Modelling reionization often requires significant assumptions about the properties of ionizing sources. Here, we infer the total output of hydrogen-ionizing photons (the ionizing emissivity, $dot{N}_textrm{ion}$) at $z=4-14$ from current reionization constraints, being maximally agnostic to the properties of ionizing sources. We use a Bayesian analysis to fit for a non-parametric form of $dot{N}_textrm{ion}$, allowing us to flexibly explore the entire prior volume. We infer a declining $dot{N}_textrm{ion}$ with redshift at $z>6$, which can be used as a benchmark for reionization models. Model-independent reionization constraints from the CMB optical depth and Ly$alpha$ and Ly$beta$ forest dark pixel fraction produce $dot{N}_textrm{ion}$ evolution ($dlog_{10}dot{N}_textrm{ion}/dz|_{z=6rightarrow8} = -0.31pm0.35$ dex) consistent with the declining UV luminosity density of galaxies, assuming constant ionizing photon escape fraction and efficiency. Including measurements from Ly$alpha$ damping of galaxies and quasars produces a more rapid decline: $dlog_{10}dot{N}_textrm{ion}/dz|_{z=6rightarrow8} =-0.44pm0.22$ dex, steeper than the declining galaxy luminosity density (if extrapolated beyond $M_mathrm{UV} lesssim -13$), and constrains the mid-point of reionization to $z = 6.93pm0.14$.
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