Sample variance denoising in cylindrical 21 cm power spectra

State-of-the-art simulations of re-ionisation-era 21 cm signal have limited volumes, generally orders of magnitude smaller than observations. Consequently, the Fourier modes in common between simulation and observation have limited overlap, especially in cylindrical (2D) k-space that is natural for 21 cm interferometry. This makes sample variance (i.e. the deviation of the simulated sample from the population mean due to finite box size) a potential issue when interpreting upcoming 21 cm observations. Here, we introduce <ns0:monospace>21cmPSDenoiser</ns0:monospace>, a score-based diffusion model that can be applied to a single, forward-modelled realisation of the 21 cm 2D power spectrum (PS), predicting the corresponding population mean on-the-fly during Bayesian inference. Individual samples of 2D Fourier amplitudes of wave modes relevant to current 21 cm observations can deviate from the mean by over 50% for 300 cmpc simulations, even when only considering stochasticity due to the sampling of Gaussian initial conditions. <ns0:monospace>21cmPSDenoiser</ns0:monospace> reduces this deviation by an order of magnitude, outperforming current state-of-the-art sample variance mitigation techniques such as fixing and pairing by a factor of a few at almost no additional computational cost (∼2 s per PS). Unlike emulators, <ns0:monospace>21cmPSDenoiser</ns0:monospace> is not tied to a particular model or simulator since its input is a (model-agnostic) realisation of the 2D 21 cm PS. Indeed, we confirm that <ns0:monospace>21cmPSDenoiser</ns0:monospace> generalises to PSs produced with a different 21 cm simulator than those on which it was trained. To quantify the improvement in parameter recovery, we simulated a 21 cm PS detection by the Hydrogen Epoch of Reionization Arrays (HERA) and ran different inference pipelines corresponding to commonly used approximations. We find that using <ns0:monospace>21cmPSDenoiser</ns0:monospace> in the inference pipeline outperforms other approaches, yielding an unbiased posterior that is 50% narrower in most inferred parameters.