simulation-based inference approach can jointly analyze the spatial and spectra data. The addition is profound: energy information drives the putative point sources to be significantly dimmer, indicating either the GCE is truly diffuse in nature or made of an exceptionally large number of sources. Quantitatively, for our best fit background model, the excess is essentially consistent with Poisson emission as predicted by dark matter. If due to point sources, our median prediction is $\mathcal{O}({10}^5)$ sources, or more than 35 000 at 90% confidence—both orders of magnitude larger than the hundreds preferred by earlier point-source analyses of the GCE, although variations allowed by background systematics could reduce the required number of sources by roughly an order of magnitude.

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• Gamma ray astronomy
• Particle dark matter
• Machine learning