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Abstract Gravitational waves (GWs) from merging compact objects encode direct information about the luminosity distance to the binary. When paired with a redshift measurement, this enables standard-siren cosmology: a Hubble diagram can be constructed to directly probe the Universe’s expansion. This can be done in the absence of electromagnetic measurements, as features in the mass distribution of GW sources provide self-calibrating redshift measurements without the need for a definite or probabilistic host galaxy association. This “spectral siren” technique has thus far only been applied with simple parametric representations of the mass distribution, and theoretical predictions for features in the mass distribution are commonly presumed to be fundamental to the measurement. However, the use of an inaccurate representation leads to biases in the cosmological inference, an acute problem given the current uncertainties in true source population. Furthermore, it is commonly presumed that the form of the mass distribution must be known a priori to obtain unbiased measurements of cosmological parameters in this fashion. Here, we demonstrate that spectral sirens can accurately infer cosmological parameters without such prior assumptions. We apply a flexible, nonparametric model for the mass distribution of compact binaries to a simulated catalog of 1000 GW signals, consistent with expectations for the next LIGO–Virgo–KAGRA observing run. We find that, despite our model’s flexibility, both the source mass model and cosmological parameters are correctly reconstructed. We predict a 11.2%✎measurement ofH₀, keeping all other cosmological parameters fixed, and a 6.4%✎measurement ofH(z= 0.9)✎when fitting for multiple cosmological parameters (1σuncertainties). This astrophysically agnostic spectral siren technique will be essential to arrive at precise and unbiased cosmological constraints from GW source populations.